atomic data and nuclear data tables 33,347-404 (1985

ATOMIC DATA AND NUCLEAR DATA TABLES 33,347-404 (1985)

EXPERIMENTAL AND THEORETICAL GAMOW-TELLER BETA-DECAY

OBSERVABLES FOR THE &SHELL NUCLEI

B. A. BROWN

Cyclotron Laboratory Michigan State University

East Lansing, Michigan 48824

and

B. H. WILDENTHAL*

Cyclotron Laboratory Michigan State University

East Lansing, Michigan 48824

A comprehensive comparison of experimentally observed Gamow-Teller beta decay with theory is presented for the &-shell (A = 17-39) nuclei. Relevant experimental data on half-lives, Q values, and branching ratios are tabulated and used to deduce experimental logu) valuesand Gamow-Teller matrix elements. These are compared with theoretical values based on complete (O&z, 1~~~2, O&r)- space shell-model wave functions. These wave functions are obtained from diagonalizations of a model Hamiltonian formulation which reproduces observed energy-level structures throughout the sd shell. The calculations are carried out both with the “free-nucleon” normalization for the Gamow-Teller single-particle matrix elements and with effective values for these matrix elements obtained from analyses of experimental Gamow-Teller magnitudes with the shell-model wave functions. CB 1985 ~adrmie seas IK

* Present address: Department of Physics and Atmospheric Science, Drexel University, Philadelphia, Pennsylvania 19 104.

0092-640X/85 $3.00 Copyright 0 1985 by Academic Press, Inc. All rights of reproduction in any form reserved. 347 Atom& Data and Nudew Dala Table% Vol. 33, No. 3. Nonnnba 1955

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller /3 Decay in s&Shell Nuclei

CONTENTS

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

II. WEAK-INTERACTION FORMALISM . . . . . . . . . . . . 350 A. General Considerations and Definitions . . . . . . . . 350 B. Evaluation of the Phase-Space Factors . . . . . . . . . . . 35 1 C. Values for the Weak-Interaction Coupling Constants 352

III. EXPERIMENTAL DATA . . . . . . . . . . . . . . . . . . . . . . . 352

IV. SHELL-MODEL THEORY . . . . . . . . . . , . . . . . . . . . . . . 353 A. Calculation of the “Free-Nucleon” Gamow-Teller

Matrix Elements . . . . . . . . . . . . . . . . . . . . . . . 353 B. Formulation for the Effective Gamow-Teller Matrix

Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 C. Results for the Effective Gamow-Teller Matrix Ele-

ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

V. COMPARISON BETWEEN EXPERIMENT AND THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

EXPLANATION OF TABLES . . . . . . . . . . , . . . . . . . . _ 362

COMMENTS ON RECENT DATA . . . . . . . . . . . . . . . 364

TABLES I. Experimental Half-Lives and Q Values . . . . . . . . . 366

II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ft Values, and Ga- mow-Teller Matrix Elements . . . . . . . . . . . . . 368

III. Theoretical Multiparticle Transition Amplitudes . . 394

1. INTRODUCTION

The study of allowed nuclear beta decay provides information both about the nature of the weak interaction and about the multiparticle structure of nuclear wave functions. In this work we focus on Gamow-Teller beta decay of nuclei which contain at least 8 but no more than 20 each of neutrons and protons. We analyze the experimental results from these nuclei in terms of the latest working out of the shell-model theory for the nuclear structure of the so-called “sd shell,” the nuclei between I60 and %a. The nuclei in this region are described in lowest order by the shell model in terms of nucleons that are confined to the 1s and Od orbitals (those with n, Z, j values of 1sI/2,0d~,2, and Od3,2). Recent full-basis calculations within this sd-model space have produced wave functions which have been quite successful in reproducing a wide range of nuclear structure properties.’ Gamow-

Teller beta decay provides a particularly sensitive test of these wave functions because the operator associated with Gamow-Teller decay is so simple. Such a test can be comprehensive and definitive since there exists a large body of precise Gamow-Teller beta-decay data in the sd- shell mass region of A = 17-39 with which the shell-model predictions can be compared.

In this paper, we bring together the relevant experimental data for the sd-shell nuclei which are needed to deduce the properties of Gamow-Teller decay to specific final states. These data are combined with a calculation of the phase-space factors to provide a consistent set of log@) values and reduced transition probabilities. These experimental transition probabilities are then compared to the &shell-model calculations. The overall comparison is interpreted in terms of a global renormalization of the

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller B Decay in s&hell Nuclei

Gamow-Teller operator. This renormalization is to be understood as a reflection of the general inadequacies inherent in the restricted shell-model formulation, that is of the need to introduce further nucleonic and nonnucleonic degrees of freedom into a complete description of the nuclear state. The comparisons between experiment and the results obtained with this renormalized operator provide a quantitative test of the capabilities of the shell- model calculations to predict the detailed state and mass dependence of the observed decay strengths.

12

II

IO

9

8

7

6

Previous investigations of how well the conventional shell-model approach can account for the trends of Gamow-Teller data in the sd shell when configuration mixing over the full basis space is allowed include Refs. 2 and 3. The wave functions used in the present study are more extensive in terms of model space and correspond to a more accurate representation of experimental level energies than is the case for earlier studies. In addition, the present wave functions are the first obtained for which it has been possible to utilize a single Hamiltonian formulation for the entire shell.

‘IN 0 I 2 3 4 5 6 7 8 9 10 II 12

Our study here of the renormalization of the Ga- mow-Teller operator follows historically from the work of Wilkinson.4 He extracted, from a comparison of data in the p shell and lower sd shell (A = 17-21) with the wave functions of Cohen and Kurath’ and ancestral ver- sions of the present sd-shell wave functions,6V3 a reduction factor (assumed orbit independent) for the effective single- particle matrix elements relative to the “free-nucleon” values of 0.897 +- 0.035. (This result was expressed by Wilkinson in terms of a renormalization for the value of gA/gv; however, one can also think of the renormalization as coming from a correction to the nuclear matrix element of sr.)

Fig. 1. Display of nuclei whose beta decays pt treated in the present study and in the study of Ref 10. The d&s indiea%e Ni, Zi V&ES

treated in the present study and the slash ma& in tbe lower right- hand comers of the squares indicate the Deutrorrrieh systems treated in Ref 10.

We have previously published results on the topic of the effective matrix elements for sd-shell beta decay which were based on shell-model wave functions obtained from the Chung-Wildenthal interactions,’ the direct an- tecedents of the present interaction. In addition, the comparisons made by Raman et al.8 for the mixed Fermi Ga- mow-Teller transitions in the sd shell were based on the Chung-Wildenthal wave functions. More recently, these Gamow-Teller matrix elements for the mixed transitions were analyzed’ with the wave functions of Ref. 1. The mixed transitions, however, represent a very small subset of all of the sd-shell Gamow-Teller data, and the results we report here are the first which take into account all data in the sd shell together with the new sd-shell wave functions.

tute most of the cases for which precise experimental measurements of the absolute partial lifrztimes for decays to specific final states have been, or are Iike& to be, carried out. These partial lifetimes provide the b&s for comprehensive and detailed tests of the theoretical wave functions and the detailed specikation of the rtm#malization of the Gamow-Teller operator. We have presented else- where” predictions and comparisons with experiment for 36 of the most-neutron-rich nuclei in the -- shell. These cases are indicated in Figure 1 by the sIash marks in the lower right corners of some of the mct@es. Eight of these neutron-rich cases are also treated in the present work, as is indicated in Figure I. The theor&& branching ratios and lifetimes for Gamow-Teller decay were calculated in Ref. 10 with an orbit- and mass-independent renormalization determined in the paent study, while the same quantities presented here are &c&ted with the alternative orbit- and rnw mnormalization. This accounts for the occasional small &&ences in these numbers between the entries in the tables of Ref. 10 and the tables of the present work.

The present study deals with Gamow-Teller decay from the 64 parent states indicated in Figure 1 by the solid dots. We focus on these nuclei because they consti-

The tables of the present work, augmented by the results of Ref. 10, encorn- esaentInIiy rrll physically re- alizable decays in which the individual firmI states can be experimentally identified and their m&x elements hence compared to individual theoretical values. Gamow-Teller

CO CO

K K

Ar Ar

Cl Cl

S S

P P

Si Si

Al Al

M!3 M!3

NCJ NCJ

Nil Nil

F F

0 0

349 Atomic Data and Nudear Data Tsbles. Vab. 33, No. 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller fl Decay in s&Shell Nuclei

transitions are important in contexts other than this, of course. One interesting area is the decay of proton-rich parents, in which the large Q values open up a much wider than average range of final-state excitation energies. These are extensions of the decays of the proton-rich isospin T = 1 and T = 312 nuclei treated in the present work. However, as is evident already in the T = 1 and T = 3/2 decays, it is impossible to match the calculated to the observed states in a consistent fashion at the higher excitation energies, where the level densities overwhelm experimental resolution.

A similar situation is found in induced-reaction ex- periments such as (p, n). Much of the strength is found at higher excitations, where individual states cannot be separated or identified experimentally, even though the distribution of Gamow-Teller strength with energy might be measured quite accurately. Comparisons of the measured strength distributions with shell-model predictions are as important for these cases as they are for the individual decays we consider here. However, the much larger numbers of states and the impossibility of setting up tables of state-by-state comparisons make the mode of presen- tation required for this aspect of Gamow-Teller phenom-

ena very different from the one employed here. We intend to deal with this type of phenomena in a later publication.

In Section IIA we present a general formulation for the treatment of allowed beta decay in nuclei. The method used for calculation of the phase-space factors is outlined in Section IIB, and our choices for the values for the weak- interaction coupling constants are discussed in Section IIC. The experimental data and their combination with the calculated phase-space factors to obtain experimental log(jQ values and Gamow-Teller matrix elements are discussed in Section III. The methods employed for the calculations of the shell-model wave functions and the one- body density matrix elements for Gamow-Teller decay are presented in Section IV; the general methods and their application to the calculation of the “free-nucleon” ob servables are presented in Section IVA and the formulation for the effective Gamow-Teller operator is discussed in Section IVB. The results of the least-squares fits to determine the values for the parameters of this effective op erator are presented in Section NC. Finally, in Section V, we discuss the comparisons of the experimental observables with those calculated with both the “free-nucleon” and the effective operator assumptions.

II. WEAK-INTERACTION FORMALISM

A. General Considerations and Definitions

We start with the familiar expression which relates t1,2, the experimental partial half-life for beta decay to a specific final state, to the corresponding nuclear structure matrix element. This expression incorporates the phase- space factor f and the constant K.’ L”

$1/2 = Kl[gt,(T)2 + gs+T)21. (1)

The partial half-life tl12 is given in terms of the total half- life Tlj2 and the branching ratio BR by

tv2 = TmiBR. (2)

The constant K is given by

K = 2?r3(ln 2)tt7/(&c4)

= 1.230618 X 10eg4 erg’ cm6 set, (3)

where n is the reduced Plank constant, h = h/2r, m, is the electron mass, and c is the speed of light. The weak- interaction vector and axial-vector coupling constants for the decay of neutron into a proton are denoted by gv and gA , respectively.

For /3& decay the nuclear matrix elements (7) for the Fermi operator and (UT) for the Gamow-Teller op erator are given by

(T) = (f I( 2 t”,lli)/\l2Ji+l k

(4)

(UT) = (fll C u%k,/Ii)/tiW,+I (5) k

where t* = (l/2)(7, + ir,,) and Ji is the spin of the initial state of the nucleus. The sum is over the nucleons in the nucleus. The matrix elements are reduced in spin-orbit space but not in isospin space and we follow the reduced matrix element convention of Edmonds.‘3

We calculate the phase-space factor for 1(1+ decay separately from that for the competing process of electron capture; in general,

L =f(B+) +fW. (6)

We use electron-capture phase-space factors which are based on the tables of Behrens and Janecke.14 In evaluating the phase-space factorsf&) we follow the procedures of Wilkinson4*‘5*‘6 (see Section IIB).

The effects of finite nuclear size and other corrections upon the phase-space factors are slightly different for the Fermi (vector) and Gamow-Teller (axial-vector)

350 Alomk Oala and Ndaw Data Tablea. Vol. 33, NO. 3. Novemh 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller p Decay in s&hell Nuclei

decays.” Taking this difference into account and rear- ranging terms, we arrive at a modified form of Eq. (I),

fAfll2 = ~/[u;/fA)~(F) + ~W-N, (7)

where c = fmd2, (8)

B(F) = (7)*, (9) and

NGT) = k&v)*++*. (10)

B(F), the reduced transition probability of the Fermi decay, is given by

B(F) = [T(T+ 1) - T,rJ’~]Gir(l - c), (11)

where 6ir allows the Fermi transition to take place only between nuclear analog states.

The quantity (1 - t) is the conventional correction factor for the Fermi decay by which the reduction in the overlap between the initial and final nuclear wave functions due to isospin mixing is taken into account. This overlap correction will be ignored for the Gamow-Teller matrix element since it is very small relative to the typical magnitudes of the corrections to this matrix element from the effects of configuration mixing, the focus of our present considerations.

For the Gamow-Teller decay, we define a reduced matrix element M(GT) by

M(GT) = [(2Ji + l)B(GT)]“*. (12)

With this definition the magnitude of M(GT) does not depend on the direction of the transition, that is

JM(GT, u - 6)) = IM(GT, b - a)], (13)

whereas

B(GT, a - b) = [(2J, + l)/(2Jb + l)]B(GT, b - a).

(14)

In terms of triply reduced matrix elements in spin- orbit and isospin space, M(GT) is given by

The operator Oar is given by

OGT = kAh?V~ c SkTk k

(16)

and s = a/2. In order to evaluate the strength of a Gamow-Teller

transition relative to some absolute standard, it is useful to consider the Gamow-Teller sum rule” by which the sums of the strengths of /3- and 8+ decays of a single initial

state to all possible final states can be related to the neutron number Ni and proton number Zi of the parent state

2 UWT-, i - f) - B(GT+, i - f)] f

= k4/&YXN - Zih (17)

For the /3- decay of neutron-rich nuclei, this equation provides a lower limit for the sum over B(GT-). For a nucleus with a neutron excess, the theoretical results sug- gest that the sum over B(GT+) is usually much smaller than the sum over B(GT-), and that hence the sum over B(GT--) is usually close to the sum-rule value (typically within 10% for these &shell calculations). These state- ments obviously also apply for the p+ decay of proton- rich nuclei. When Ni = Zi, the sum rule is not useful but simply restates the obvious fact that B(GT+) = B(GT-) in this case.

B. Evaluation of the Phase-Space Factors

The phase-space factors J&3) and f&3) are calculated in the present study as prescribed by Wilkinson and collaborators.4*‘s~‘6 The starting point is the analytic result for a nucleus of Z = 0 given by

f&o = ( l/60)(2 I+‘$ - 9 I+‘; - 8)po

+ (1/4)Woln(Wo + PO). (18)

In this expression W. is the total electron (positron) endpoint energy in units of&c* and po = ( I+‘$ - 1)“‘. Several correction factors are applied to Eq. ( 18) to obtainf* , the relation being expressed as

h = bwW&=O. (19) The most important of these correction factors is

dWM, the values of which are tabulated by Wilkinson and Macefield” in the form

6WM = exp [

2 a&n EO)” , 1 n=0,3 (20)

where E. is the endpoint energy of the electron in units of MeV (EO = ( W. - 1 )m,c*):

and Eo = (Q + EJ - Ef for B-

EO = (Q f EJ - Ef - 2112~~ for P+ , (21)

where Q is the beta-decay Q value and E; and Ef are the excitation energies of the initial and final states. The calculation of 8WM uses electron wave functions for an atom generated from a uniform spherical nuclear charge distribution whose radius is adjusted to tit the appropriate electron scattering and muonic x-ray data and which is corrected for the screening of the atomic electrons. Also included in the values of 8WM are the effects of the energy-

351 Atomic Data and Nuclear Data Tabcls. Vol. 33, No. 3. Nwmber 1985

B. A. BROWN and 9. H. WILDENTHAL Gamow-Teller (3 Decay in sd-!Shell Nuclei

dependent “outer” radiative correction to order a. The parametrization of the values of 6wM by E!q. (20) is accurate to better than 0.1% througbout.‘5

The factor & incorporates the effects of the “outer” radiative correction to orders Z&r and Z*o? and is given’**’ by

bR = 1 + 3.67 x 10-9 + 3.60 x 1o+z*, (22)

where Z is the proton number of the daughter nucleus. The factor So incorporates the effects of the diffuseness of the actual nuclear charge distribution’6

&, = 1 + 1.8 X 10-sZ’.36 - 1.2 X 10-6ZH’& (23)

The Fermi p&se-space ftiorfv is relatedi to the factor fA by

$4 = wi, (24) where

6v = 1 f (2/15)(W&/l97)aZ - (4/105)(W&/197)*

(25)

for beta + decay, where Q = 1 j 137 and where we have used

R = l.35Aif3. (26)

C. Values for the Weak-Interaction Coupling Constants

The values of the coupling constants for Fermi decay, gv, and Gamow-Teller decay, gA, in the combina- tions in which they appear in Eq. (7) are obtained as follows.

For a O+ - O+ nuclear transition B(GT) = 0 and for a transition between T = 1 analog states Eq. (7) reduces to

c = KItgvP = h&2(1 - 4. (27) The half-lives and Q values for several O+ - O+ analog transitions have been measured with great accuracy. With some plausible assumptions about the Z dependence of c [t(Z = 0) = 01, the deduced values for C extrapolate at Z = 0 to the valueI

C(Z = O)= 6170 If: 4sec. (28)

This result, together with the value of K in Eq. (3), can be used to obtain gv.

The value we use for E takes account of the empirical mass or, equivalently, Z dependence of C for the s&hell nuclei. It will be adequate to use a constant average value together with an error which encompasses the range of values experimentally observedI in the s&hell nuclei

from tron.

e = 0.003 zk 0.003. (29)

The “free-nucleon” value for gA can be obtained the mixed Fermi/Gamow-Teller decay of the neu- Our calculations are based on the 1973 analysis of

Wilkinson4 which gave

I&/&l = 1.251 + 0.009. (30)

This value is consistent with the value of 1.2606 + 0.0075 obtained by Wilkinson in a more recent analysis.‘*

III. EXPERIMENTAL DATA

The data which are used to obtain the experimental Gamow-Teller matrix elements are presented in Tables I and II. Many of the luSlife, branching ratio, and energy- level data were taken directly from the compilations of Ajzenberg$elover9~ for A = 17 and A = 1 S-20 and Endt and van der Lcun” for A = 2 l-39. Most of the Q values were taken from the compilation of Wapstra.** References and comments on the mono recent data considered for Tables I and II are given at the end of the main text.

The total half-lives Tl12 and the Q values are given in Table I. The experimental energies and spin-parity- &spin values of the final states and the branching ratios to these states am given in Table II. Other entries in Table II include the logarithm of calculated phase-space factor fA = fA(@) +fA(ec), wbeie the beta-decay phase+pace faC- to= ii(@) - calcuiated according to the prescription outlined in Section W and the electron-capture phase-

space factors are based on the tables of Behrens and Ja- necke.14 The calculated percentage electron capture probability is given under the heading P(ec). Also in Table II we give the value of 1ogcfAf) obtained from the experimental partial half-life tl12 and the calculated phase-space factorf: The experimental Gamow-Teller matrix element is given in Table II as obtained according to the prescription

M(GT)(exp) = [(2Ji + l)B(GT)(exp)]“*, (31) where

WWtexp) = W170 + Wih&xp)l - ti/h)@FKth). (32)

B(F)(th) is the calculated Fermi decay matrix element given by Eq. (11) with c = (0.003 f 0.003). The ratio&/ fA calculated according to Eqs. (24) and (25) is given in Table II in the form F(V/A) = lOO[cfv/S,) - I].

352 Alomk Data and Nudslv Data 1&4ss. Vol. 33, NO. 3. N- 1333

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller @ Decay in s&Shell Nuclei

IV. SHELL-MODEL THEORY

A. Calculation of the “Free-Nucleon” Gamow-Teller Matrix Elements

The foundation of the present analysis is a new set’ of shell-model wave functions generated in an attempt to reproduce all features of &shell spectroscopy from a uni- fied formulation of the model Hamiltonian. These wave functions span the complete spaces of O&,2, 1~1~2, O&Q configurations, which is a critical aspect when considering matrix elements of operators, such as the spin operator, for which the transitions between the spin-orbit partners are of paramount importance.2

Beyond the limitation to the &-shell model space, the shell-model calculations upon which the present predictions of M(GT) are based assumed the constraint of a Hamiltonian which conserves isospin. This Hamiltonian is limited to one- and two-body interactions and, more specifically, has a fixed one-body spectrum and a single set of two-body matrix elements. These two-body matrix elements are scaled for application to a given A value by the factor ( 1 8/A)“.3. Hamiltonian matrices based on these parameters were diagonalized to produce a family of wave functions INTJn), where N = A - 16, T and J designate the total isobaric and angular momentum spin values, and n is the counting index which identifies a particular eigenstate of the NTJ set. Within this family we find the particular wave functions assumed to correspond to the pairs of initial and final states for which we wish to calculate the Gamow-Teller matrix elements M(GT).

The reduced matrix element of any one-body op erator O’tiAT’ of tensor rank AJ in spin-orbit space and tensor rank AT in isospin space between multiparticle shell-model wave functions can be expressed as a sum of the products of the elements of the multiparticle transition amplitude (A) times single-particle matrix elements (S), where the sum runs over all single-particle states (Y = (n, 1, j) (see Ref. 23)

(flIlOQJJ=) I/Ii) = C A(AJ, AT, a, a’, f, i) a,a’

where

x s(o’~A~, a, a’), (33)

A(AJ, AT, a, (Y’, f, i) = [(2AJ + 1)(2AT + 1)]-‘j2

X (fllI[a+(a) @ Z(a?]‘tiAr)llli) (34)

and S(O(uA=), a, a’) = (al(lO(uA=)(l(a’). (35)

(The operator a’(a) creates a particle in orbit LY and the operator Li(o’) destroys a particle in orbit a’.) Hence, the theoretical values of M(GT) are obtained from a sum of

353

products of the multiparticle matrix elements of a+(a) @ ii(d) as evaluated with the shell-model wave functions of Ref. 1 and the single-particle matrix elements of the Gamow-Teller operator for the &shell orbits.

The multiparticle transition amplitudes A embody the entire predictive content of the shell-model calculations. They are uniquely and completely determined by the specification of the model Hamiltonian. These amplitudes for an operator with AJ = 1 and AT = 1 for the transitions we consider in this work are given in Table III. The high degree of configuration mixing predicted by the present shell-model calculations is evident in the significant contributions of several single-particle paths to a typical transition. These individual components from which the net theoretical strengths are constructed are basic to further theoretical considerations of Gamow- Teller phenomena. Comparisons of predictions of orbit- dependent renormalizations, for example, require the availability of these individual orbit contributions. Study of the s to d transitions, forbidden in the lowest order, can focus on those initial and final states for which this path is dominant, as predicted by the entries of Table III.

The reduced single-particle matrix elements for the Gamow-Teller operator of Eq. ( 16) (AJ = 1 and AT = I) are given by

S(GT, a! 4 = Ig,/gvI(~I~~s~~~1~‘). (36)

Upon interchange of a! and (Y’

S(a’, a) = (- 1 )j-“S(C,, cy’). (37)

Thus, for the sd-shell model space there are five unique single-particle matrix elements, correponding to the (Y--(Y’ transitions Od+lds/2, Od~/rOd3/2, h/2-&2, h/2-

Od312, and Od3,2-Od3,2. The values of S(GT) obtained with IgA/gvl = 1.251 are given in Table A. We will refer to these as the “free-nucleon” single-particle matrix elements, or S’““.

B. Formulation for the Effective Gamow-Teller Matrix Elements

There are several reasons why the “free-nucleon” calculations of M(GT) may differ from the corresponding experimental values. In reality, the nuclear wave functions must be more complicated than those of the theoretical model we use. Real nuclear states must involve nucleon degrees of freedom beyond the sd-shell space. In addition, nonnucleonic degrees of freedom of the nucleus which involve delta isobars and mesons may be important in the observed rates. The calculation of the corrections to the standard shell-model predictions which arise from

Atomic Data and NixJew Data Tables. Vol 33. NO 3, November 19%

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller ,9 Decay in s&hell Nuclei

TABLE A. Values of the “Free-Nucleon” and Effective Single-Particle Matrix Elements of the Gamow-Teller Operatora

a n. 1. i Free nucleon

Effective (A = 28) Effective

Value Ratio to free A = 17 A = 39

w5i-2 Od5/2 4.440 3.443 0.778 3.803 w5i2 WI2 -4.747 -3.513 0.740 -3.711 w/2 W/P -2.373 -1.813 0.764 -1.903 $2 191/z 3.753 2.904 0.774 3.040 191/z w3i2 0.000 0.056 0.047

’ The effgctive matrix elements are based on the massdependent S parameters obtained in the “final fit.”

3.321 -3.362 -1.745

2.800 0.063

these sources have been the subject of many theoretical investigations. Most recently, extensive calculations of these effects were carried out by Towner and Khanna.24 For references and comparisons to the earlier works, see Refs. 24 and 9.

There are a number of uncertainties in the calculations of these corrections. For example, there are many questions about the role of the delta isobar correction in Ref. 25. Our approach to this problem is to assume that these corrections can be incorporated into “renonnalizations” of the “free-nucleon” values of the single-particle matrix elements; that is to say, into an “effective” one- body operator for Gamow-Teller decay in the context of the s&hell model space. Since the most general effective operator can be expressed in terms of the five single-particle matrix elements given above and since there are many experimental data, effective values for these five matrix elements can be found by the standard technique of a least-squares fit to the experimental data. The main focus of the present work is the determination of these effective single-particle matrix elements and the comparison of the experimental data to the values calculated by combining this effective operator with the shell-model wave functions of Ref. 1, as condensed into the multiparticle transition amplitudes of Table III.

The fitting procedure by which the effective single- particle matrix elements are obtained follows that of Ref. 9. It is convenient to express the five effective matrix elements in terms of the five 6 parameters associated with the effective GT operator

@ii = t&h’)@ + 8&T), (38)

where

s&T = &(d-d)S(d-d) + 6,(+@0+) + &(d-d&(d-d)

+ GJs-d)P(s-d) + G#d)P(d-d) (39)

and

1) = Sf”( 1 l)[ 1 + 6&s)], se”< 1

and

sq 1 3) = lgA/g,r16(5)-“2~p(s-d) = 3.357&@-d), (42)

s = CSkTk,

L = ClV,

and where

P = CpV (40)

pk = (87r)“2[ fi2’(rk) 8 sk]? (41)

The 6 coefficients characterize the renonnalizations which are needed when working within the s&hell model space. The notation (d-d), (s-d), and (S-S) identifies the respec- tive pairs of orbits, 1 = 2 (Ods12 and Od3,2) and 1 = 0 ( Is,,~), which are acted on by the operators. The reduced single-particle matrix elements for the individual operator components S, L, and P are given in Ref. 9. The effective sd-shell single-particle matrix elements Sdf(2j 2j’) are given explicitly in terms of the 6 parameters by9

SCff(55) = Sf”755)

X [ 1 + &(d-d) + 46,(d-d) + (4/7)6,(d-d)],

S”733) = Sf”(33)[1 + &(d-d) - 66,(d-d) + 26,(d-d)],

S”ff(53) = Sf753)

x [ 1 + &(d-d) - Gr(d-d) - (1/2)6,(d-d)],

where the Sf”(2j 2j’) are the “free-nucleon” GT matrix elements. Conversely, the three 6 parameters for the d

354 Atomic Data and Nuclear Data Tabk Vol. 33. No. 3. November 1995

B. A. BROWN and B. H. WILDENTHAL

orbit can be expressed in terms of the effective matrix elements

add-d) = [ 146(55) + 46(33) + 326(53)]/50,

6,(d-d) = [76(55) - 36(33) - 46(53)]/50,

6,(d-d) = [146(55) + 146(33) - 286(53)]/50, (43)

where 6(2j 2j’) = [Seff(2j 2j’)/SfR’(2j 2j?] - 1. (44)

We expect some mass dependence in the 6 parameters since the renormalizations are theoretically some- what different for the particle states in A = 17 and the hole states in A = 39.24 We will assume that this mass dependence is smooth, and parameterize it in the form

6(A) = A(,4 = 28)(,4/28)“.35. (45)

In principle, the power ofA could be taken as an additional parameter in the fit, but, in practice it is highly correlated with the orbit dependence in 6 and hence could not be determined uniquely. We have chosen to use the value of 0.35, based on the calculations of Towner and Khanna.24 This value was obtxinedby averaging their results for 6, given in Table V of Ref. 9 for A = 16 and A = 40, which would give 0.37 for G&&d) and 0.32 for G&-s).

The effective single-particle matrix elements which we determine empirically can be compared to the results of calculations which attempt to take into account the effects of higher-order nucleon configuration mixing and nonnucleonic degrees of freedom, such as those of Towner and Khanna.24 These calculations can be carried out only for the simple systems of one particle or one hole in the sd shell. However, there are ambiguities inherent in the comparison of these one-particle-model results to the real situations in A = 17 and A = 39. The single-particle wave functions for these nuclei may be fragmented by admix- tures with the four-particle four-hole excitations of the core.’ In addition, the experimental information for the transitions between all of the states in A = 17 and A = 39 is incomplete. We are able to extract from the wealth of experimental data for the multiparticle sd-shell systems the complete set of effective single-particle matrix elements. Our results have been compared with the calculations of Towner and Khanna in Ref. 9 and we refer the reader to this paper for a discussion of the comparison.

C. Results for the Effective Gamow-Teller Matrix Elements

We have obtained empirical values for the five 6 parameters defined in Section IVB by making a least- squares fit to all data for which the experimental error in the matrix element is 10% or less. There are 189 data which meet this criterion.

Gamow-Teller B Decay in sd-Shell Nuclei

The experimental and theoretical matrix elements were first converted into “dimensionless” quantities by dividing both by the common factor

W = IgA/&l[(2Ji + 1)3(Ni - Zi)]“’ for Ni Z Zi

or

W = Ig.,Jgvl[(2Jf + 1)3(Nf - Zf)]‘/2 for Ni = Zi. (46)

On the basis of the sum rule of Eq. ( 17) the upper bounds on the quantities R(GT) defined by

R(GT) = M(GT)/ W (47)

are on the order of unity since, as mentioned, B(GT+) is small. The numerical values for the conversion factors W are given in Table II.

The initial fit gave a root-mean-square (rms) deviation A = 0.029 between the experimental and theoretical quantities R(GT). This can be interpreted as a 2.9% deviation relative to a sum rule of unity. The rms deviation in the experimental errors in R(GT) is only 0.006. Thus, the 2.9% rms deviation between experiment and theory arises more from systematic errors in the theory than from the experimental uncertainties. We have folded a systematic error of 0.030 in quadrature with the experimental errors in order to give proper weight to the individual data as well as to assign a more realistic uncertainty to the resulting parameters of the fit. The results for this five- parameter fit are given in Table B.

Towner and Khanna obtain in their calculations the values &(d-d) = 0.0 16 and &As-d) = 0.027 (see Table V of Ref. 9). Since the orbit dependence in these theoretical 6, parameters is comparable to the uncertainty with which they can be individually determined by the tit, we have considered the results obtained by combining the two p operators into the single operator

6,P = GJd-d)P(d-d) + G,(s-d)P(s-d). (48)

The results of this four-parameter fit are also given in Table B. The four-parameter and five-parameter fits are essentially equivalent in terms of the rms deviation. Thus, we have chosen to make all further comparisons with this four-parameter, mass-dependent fit, which will be referred to as the “final fit.” The effective single-particle matrix elements for A = 17,28, and 39 obtained with the “final- fit” parameters are given in Table A.

The results of the present fit are consistent with the results we have obtained previously’ (see Table B), from a consideration of the GT transitions between the analog states of the odd-even mirror nuclei (the mixed Fermi Gamow-Teller transitions). The main improvement in the present work is that the uncertainty in the parameters has been reduced by about a factor of 2. The significance of these results in terms of a comparison with the renormalization of the magnetic dipole operator and in com-

Atomic Data and Nuclear Data Tables. Vol. 33. No. 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller @ Decay in s&hell Nuclei

TABLE B. Results for the 6 Parameters for A = 28a

W-4 M+4 6&-s) Ud-d) 4(s-4

-0.276(20)

-0.239(12)

-0.252(12)

-0.248(11)

0.004(4)

O.OOs(3)

0.005(3)

o.OOyg

-0.227(26)

-0.231(10)

-0.237(16)

-0.226(16)

0.016(16) 0.023(12) 0.003(14)

0.027(11) 0.003(13)

0.017(6)

Mirror data only with mass dependenoe (from Table IV of Ref. 9)

Present five-parameter fit without mass dependence (rms = 0.0293)

Present five-parameter fit with mass dependence (mts = 0.0266)

(“Final fit”) present four-parameter fit with mass dependence (rms = 0.0269)

’ Uncertainties are given in parentheses foflowing the numerical values. rms is the root-mean-square deviation between the experimental and fitted quantities R(GT) defined by Eq. (47). The mass dependence is given by Eq. (45).

parison with the calculations of Towner and Khanna has been discussed in Ref. 9.

It is interesting to note that 6, and S, are small relative to 6,. This is related to the fact that the orbit dependence in the quenching of the single-particle matrix elements is small (see Eqs. (42)). The ratios of the effective to the “free-nucleon” single-particle matrix elements given in Table A range only between 0.74 and 0.78 for A = 28. This orbit dependence is significantly smaller than that obtained previously with the older Chung-Wildenthal sd- shell wave functions, 26 which gave ratios from 0.69 (for the d5,2-d3,2 matrix element) to 0.85 (for the d5,,-ds,2 matrix element). Part of this change is due to the mass dependence of Eq. (45), which was not included previously. When the mass dependence is not included in the present fit (see Table B), the ratio for the d5,2-dS,2 matrix element is 0.8 1. However, the change in the orbit dependence is also partly due to going from the older Chung-Wildenthal wave functions to the new and more comprehensively reliable wave functions of Ref. 1.

Our average quenching factor of 0.76 + 0.03 for the sd shell (A = 28) can be compared to the average

356

quenching factor of 0.897 + 0.035 which Wilkinson4 obtained in a similar analysis for the mass region A = 6-2 1. The difference between these results is indicative of the fact that the quenching on the average is smaller for the p-shell and lower sd-shell nuclei than for A = 22-39.

The small S, value means that the I-forbidden OdJlz - Is,,~ single-particle matrix element is small. Re- cently, the weak branch for the beta decay of the “Ca 5’ state to the $’ state in 39K has been measured.*’ In the sd-shell model these levels arc just the Od3,2 and IsI/ single-particle states and the3 value for this transition thus directly provides a value for the l-forbidden matrix element or equivalently for the parameter GAS-d). From the A = 39 datum alone a value of IS,(s-d)l = 0.017 + 0.003 is obtained. From our fits (which do not include the A = 39 datum since its experimental uncertainty was greater than 10%) we obtain (for A = 39) &(s-d) = 0.030 f 0.0 11 in the five-parameter fit and S, = 0.021 + 0.008 in the four-parameter fit. Within the uncertainties the agreement between these independent results is good. Our results indicate that S, is positive as expected theoretically.24

V. COMPARISON BETWEEN EXPERIMENT AND THEORY

In this section we discuss the comparison of the experimental Gamow-Teller observables with those calculated with the “free-nucleon” and effective Gamow- Teller operators. In Table II the experimental transitions have been matched with their theoretical counterparts for those cases in which the correspondence is fairly clear from the agreement in the excitation energies. For these matched cases, the experimental excitation energy has been used to calculate the phase-space factors fA and JV .

The “free-nucleon” matrix elements were obtained by combining “free-nucleon” single-particle matrix elements given by Eq. (36) with the multiparticle transition

amplitudes given in Table III according to Eq. (33) and finally relating this triply reduced matrix element to M(GT) according to Eq. (15). The results are compared in Table II to the experimental matrix elements obtained from Eqs. (31) and (32).

We construct visual displays of theory vs experiment comparisons by representing transitions as points in the (x, y) plane such that the experimental value is plotted as the y coordinate of the point and the theoretical value as the x coordinate. In Figure 2 we show the quantities RexP(GT) and Rfrre(GT) plotted in this fashion for the transitions whose values have an experimental error of

Atomic Data and Nudwr Data TalSes. Vol. 33, No. 3. November 1935

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller 0 Decay in sd-Shell Nuclei

R(GT) THEORY (“FREE-NUCLEON”)

Fig. 2. Comparison of the experimental matrix elements R(GT) with the theoretical calculations based on the “free-nucleon” Gamow-Teller operator. Bach transition is indicated by a point in the x-y plane, with the theoretical value given by the x coordinate of the point and the experimental value by the y coordinate. The R(GT) are related to the M(GT) given in Table II by Eqs. (46) and (47). Ex- perimental values with uncertainties of 10% or less are shown. The lines in the figure pass through the origin and the points (1, I) and (1.0.77).

10% or less (that is those in the least-squares fit discussed in Section IVC). R(GT) and M(GT) are related by Eqs. (46) and (47). Two straight lines are drawn in this figure, one at 45’ and the other passing through the origin and the point (1, 0.77). The points would cluster about the 45” line if the experimental data were best reproduced with the “free-nucleon” theory. This is not the case; rather, the points cluster about the second line, which indicates that the experiment is reduced relative to the “free-nucleon” theory systematically by a factor of about 0.77.

As mentioned above, the maximum values of R(GT) are expected to be on the order of unity. Only two of the transitions considered are in fact close to unity, the I+ 7 - $+ transition in i9F (the point with R hrx = 0.967 and Rap = 0.742) and the O+ - l+ (and I+ - Of) transition in A = 18 (the point with Rfn" = 0.918 and Rexp = 0.723). It can be seen in Figure 2 that the quenchings for these two strong transitions are consistent with those for the weaker transitions.

Most R(GT) values, as can be seen in Figure 2, are significantly smaller than unity. The causes of these re- ductions are multiple. Frequently the decay strength from a parent state is fragmented over several final states. Moreover, some of the strength can lie outside the beta- decay Q-value window. In order to distinguish between

0.8 -

go.7-

Y E0.6- W %0.5-

FO.4 - 52 co.3-

0.0 T ?G: ) THE&Y (“F::E N”co;&N’,

1.0

Fig. 3. Comparison of the experimental values of the sums T(GT) with the corresponding theoretical value based on the “free-nucleon” Gamow-Teller operator. Each sum is indicated by a point in the x-y plane with the theoretical value given by the x coordinate of the point and the experimental value by the y coordinate. T(GT) and R(GT) are related by Eq. (49). Experimental values with uncertainties of 10% or less are considered. The lines in the figure pass through the origin and the points ( 1, I) and ( 1, 0.77).

simple fragmentation and loss of strength outside the Q window, we plot in Figure 3 the quantities T(GT) obtained by summing the values of R2(GT) over the observed final states (which have an experimental error of 10% or less) and the corresponding theoretical values. The quantity 7(GT) is defined by

T(GT) = [z R’(GT, i - f)]‘12. (49)

In this plot there is one point for every initial nucleus considered. It is evident that there remains a significant reduction of the values from unity. This reduction in Fig- ure 3 is due to the fact that a fraction of the GT strength lies outside of the beta-decay Q-value window. For the A = 26 O+ T = 1 initial state, this has been confirmed experimentally in a recent 26Mg(p, n) experiment,2s in which considerable GT strength has been observed above the Q- value window.

The scatter of points in Figure 2 is representative of the theoretical systematic rms error of 0.029 which was discussed in Section IVC. The scatter in the R(GT) plot of Figure 2 is larger than that in the T(GT) plot of the summed strength in Figure 3. This is because in some cases the final states of the same spin and isospin lie close

357 Atomic Data and Nuclear Data Tables, Vol. 33. No. 3. November 1995

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller /3 Decay in s&hell Nuclei

Fig. 4. Comparison of the experimental matrix elements R(GT) with the theoretical calculations based on the effective (“final-fit”) Gamow- Teller operator (see caption to Figure 2).

together. In such cases, the uncertainties in the effective Hamiltonian may randomly mix these states and alter the individual matrix elements, while not significantly chang- ing the sum of the squared matrix elements. An example of this effect is provided by the decay of ‘*K to the three 1 + T = 0 states of 38K, found in Figure 2 at the loci (0.142, 0.099),(0.540,0.517), and(0.552,0.197). Thelast ofthese appears to be particularly anomalous in Figure 2. How- ever, the summed strength in Figure 3, at the point (0.786, 0.562), fits in nicely with the systematics.

The comparisons of experiment to the R(GT) and T(GT) values calculated with the effective Gamow-Teller operator are shown in Figures 4 and 5, respectively. The effective matrix elements are obtained according to Eqs. (42), (45), (36), (33), and (15) by using the 6 parameters obtained in the “final fit” (see Table B). The points for T(GT) in Figure 5 cluster about the 45’ line and show an overall impressive agreement between experiment and theory. Good agreement is obtained for the smallest values (the points near the origin for the decays of ‘*Si and 32P) as well as for the largest values (the A = 18 and 19Ne decays mentioned above). The most anomalous point in Figure 5 is that at (0.409, 0.538 + 0.016) for the 34Ar decay. In this case the largest GT matrix element is for the decay to the fourth l+ T = 0 state in MC1. The experimental branch to this state is small, however, and it would be worthwhile to have a new and more accurate measurement.

Fig. 5. Comparison of the experimental sum T(GT) with the theoretical calculations based on the effective (“final-fit”) Gamow-Teller op erator (see caption to Figure 3).

Further comparisons of experiment and theory are made in Table II, for the branching ratios and log(j) values. These comparisons are made only for the (“final-fit”) effective operator. The phase-space factors needed for the theoretical branching ratios were calculated by using experimental excitation energies in those cases in which correspondences between the experimental and theoretical final states could be made and by using the theoretical excitation energies otherwise. The theoretical branching ratios have been renormalized to add up the experimental sums in order to take into account the possibility of other experimental decay modes. (Round-off errors in the experimental branching ratios sometimes make the summed branching ratio slightly different from 100%). The purpose of directly comparing the branching ratios is to see how much strength to unobserved final states might be missed experimentally.

In the case of the *‘O decay, the ground-state to ground-state branch was not measured in the gamma- decay experiment of Ref. 29. The calculated branching ratio is in fact very small for this case, and to a good approximation it can be ignored in the analysis of the absolute GT strength to excited states. However, we expect a total of 11.7% branching to states in *‘F between 4.6 and 7.0 MeV in excitation, which has probably been missed experimentally. This would mean that the experimental branching ratios for the lower states should be renormalized downward by about 10% and would improve the agreement between experiment and theory.

358 Atonk Data and Nuclear Data Tab&. Vol. 33. No. 3. November 1085

B. A. BROWN and B. H. WILDENTHAL

Other cases where some significant branching to excited states may have been missed experimentally are for the decays of ‘*F (lo%), 27Na (4%), *‘Na (18%), 29Mg (8%), and “Mg (9%).

In our calculations isospin is assumed to be a good quantum number. At some level of detail, isospin mixing should be taken into account to improve the agreement between experiment and theory. Perhaps the largest deviation due to isospin mixing in the present data set occurs for the transitions from 24Alm to the 9828- and 9965keV levels in 24Mg. The experimental matrix element for the transition to the 9828-keV I+ T = 0 is much larger than theory predicts. This is very likely due to isospin mixing with the nearby 9965keV 1+ T = 1 state, which has a much larger GT matrix element.

Another consequence of isospin mixing is that the M(GT) values for mirror pairs of transitions are not equal. There are six cases in Table II which can be compared, those for the ground state to ground state transitions in- volving the pairs of nuclei, (‘*F, “Ne), (*OF, *ONa), (24Na, 24A1), (28A1, **P), (30P, ‘OS), and (32P, “Cl). These have experimental differences A&GT) = R(GT, neutron rich) - R(GT, proton rich) of -0.003(3), 0.0015(9), 0.0008(9), -0X)22(5), -0.007(2), and -0.008(2), respectively. These differences are small compared to the rms deviation of 0.029 between experiment and theory in the best fit, which indicates that our conclusions will not be strongly affected by isospin mixing.

In summary, our conclusion from this study is that the Gamow-Teller data for all the nuclei of the sd shell are in excellent agreement with predictions based upon the assumption of an effective one-body Gamow-Teller operator and one-body densities from the new shell-model wave functions of Ref 1. In the middle of the sd shell the effective matrix elements are quenched by an overall factor of 0.76 & 0.03 relative to the “free-nucleon” values based on the neutron beta decay. This result, considered in the context of the analogously extracted magneticdipole operator for the sd shell and the calculations of Towner and Khanna,24 suggests that about half the Gamow-Teller quenching comes from the effects of higher-order nucleon configuration mixing and half from the presence of the delta isobar in the nuclear wave functions.’ The giant Ga- mow-Teller resonance has recently been studied over a wide mass range by the (p, n) reaction.30 It is interesting that the average quenching of about 60% relative to the sum-rule value of 3(N - 2) observed in the cross sections for these reactions for A > 40 is very close to our sd-shell result of (0.76)* = 0.58. However, the details of the dependence of the quenching on A, (N - Z), and the shell closures remain to be explored. With recent techniques

359

Gamow-Teller ,!3 Decay in s&hell Nuclei

developed for studying the properties of nuclei in the sd shell that are very neutron rich,3’q32 we should be able to check our predictions” for large values of (N - 2).

Acknowledgments

This research was supported in part by the National Science Foundation under Grants PHY-80- 17605 and PHY-83- 12245.

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361 Atomic Data end Nuclear Date TsMes. Vol. 33. No. 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller @ Decay in sd-Shell Nuclei

EXPLANATION OF TABLES

TABLE I. Experimental Half-Lives and Q Values

Ai, 5 Initial nucleus Af, & Final nucleus 2Ji, 2Ti Twice the values of the initial-state spin and isospin (all states

have positive parity) 7.~2 Experimental half-life in units of seconds ATI/z Experimental error in T,,2, in percentage Q + E Experimental beta-decay Q value between the initial state

and the ground state of the final nucleus, in units of keV

AQ Experimental error in Q, in units of keV.

TABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ft Values, and Gamow-Teller Matrix Elements

The calculated phase-space factors fA, fv, and & are also given here. This Table extends across two pages.

Left page: Ai, Z Af, Zf 2Ji, 2Ti

2Jr, 2Tf

nf

E&w)

Ah

ABR/BR(exp)

Initial nucleus Final nucleus Twice the values of the initial-state spin and isospin (all states

have positive parity) Twice the values of the final-state spin and &spin (all states

have positive parity). The space is left blank if the value is not experimentally known.

Counting index of the final state of the indicated J and T associated with the (nf)‘h theoretical state

Experimental final-state excitation energies in keV. The Q value from Table I is given at the end of each block after “Emax = .”

Experimental error in Ef in keV (relative to the ground state). A value of <l indicates an error of less than 1 keV.

Theoretical final-state excitation energies in keV Experimental branching ratio in percentage. The notation

E-4 on the right-hand side indicates that the value has been multiplied by 104. The sum of these numbers is given at the end of each block after “Sum = .” In some cases this sum is not exactly 100% due to round- off in the individual values. In other cases the sum is not 100% due to competing beta-decay branches to negative-parity final states or competing particle-decay branches. When the deviations from 100% are significant, they are explained in comments to the tables.

Percentage error in the experimental branching ratio. A value of < 1 indicates an error of less than 1% and a value of >99 indicates that the branching ratio is an upper limit. The value - 1 indicates that the branching ratio has not been measured but for purposes of comparison has been assigned the value given.

362 Atomic Data and Nudear Data TaCks. Vd. 33, No. 3, November 1965


EXPLANATION OF TABLES continued

BR(th) Theoretical branching ratio in percentage, as calculated with the effective (“final-fit”) Gamow-Teller operator

Right page: hm log(Q where fA is the sum of the ,&decay and electron-

capture Gamow-Teller (axial vector) statistical rate famm: Xi = Ai(ec) + f&O

W/N Percentage difference between the phase-space factors for the Gamow-Teller (axial vector) and Fermi decays (vector), W/A) = 100 KhlfA) - 11

P(ed Percentage electron-capture probability: P(ec) = 100fA(ec)/ tit@ + fA@I

log(fAt): exp Experimental bgCfAt) Value. logvAt) = log(&) + log(t&, where tl12 = T,,2/BR is the experimental partial half- life.

AlOg(f,t): eXp Error in logCfAt) due to experimental errors in Q, Ef, Tl,2, and BR values

lOg(f,t): th Theoretical value calculated with the effective (“final-fit”) Gamow-Teller operator

WG-U Reduced Gamow-Teller matrix element. This is related to the reduced transition probability by E(GT) = [M(GT)12/(Wi + 1). In some cases when the error in the experimental branching ratio is large for the transitions between analog states, B(GT) is negative but consistent within error with zero. These cases are indicated in the table by the symbol >O. The value of the conversion factor given by Eq. (47) is given at the end of each block after “W = .”

M(GT): exp Experimental value obtained from Eqs. (3 1) and (32) in the text

AM(GT): exp Error in M(GT): exp M(GT): th(eff) Theoretical value calculated with the effective (“final-fit”)

Gamow-Teller operator M(GT): th(free) Theoretical value calculated with the “free-nucleon” Ga-

mow-Teller operator

TABLE III. Theoretical Multiparticle Transition Amplitudes

Ai, Z Af, Zf 2Ji, 2Ti

2Jf, 2Tf

nf

Ef Nii’)

Initial nucleus Final nucleus Twice the values of the initial-state spin and &spin (all states

have positive parity) Twice the values of the final-state spin and isospin (all states

have positive parity) Counting index of the final state of a given J and T values Theoretical final-state excitation energies in keV Multiparticle transition amplitude:

(flll[aj+ QD &]A’=‘*Ar=‘]]]i)/3 The individual columns are labeled with 2j - 2j’, i.e., 5-5

means j = $ and j’ = 2.

363 Atomic Data and Nuchr Data Tables. Vol. 33. No. 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller @ Decay in sd-Shell Nuclei

COMMENTS ON RECENT DATA

“F + “0 T,,z from Ref. 33 *‘(-J - *‘F T,,z, J”, Ef, and BR from Ref. 29. Errors of 1% for the BR

and 2 keV for Ef were assumed. The BR to the *IF ground state was assumed to be less than 10%. The branching ratios add to 100% when the two upper limits to the states at 1755 and 3639 keV are included in the sum (see Table IV in Ref. 29).

*‘F + *‘Ne T,,*, J”, Ef, and BR from Ref. 34. Errors of 1 keV were assumed for Ef.

*‘Na - *‘Ne J”, Ef, and BR from Ref. 35. Some of the BR given in Ref. 33 disagree with those given in Ref. 35.

*‘Mg - *‘Na BR to excited states from the proton decay experiment of Ref. 36

**F -+ **Ne J” = 3+ and 5+ assumed for the 7341- and 7424-keV levels, respectively

23Ne - 23Na Tlj2 from Ref. 37 24A1 - 24Mg J”, Ef, and BR from Refs. 38, 39, and 40. Additional exper-

imental information not included here has been obtained from beta-delayed particle emission (Ref. 38)

24,41m --+ 24Mg J”, Ef, and BR from Ref. 38. Ei = 426 keV for the 24Alm 1” state from Refs. 41 and 38. The dominant decay mode (82.5%) for this state is by gamma decay to the 24A1 ground state. Additional experimental information not included here has been obtained from beta-delayed particle emission (Ref. 38).

25Ne - *‘Na J” = t’ assumed for the 3688-keV level 25Na - 25Mg Tgj2 from Ref. 42 averaged in with compiled value. BR from

Ref. 43 25Al + 25M g J”, Ef, and BR from Refs. 44 and 33. The BR to the 975-

keV level is taken from Ref. 44, which differs from the BR to this level given in Ref. 33.

26~1”’ + 26Mg Q from Ref. 16 and T,,z from Ref. 45 26Si --* 26A1 Tlj2, J”, Ef, and BR from Ref. 35 *‘Na - *‘Mg J”, Ef, and BR from Ref. 31 *‘Si - *‘Al J”, Ef, and BR from Refs. 46 and 33 28Na - *‘Mg J”, Ef, and BR from Ref. 3 1 28~ -a *8si J”, Ef, and BR from Ref. 47. Additional experimental infor-

mation not included here has been obtained from beta- delayed particle emission (Ref. 48).

29Na - 29Mg J” for the initial state from Ref. 49. The experimental level scheme of 29Mg is not known; see Refs. 50 and 3 1.

29Mg - 29A1 J”, Ef, and BR from Ref. 3 1 and T,,2 from Refs. 2 1 and 3 1. The beta decay competes with a 3 1% neutron decay branch (Ref. 3 1).

29Al - 29si BR from Ref. 43 29~ - 29si Tti2, J”, Ef, and BR from Ref. 35

364 Atomk Data md Nuclear Data Tables, “~4.33, No. 3. Novmber 1935


COMMENTS ON RECENT DATA continued

93 + *9p

30Na - “Mg

30Mg - “Al

3op + 3oSi 33 4 3op 3’Al + 3’Si

3’s 4 3’p 32f3 4 32p

32~1 -+ 32s

33Cl - 33s

33Ar - 33Cl

34(-l --+ 34s

34C]” --+ 34s

35 P- 35S

35Ar - 35Cl 35K ---a 35,4r

36K --f 36Ar

37Ca + 37K

38K --+ 38Ar 38Km + 38,4r 38Ca 4 38K 39Ca + 39K

TIj2, J”, Ef, and BR from Ref. 5 1. The BR to the lowest four states which are bound to particle emission were not measured in the proton decay experiment of Ref. 5 1.

Q, J”, Ef, and BR from Ref. 3 1. An error of 100 keV was assumed for Q.

T,,*, Q, J”, Ef, and BR from Ref. 3 1. An error of 100 keV was assumed for Q. The beta decay competes with a 16% neutron decay branch (Ref. 3 1).

J”, Ef, and BR from Ref. 35 T,,2, J”, Ef, and BR from Ref. 35 J”, Ef, and BR from Refs. 52 and 31 Tl12, J”, Ef, and BR from Ref. 35 T,,* average of values from Ref. 53 (108 + 18~1) and Ref. 54

(101 + 18y) Additional experimental information not included here has

been obtained from beta-delayed particle emission (Ref. 48).

J”, Ef, and BR from Ref. 35. A value of J” = $’ is assumed for the 4 144-keV level.

BR from Ref. 55 and J” and Ef from Refs. 55 and 2 1. The BR to the lowest three states which are bound to particle emission were not measured in the proton decay experiment of Ref. 55.

Q from Ref. 16; T1,2 from Ref. 45; J”, Ef, and BR from Ref. 35

Q from Ref. 16; J”, Ef, and BR from Ref. 35. The beta decay competes with gamma decay to the 34Cl ground state.

Relative BR from Ref. 2 1 (a 10% error was assumed). The absolute BR were obtained by assuming that the BR to the ground state was less than 1%. J” = 3’ is assumed for the 2939-keV level.

J”, Ef, and BR from Ref. 35 T,,*, J”, Ef, and BR from Ref. 56. The BR to the ground

state which is bound to particle emission was not measured in the proton-decay experiment of Ref. 56.

J”, Ef, and BR from Refs. 57 and 2 1. An error of 10% was assumed for each BR. Additional experimental information not included here has been obtained from beta- delayed particle emission (Ref. 58).

J”, Ef, and BR from Refs. 59 and 2 1. The BR to the ground state, which is bound to particle emission, was not measured in the proton-decay experiment of Ref. 59.

Q from Ref. 16 and TI12 from Ref. 45 Q from Ref. 16 T,,2, J”, Ef, and BR from Ref. 35 f’ to 4’ BR from Ref. 27

365 Atomic Data and Nudear Data Tat&% Vol. 33. NO. 3. November 1985

B.A.BROWNandB.H.WILDENTHAL Gamow-Teller @ Decay in &Shell Nuclei

TABLE I. Experimental Half-Lives and Q Values See page 362 for Explanation of Tables

Ai Zi Af Zf

l7F - 170

l*F - 180

18Ne - 1aF

190 - 19F

19Ne - 19F

200 - *OF

*OF - *'Ne

*ONa - *'Ne

210 - *IF

21F - *lNe

*lNa - *lNe

*lMg - *lNa

**F - **Ne

**Na - **Ne

**Mg - **Na

*3Ne - 23Na

23Mg - 23Na

*4Ne - 24Na

24Na - 24Mg

24Al - 24Mg

24Alin - 24Mg

*5Ne - 25Na

*'Na - *'Mf

25A1 - 25Mf

*$Ja - 26Mf

26Al~ - *hf

26Si - 26A1

27Na - 27Mg

27M~ - 27A1

27Si - 27Al

*SNa - *SMcj

2aMg - *'Al

*aAl - *aSi

28P - *aSi

2Ji 2Ti

5

2

0

5

1

0

4

4

5

5

3

5

8

6

0

5

3

0

8

a

2

1

5

5

6

0

0

5

1

5

2

0

6

6

1

0

2

3

1

4

2

2

5

3

1

3

4

0

2

3

1

4

2

2

2

5

3

1

4

2

2

5

3

1

6

4

2

2

0.64310E+02 ( 0.14)

0.658623+04 ( 0.05)

0.167203+01 ( 0.30)

0.269103+02 ( 0.30)

0.172203+02 ( 0.12)

O.l3510E+02 ( 0.37)

O.llOOOE+02 ( 0.18)

0.446003+00 ( 0.67)

0.34200E+Ol ( 2.92)

0.415803+01 ( 0.48)

0.224803+02 ( 0.13)

O.l2250E+00 ( 2.29)

0,42300E+Ol ( 0.95)

0.82110E+08 ( 0.07)

0,38570E+Ol ( 0.23)

0.37240E+02 ( 0.32)

0.113173+02 ( 0.10)

0.20280E+03 ( 0.59)

0,54070E+05 ( 0.06)

0,20660E+Ol ( 0.48)

O.l3000E+00 ( 3.85)

0.60200E+OO ( 1.33)

0.596003+02 ( 1.17)

0.718303+01 ( 0.17)

O.l0720E+Ol ( 0.84)

0.634623+01 ( 0.04)

0.22340E+Ol ( 0.40)

0.30200E+OO ( 2.32)

0.567503+03 ( 0.12)

0,41600E+Ol ( 0.48)

0.30500E-01 ( 1.31)

0.752403+05 ( 0.15)

O.l3443E+03 ( 0.02)

0.27030E+OO ( 0.18)

Tl/z(sec) AT1/2(%) Q+Ei(keV) AQ(keV)

2761.6 +/- 0.8

1655.5 +/- 0.6

4447.0 +/- 5.0

4818.8 +/- 2.7

3236.3 +/- 0.6

3816.0 +/- 8.0

7026.0 +/- 0.7

13887.0 +/- 7.0

8170.0 +/- 70.0

5686.0 +/- 7.0

3547.3 +/- 1.2

13098.0 +/- 16.0

10853.0 +/- 30.0

2842.1 +/- 0.5

4789.9 +/- 2.0

4374.5 +/- 2.2

4058.9 c/- 1.4

2468.0 +/- 10.0

5513.0 +/- 0.7

13878.3 +I- 3.9

14304.3 +/- 3.9

7200.0 +/-100.0

3833.0 +/- 7.0

4278.0 +/- 1.2

9325.0 +/- 23.0

4232.8 +/- 0.4

5064.4 +/- 3.1

8960.0 +/- 80.0

2609.3 +/- 1.2

4809.0 +/- 1.3

13890.0 +/-120.0

1831.8 +/- 2.0

4643.1 +/- 0.6

14331.7 +/- 3.7

366 Atomic Data and Nuclear Data T&b& Vol. 33. No. 3. N-b 1935

B.A.BROWNandB.H.WILDENTHAL Gamow-Teller 0 Decay in s&hell Nuclei

TABLE I. Experimental Half-Lives and Q Values See page 362 for Explanation of Tables

Ai Zi Af zf 2Ji 2Ti T1/2(sec) ATl/2(%) Q+Ei(keV) AQ(keV)

*‘Hg - *‘Al 3 5

*'Al - 2gsi 5 3

29P - 2gSi 1 1

29s - *9p 5 3

3oM~ - 3oAl 0 6

30Al _ 3Osi 6 4

30P - 3Osi 2 0

30s - 3op 0 2

31A1 - 31si 5 5

31Si - 31p 3 3

31s - 31p 1 1

32Si _ 3*p 0 4

32P - 3*s 2 2

3*c1 _ 3+ 2 2

33P - 33s 1 3

33Cl - 33s 3 1

33Ar - 33Cl 1 3

34P - 34s 2 4

34Cl - 34s 0 2

34Clrn - 34s 6 0

j4Ar - 34Cl 0 2

35P - 35s 1 5

3515 - 3%1 3 3

35Ar - 35Cl 3 1

35K - 35Ar 3 3

36K - 36Ar 4 2

3'Ar - 3'Cl 3 1

3'K - 37Ar 3 1

3'Ca - 37K 3 3

3*1( - 38Ar 6 0

38Knl - 38Ar 0 2

38Ct3 - 38~ 0 2

3gCi3 - 39K 3 1

0,12500E+Ol (10.40)

0.393603+03 ( 0.91)

0.41170E+Ol ( 0.92)

0,18800E+00 ( 2.29)

0.325003+00 ( 9.23)

0.36000E+Ol ( 1.6')

O.l4988E+03 ( 0.16)

O.l1790E+Ol ( 0.42)

0.64400E+OO ( 3.88)

0.943803+04 ( 0.19)

0.25620E+Ol ( 0.47)

0.33000E+lO (12.12)

O.l2320E+07 ( 0.24)

0.298003+00 ( 0.6')

0.218903+07 ( 0.46)

0.25110E+Ol ( 0.12)

O.l7300E+OO ( 1.16)

0.124303+02 ( 0.64)

O.l5277E+Ol ( 0.14)

0.192003+04 ( 0.13)

0.844503+00 ( 0.40)

0.473003+02 ( 1.48)

0.756103+07 ( 0.13)

0.177503+01 ( 0.23)

O.l9000E+OO (15.79)

0.342003+00 ( 0.58)

0.302703+07 ( 0.13)

O.l2260E+Ol ( 0.57)

O.l7500E+OO ( 1.71)

0.45820E+03 ( 0.24)

0.92420E+OO ( 0.03)

0.435003+00 ( 2.07)

0.859603+00 ( 0.16)

7470.0 +/- 50.0

3681.0 +/- 5.0

4944.4 +/- 1.8

13790.0 +/- 50.0

6530.0 +/-100.0

8539.0 +/- 40.0

4227.2 +/- 2.6

6142.0 +/- 4.0

7850.0 +/-100.0

1490.8 +/- 0.8

5395.3 +/- 1.6

213.0 +/- 7.0

1710.4 +/- 0.6

12687.0 +/- 8.0

249.0 +/- 2.0

5582.9 +/- 0.9

11618.0 +/- 30.0

5380.0 +/- 40.0

5491.9 +/- 0.3

5638.3 +/- 0.3

6059.0 +/- 3.1

3910.0 +/- 70.0

167.5 +/- 0.2

5964.9 +/- 1.6

11880.0 +/- 20.0

12805.0 +/- 8.0

813.8 +/- 0.6

6148.5 +/- 1.5

11636.0 +/- 39.0

5912.5 +/- 0.8

6042.9 +/- 0.8

6742.0 +/- 9.0

6524.0 +/- 5.0

367 Atomic Oata and Nudear Data Tablua. Vol. 33, No. 3, Novambw 1935

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller j3 Decay in sd-Shell Nuclei

TABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ft Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

Al 6 At 21 2J,2T, 2Jf 2Tf n,

“F

‘8,

“Ne

'90

‘9Nt3

200

2OF

ZONa

“0 (51)(51 1) (3’ 1) --- Emax =

‘80 ( 2 0) ( 0 2 1) --- Emax =

‘8F (02)(20 1) (02 1) (20 (20 2; --- Emax =

‘9F (53)(51 1) (31 1) (3 1 (71 1;

(31 2) --- Emax =

‘9F (11) (11 1) (31 1)

--- Emax =

20F (04)(22 1) (22 2) (22 3) (22 4) --- Emax =

2oNe(42) (40 1) --- Emax =

20Ne(42) (40 1) (40 2) (40 (40

Edexp) Ah Wh) W4 WV) WV)

BR(exp) ABR/BR (exp) BR(th)

(3 W) (“4

100.000 (< 1) 100.000

---------- Sum = ‘00*000

100.000 (< 1) ---------- Sum =

100.000 100.000

O( 0) 0 5595

2761 ____________

O( 0) 0 ,655 ------------

O( 0) 0 1041 ( 1) 1194 1700 ( 2)

4108 4447 -----------_

92.110 (< 1) 7.660 ( 2) 0.210 ( 14)

---------_ Sum =

92.610 7.370

O.O90E-4 99.980

197 (< 1) 99 1554 (< 1) 1698 3908 (< 1) 4378 ( 1) 4871

6627 4818 ------------

45.400 ( 3) 54.400 ( 2) 8l.OOOE-4( 6)

0.098 ( 3)

37.254 62.514

0.138

---------- Sum = 99.907

O( 0) 0 99.986 (< 1) 99.988 1554 (< 1) 1698 21.000E-4( 14) 0.202E-4

3238 -̂-------_-- ---------- Sum = 99.988

1057 (< 1) 1048 3348 4882 5211

3816 ------------

100.000 (< 1) 99.799 0.201

---------- Sum = 100.000

1634 (< 1) 1776 99.980 (< 1) 99.980 7026 ------w--m-- ---------- Sum = 99.980

81.550 13.961

0.123 3.007 0.962

0.180

0.047 0.165

16.265E-4

19.438E-4 0.279E-4 2.278E-4 O.O53E-4 O.O60E-4 O.O38E-4 O.O03E-4 O.OllE-4 O.O09E-4 O.O04E-4 O.OOlE-4

99.998

0.150 32.518

6.035 26.553

0.543

I :; ( 8) (>99)

I 5:; ( 7)

( 10)

I 3:; ( 12) ( 11)

1634 (< 1) 7421 ( 1) 7829 ( 2) 8820 ( 100) 9508 ( 12) 9873 ( 4)

10272 ( 2)

1776 7316

10230 10148 10437

79.180 16.370

0.674 0.034 0.247 0.027 2.940

10584 ( 7) 0.087 10737

10840 ( 5) 10884 ( 3) 11261 ( 5)

11322 ( 17) 11436 (< 1) 11852 ( 8)

10746 11196

0.193 0.039 0.203 0.036

11437

12234 12243 12346

16.000E-4( 25)

is0 (60 1; (42 1) (40 3) (40 (40 4; (40 (62 1; (22 1) (40

(60 2; (40 1

::i :;

(62 2) (40 5) (62 3)

12955 13044

(60 3) (40 6)

13060 13307 13496 13509 13510 13561

,------

122 2) i60 4j (42 3) (40 7) --- Emax =

2’F (55)(53 1) (33 1) (33 2) (53 2) (73 1) ( 1

13887 ------ ---------- Sum =

2'0 O( 0) 0 1730 ( 2) 1853 3460 ( 2) 3512 3518 ( 2) 3681

10.000 (>99)

37.000 12.300 I ii; 29.500 ( 3)

2.000 (>99) 10.500 ( 9)

3639 i 2j 3611 4572 ( 2)

368 Atomic Data and Nuclear Data TabW. Vol. 33, NO. 3, November 1965

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller fl Decay in &Shell Nuclei


Wf A) W/A) WC) WI (“4

1.555 0.02 0.15 0.00

-0.239 0.01 3.36 3.579 (0.002) 3.569 2.209 (0.0041 2.235 2.814 ------------------- ------__------_------ ----------------- w = 3.064

2.839 0.04 0.03 3.098 (0.003) 3.092 2.139 0.04 0.08 3.478 (0.013) 3.491 1.531 0.03 0.22 4.432 (0.062)

-2 -949 0.00 100.00 4.314 -_-------_-------_- ---------------------

3.613 -0.12 2.933 -0.08 0.614 -0.03

-0.576 -0.02

2.000 0.03 0.10 -0.172 0.02 4.14

2.611 -0.07 -0.481 -0.02

-----------------_-

3.932 -0.15 ----__-----_----___

5.238 0.03 0.00 3.751 0.06 0.01 3.595 0.06 0.01 3.158 0.06 0.02 2.791 0.05 0.04 2.567 0.05 0.06 2.291 0.04 0.09 2.165 0.04 0.11 2.046 0.04 0.13 1.914 0.04 0.16 1.821 0.04 0.19 1.779 0.04 0.20 1 .386 0.03 0.38 1.315 0.03 0.42 1.174 0.03 0.53

0.554 0.02 1.53 -0.259 0.02 6.57 -0.283 0.02 6.86 -0.573 0.02 11.77 -1.939 0.00 100.00 -2.027 0.00 100.00 -2.043 0.00 100.00 -2.352 0.00 100.00 ,-2.695 0.00 100.00 -2.724 0.00 100.00 -2.727 0.00 100.00 -2.853 0.00 100.00 ------------------- ------_-_----__------ -________--_-____ w = 6.852

4.762 -0.25 s6.296 8.171 <o. 137 0.016 0.001 4.278 -0.18 5.243 (0.028) 5.351 0.460 (0.015) 0.406 0.409 3.651 -0.12 5.095 (0.048) 5.456 0.545 (0.030) 0.360 0.408 3.626 -0.12 4.691 (0.036) 4.788 0.869 (0.036) 0.777 0.953 3.574 -0.12 >5.807 6.425 CO.240 0.118 0.139 3.122 -0.09 4.634 (0.058) 0.927 (0.061)

log(W) AQ(fd) @l(M) ew exp th

3.364 (0.001) 3.403 3.605

---------------------

WW AM(GT) M(GV WGV ew ew th(eff) th(free)

3.168 (0.007) 2.942 3.626 3.030 3.876

__-------_------_ w = 5.308

2.219 (0.008) 2.235

0.478 (0.034) 0.547

_____--____----__ w =

2.814

0.664 3.064

5.386 (0.014) 5.547 0.390 (0.006) 0.324 4.627 (0.010) 4.641 0.934 (0.011) 0.919 6.135 (0.027) 0.165 (0.005) 3.861 (0.017) 3.788 2.257 (0.044) 2.455

5.136 0.521 --------------------- ___------_------- w =

0.368 1.119

3.083 0.654 9.193

3.236 (0.001) 3.214 2.273 (0.003) 2.355 2.964 5.741 (0.062) 7.736 0.150 (0.011) 0.015 0.061 --------------------- ----------------- w = 3.064

3.741 (0.006) 3.983 1.058 (0.007) 0.801 0.976 3.586 1.265 1 .609 4.193 0.629 0.800 3.893 0.889 1.160

-------------__--_-_- --------__------_ w = 4.334

4.973 (0.001) 4.960 0.573 (0.001) 0.569 0.689 --------------------- ----------------- w = 6.852

4.989 (0.009) 4.187 (0.034) 5.415 (0.036)

>6.276 5.047 (0.036) 5.781 (0.220) 3.472 (0.033)

4.756 (0.046)

4.184 (0.037) 4.835 (0.154) 3.728 (0.057) 4.408 (0.053)

4.999 (0.110)

4.980 4.260

0.569 0.689 1.303 1 .654

5.132 3.466 3.635

0.563 (0.006) 1.417 (0.056) 0.344 (0.014)

co.128 0.526 (0.022) 0.226 (0.057) 0.665 (0.597)

0.736 (0.039)

1.420 (0.061) 0.671 (0.119) 2.403 (0.156) 1 .099 (0.067)

0.556 (0.071)

0.477 0.626 0.756 0.968 2.123 2.716

4.312 1 .227 1 .563

4.763 3.822

0.730 0.914 2.156 2.717

5.616 0.273 0.318

4.106 1.554 1.978 5.926 0.191 0.226 4.723 0.764 0.925 4.986 0.565 0.712 4.650 0.660 0.030 5.031 0.636 0.651 5.772 0.228 0.207 4.903 0.621 0.010 4.955 0.585 0.748 5.346 0.372 0.480 6.044 0.167 0.231

369

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller j3 Decay in s&Shell Nuclei


A( ZI At Zt 2J, 2T, 2J, 2T, n,

:33 3; (53 3j

(73 2) (33 4) (53 4) (73 3) (33 5) (73 4) (73 5) (53 5) (53 6)

:z ;; (53 8) (73 6) (53 9) ( 5 3 10) (73 7) (33 7) (73 6) (33 6) (73 9) --- Emax =

2'F 21Ne ( 5 3) ( 3 1 1)

(51 '1 (71 '1 (51 2) (5' 3) (31 2) (71 2) --- Emax =

21Na 21Ne ( 3 1) ( 3 1 1)

--- Emax =

2’Yg 21Na (53)(31 1) (51 1)

1;; ') (51 z;

i3' 2, 1

I

: I

( ( i

I ; i i ( 1 ( 1 (53 li (71 2) (31 3) (71 3) (31 4) (71 4) (51 4) (71 5) (31 5) (51 5) (51 6) (31 6)

Edexp) AEI

WV) WV)

4565 ( 2)

6170 -------

O( 0) 351 (< 1)

1746 (< 1) 3736 (< 1) 4525 (< 1) 4665 (< 1)

5666 -------

O( 0) 351 i< 1)

2796 (< 1) 3547 ------_

O( 0) 332 (< 1)

1723 (< 1) 3545 i 2) 4294 ( 3) 4468 ( 5) 5022 ( '5) 5306 ( 10) 5758 ( 35)

0 247

1795 3731 4575 4789

6094 ( 35) 6210 ( 50) 6341 ( 20) 6500 ( 20) 8301 ( 15) 6417 ( 15) 6616 ( 10) 8970 ( 4) 8690

5377 5761 6267 6439

Wh) WV)

4097 4269 4427 4660 5122 5263 4692 5602 5720 5956 6264 6534 6562 6790 6956 7313 7435 7459 7660 7945 8162 6245

.----_

0 247

1795 3731 4575 4709 5377

._----

0 247

2670 .-----

6974 7275 7379 7560 7667 6092 6306

BWexP) (%I

5.300

ABR/BR (exp) BR(th)

rw (W

( '8) 13.119

1.965 1.764 0.512 0.051 3.335 1.406 3.025 2.014 0.130 1.262 6.762E-4 4.497E-4 0.094 0.099

12.329E-4 31.949E-4

1.338E-4 2.906E-4 0.26OC-4

---------- Sum = 94.600

9.600 ( 31) 16.066 74.100 ( 4) 67.013 16.100 ( 6) 16.540

"ylIl;E-4i 12i 536.332E-4

( 6) 0.131 0.077 ( 6) 0.096

0.926E-4 ---------- Sum = 99.923

94.900 (< 1) 94.620 5.020 i 2j 5.160 3.960E-4( 18) 3.200E-4

---------- Sum s 100.000

0.450 5.360

10.450 2.530 2.430 0.340 0.626 0.470 0.140 0.140 0.060 1.070

0.310 0.160 1.190 2.790

7.956 36.764 20.612

( 15) 0.584 : s; 9.251 7.626

: "8;

( 12, ( 7) ( 14) ( 8)

I x; ( '1) ( '0) ( 5) 3.167

0.391 2.306 0.627 1.260

0.077 0.430 0.034 1.234 1.320

0.276 0.320

370

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller fl De-cay in s&Shell Nuclei

TABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ji Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

NJ’) AM(GT) MW) em ew th(eff)

0.664 (0.070) 0.739 0.315 0.330 0.204

MGT) th(free)

los(fA) JWIA) WC) (W PM

-0.09 -0.10 -0.10 -0.10 -0.09 -0.08 -0.07

QuAt) A~w(fd) @#At) w ew th

4.924 (0.091) 4.831 5.571 5.532 5.949 6.678 4.759 5.378 4.579 4.667 5.668 4.384 7.396 7.542 4.948 4.698 6.005 5.334 6.657 5.778 5.523 4.733 5.251

3.115 3.364 0.896

0.352 0.407 0.233 0.111 0.962 0.481 1 .233 1.087

a.354 1.565

0.023 0.011 0.802 1.128 0.242 0.503 0.132

3.279 3.199 3.073 2,801 2.697 2.941 2.475

0.088 0.803

-0.08 -0.06 -0.06 -0.06

0.394 0.988 0.892 0.282 1 .236 0.039 0.033 0.646 0.861 0.191 0.414 0.090 0.249 0.333

2.386 2.196 1.900 1 .641 1.610 1.336 1.110

0.511 0.253 0.198

-0.344 -1 .615

-0.05 -0.04 -0.04 -0.04 -0.03 -0.03 -0.02 -0.02 -0.02 -0.01

0.344 0.455

0.828 0.456

1.004 0.588

11.868

0.280 (0.044) 0.298 0.369 4.038 -0.17 5.675 (0.136) 5.620 3.911 -0.15 4.660 CO.0181 4.873 3.311 -0.11 4.723 (0.027) 4.880 1.974 -0.05 7.102 (0.056) 6.031 1 .046 -0.03 5.032 CO.0321 4.716

0.790 -0.03 4.523 (0.031) 4.597 -1.111 -0.02 5.711

------------------- ~----__~~--__-_~~-___

0.900 iO.OlQi 0.704 0.862 0.837 (0.026) 0.698 0.835 0.054 (0.004) 0.186 0.256 0.587 (0.022) 0.844 1 .064 1.054 (0.037) 0.967 1 .236

0.268 0.322 ----------------- w = 9.193

1.419 (0.007) 1 .425 1.817 0.782 (0.010) 0.796 1.023 0.765 (0.072) 0.687 0.884 __--_-----------_ w = 4.334

2.240 0.04 0.10 3.614 (0.001) 3.613 1.955 0.04 0.15 4.606 (0.011) 4.591

-2.127 0.00 100.00 4.625 (0.082) 4.718 ------------------- -_--~~~-~---~_~~~--_-

5.381 0.04 0.00 5.323 0.04 0.00 5.060 0.06 0.00 4.660 0.07 0.00 4.470 0.07 0.00 4.424 0.07 0.00 4.269 0.08 0.01 4.161 0.08 0.01 4.044 0.07 0.01 4.009 0.07 0.01 3.972 0.07 0.01 3.934 0.07 0.01 3.094 0.07 0.01 3.848 0.07 0.01 3.791 0.07 0.01 3.013 0.06 0.04 2.951 0.06 0.04 2.725 0.06 0.06 2.631 0.06 0.07 4.164 0.08 0.01 4.037 0.07 0.01 3.867 0.07 0.01 3.813 0.07 0.01 3.612 0.07 0.02 3.490 0.07 0.02 3.447 0.07 0.02 3.368 0.07 0.02 3.320 0.07 0.02 3.119 0.06 0.03 3.009 0.06 0.04

5.619 4.873 4.881 6.032 4.716 4.597

3.269 5.711 4.813 5.089 4.852 5.867 4.996 6.050 4.416 4.339 4.814 4.643

0.298 0.704 0.698 0.186 0.844 0.967

0.369 0.862 0.835 0.256 1 .064 1 .236

6.094 (0.068) 4.829 (0.027) 4.493 co.0221 4.954 (0.045) 4.863 (0.039) 5.601 (O-041)

0.173 (0.014) 0.740 (0.023) 1.091 (0.028) 0.641 (0.033) 0.712 (0.032) 0.305 to.015,

5.305 (0.03lj 5.388 (0.057) 5.876 (0.035) 5.836 (0.065) 5.002 CO.0381 4.850 iO.028j 4.609 (0.045) 4.784 (0.051) 3.737 (0.050) 3.273 (0.029)

0.428 (0.015) 0.389 (0.025) 0.222 (0.009) 0.232 (0.017) 0.607 (0.026j 0.723 (0.023) 0.954 (0.049) 0.780 (0.046) 2.603 (0.149) 1.335 (0.490) 1.403 1.772

0.260 0.322 0.755 0.974 0.549 0.683 0.722 0.921 0.224 0.326 0.612 0.794 0.182 0.230 1.193 1.494 1.302 1.687 0.754 1.008 0.918 1.172

371 Atcmlc Data and NucIear Data Tables, Vd. 33. ND. 3. N- 1995

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller @ Decay in &Shell Nuclei


AI ZI 2J, 2T, 2J, 2T, nl E,(exp) AEI E&W

(kev) (kev) NW

8592 8600 8697

13098 ------------

3357 (< I) 3378 5523 (< 1) 5480

BR(exp) ABR/BR (eXp) BR(th)

WI (3 (“a

1.426 1 .OOl 0.740

---------- Sum = 100.030

23Ne

(31 7) --- Emax =

22Ne ( 8 4) ( 8 2 1)

(62 2) (82 4) (62 3) (10 2 1) (62 4) (10 2 2) --- Emax =

3.400 0.001 59.300 53.914 18.000 ( 4) 20.947

7.700 ( 18) 6.653

5641 is lj 5635 6345 (< 1) 6430

6519 6992

7341 (< I) 7741 7424 (< 1) 7461

8435 8696

10853 _--------we-

1275 (< 1) 1368 2842 _-----------

583 (< 1) 391 657 (< 1) 664

1937 (< 1) 2024 3985 5673

4789 _-__--------

O( 0) 0 440 (< 1) 411

2076 (< 1) 2131 2982 (< 1) 2747

3893 4636

4374 __--a-------

1.300 ( 15) 9.600 ( 4)

2.256 6.554

22Na(60) (42 1) --- Emax =

22Na(02) (20 1)

(02 1) (20 2) (20 3) (20 4) --- Emas. =

23Na(53) (31 1)

(51 1) (71 1) (31 2) (51 21 (71 2) --- Emax =

0.609 7.599

94.267E-4 0.757

99.300

99.940 99.940

48.299 47.993

3.657 3.01 lE-4

99.950

60.494 39.230

0.255 0.153 3.265E-4

91.444 8.550

114.268E-4 11.943E-4

100.007

90.265 9.735

100.000

99.895

---------- Sum =

99.940 (< 1) ---------- Sum =

40.200 ( 2) 54.000

5.750

---------- Sum =

67.000 ( 1) 32.000 ( 3)

1.070 ( 3) 0.063 ( 4)

+&I 23Na ( 3 1) ( 3 1 1) O( 0) 0 (51 1) 440 (< 1) 411 (11 1) 2391 (< I) 2323 (31 2) 2982 (< I) 2747 --- Emax = 4058 ___---------

24Ne 24Na(04) (22 1) 472 (C I) 448 (22 2) 1347 (< 1) 1092 --- Emax = 2468 ___---------

24Na 24Mg(82) (80 1) 4123 (< 1) 4379

tl (60 11 5236 (< 1) 5097 --- Emax = 5513 -w--e--- ----

91.800 (< 1) 8.200 ( 3)

69.000E-4( 13) 5.000E-4(>99)

-- ---_-- -- Sum =

92.000 (< 1) 8.000 ( 3)

---------- Sum =

99.950 (< 1) 0.053 ( 7)

-________- Sum =

7.200 ( 8) 1.300 ( 7) 1.200 ( 8) 0.050 ( 40)

50.000 ( 2)

0.108 100.003

244 1 z4tb4g (82)(80 1) (60 1) (80 2)

4123 (< 1) 5235 (4 1) 6010 (< 1) 7812 (< 1)

4379 11.686 2.795 2.617 0.208

47.044 2.142 0.035

34.210

5097 5935

ilo 0 lj (80 3)

7884 8374 9640 9596

8437 i< lj 9300 (< 1) 2.400 i 4j

0.033 ( 51) (80 4) (60 2) (82 1)

9456 ix 1) 9515 (< 1)

10576 (’ 1) 10824 (< 1)

9543 10565

38.600 0.670 0.120 ( 8)

0.723 0.102

(60 3)

K : 5, 1) 11017 (< 1)

11318 (< 1) 11694 (< 1)

10917 10804 11039 11092 11294 11224 11376 11580 11723 11746 12103

28.889E-4 0.028 0.035 5.597E-4 0.038 0.013 0.874E-4 5.663E-4

19.927E-4 2.16lE-4

0.050 ( 30)

0.035 0.026 (80 61

(60 5) i62 3j

(80 7) (82 2)

372 Atomk Oaa and Nudaar Data TatMa. Vd. 33. No. 3. November 1986

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller j3 Decay in d-Shell Nuclei


Wfd W/A) VW Wfd) AWfA Qm MGT) AM(GT) WV

(W w exp w th ew w th(eff )

2.855 0.06 0.05 3.840 2.314 2.850 0.06 0.05 3.989 1.950 2.795 0.06 0.05 4.065 1.707 _-_~__-___-_---__-- -~I--_~__-_--~~---__- ----------------- w =

4.597 -0.24 6.692 (0.217) 10.122 3.909 -0.16 4.762 (0.017) 4.838 3.864 -0.15 5.235 (0.023) 5.204

3.576 -0.13 5.316 (0.080) 5.414 3.498 -0.12 5.606 3.271 -0.11 5.115 3.086 -0.10 5.599 (0.069) 5.962 3.040 -0.10 4.684 (0.025) 4.820 2.374 -0.07 7.060 2.161 -0.06 4.942 ------------------- _~~---_--~-_~~--~-__-

0.106 (0.027) 0.002 0.012 0.980 (0.019) 0.898 1.109 0.569 (0.015) 0.589 0.726 0.518 (0.048) 0.463 0.532

0.295 0.334 0.652 0.827

0.374 (0.030) 0.246 0.301 1.072 (0.031) 0.916 1.107

0.069 0.079 0.796 0.945

-------__--_---__ w = 13.001

-0.495 0.02 10.17 -------------------

7.420 (0.002) 8.289 0.041 (0.000) 0.015 --------------------- ----------^-----_ w =

2.679 0.06 0.06 2.634 0.06 0.07 1.623 0.04 0.34

3.661 (0.012) 3.534 3.488 (0.009) 3.491 3.449 (0.015) 3.598

4.109 6.036

---------------------

1.160 (0.016) 1.344

1.461 (0.026) 1.248 0.693 0.075

-------_--------- w =

-1.951 0.00 100.00 0.00

3.528 -0.14 3.320 -0.12 2.29.1 -0.07 1.379 -0.04

-0.399 -0.02

-------------------

5.273 (0.007) 5.469 0.444 (0.003) 0.355 5.386 (0.014) 5.449 0.390 (0.006) 0.363 5.833 (0.016) 6.606 0.233 (0.004) 0.096 6.151 (0.021) 5.917 0.162 (0.004) 0.212

6.809 0.076 5.706 0.246

_-_____-__-___-___--_ ----------------- w =

2.587 0.06 0.07 3.678 (0.002) 3.668 2.285 0.05 0.12 4.425 (0.016) 4.395

-0.224 0.02 8.08 4.991 CO.0571 4.760 -1 .697 0.00 99.85 ‘4.658 4.260

~~~-~~~--_---___--_ -------------^-------

2.030 -0.06 4.373 (0.010) 4.496 1 .ooo -0.04 4.404 (0.023) 4.434 -------_---__-_____ ~~~~~~--_~---_--__-_-

1.391 -0.05 6.124 (0.001) 5.890 -1.234 -0.02 6.774 (0.033) 6.232

--------__---___--_ ---------------------

4.700 0.09 0.00 4.419 0.09 0.01 4.200 0.09 0.01 3.581 0.08 0.02 3.317 0.08 0.03 2.887 0.07 0.06 2.799 0.07 0.07 2.764 0.07 0.07 2.028 0.05 0.23 1 .810 0.05 0.32 1 .828 0.05 0.31 1 .600 0.05 0.45 1 .622 0.05 0.44 1.319 0.04 0.72 1 .291 0.04 0.75 0.782 0.03 1 .76 0.950 0.04 1.33 0.736 0.03 1.91 0.700 0.03 2.03 0.027 0.03 6.62

6.158 (0.036) 6.621 (0.034) 6.436 (0.036) 7.197 co.1741 3.933 (0.009) 4.822 (0.018) 6.595 (0.224) 3.493 (0.009) 4.517 (0.039) 5.045 (0.036)

5.238 (0.130)

5.062 (0.087) 4.682 (0.100)

5.891 6.232 6.041 6.523 3.903 4.815 6.517 3.489 4.427 5.059 6.626 5.413 5.336 6.830 4.964 4.920 7.267 6.242 5.659 5.951

373 Atomic Data and Nuclear Data Tab&. Vol. 33. No. 3. November 1935

0.406 0.427 0.100 0.274 0.104 0.319 9.193

1.092 (0.011) 1.145 1 .472 0.964 (0.016) 0.997 1 .279 0.502 (0.033) 0.655 0.893

co.737 1.154 1.514 _--__--_-__-____- w = 4.334

0.511 (0.006) 0.444 0.493 (0.013) 0.476 ---------------__ w =

0.204 (0.000) 0.267

0.097 (0.004) 0.180 --------------___ w =

WGT) th(free)

2.971 2.505 2.275 9.193

0.030 6.852

1 .721

1 .633 0.859 0.073 3.064

0.530 0.617 4.334

0.327 0.239 9.193

0.197 (0.008) 0.115 (0.004) 0.143 (0.006) 0.059 (0.012) 2.546 (0.027) 0.915 (0.019) 0.119 (0.031)

>O 1.300.(0.059) 0.707 (0.030)

0.566 (0.085)

0.694 (0.070) 1.075 (0.124)

0.267 0.327 0.180 0.239 0.225 0.277 0.129 0.166 2.637 3.339 0.923 1.185 0.130 0.194 0.255 0.294 1.441 1 .a21

0.697 0.870 0.115 0.189 0.463 0.612 0.506 0.597 0.091 0.098 0.777 1.045 0.017 1.058 0.055 0.082 0.178 0.250 0.349 0.458 0.249 0.297

B. A. BROWN and B. H. WlLDENTHAL Gamow-Teller fi Decay in s&hell Nuclei

rABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ft Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

4 & At z, 2J, 2T, ~JI ~TI n, E,(exp) AEf Wh) WV) WV) NW

ix: :; 12128 12192 (10 0 3) 12296 (82 3) 12426 --- Emax = 13878 ------------

24Alm 24#g (22)(00 1) If00 :; (20 2) (22 1) (42 1) (00 4) (40 (40 ( i (40 (40 ; (40 (00 2; (40 3) (20 1) :“o: 2 is0 5j

(22 2j (40 6)

(42 2)

0 1369 4238 9828 9965

10059 10682 10922 11017 11457 11521 12405 12470

0) L 1) (< 1) : 2)

2) 2)

I: 1) 1)

(< 1) (< 1) (< 1) (< 1) (< 1)

0 1510 4123 9987 999 1

10131 10679

7562

10635

7443 7764

10676

894 1 9561 9877

10479

(42 3) 11146 (40 7) 11110 (40 8) 11820 (40 9) 11956 ( 4 0 10) 12289 i42 4j 12369 (22 3) 12753 (02 1) 12872 (22 4) 13142 --- Emax = 14304 _-_--_--_---

25Nt? 25Na(15)(33 1) 90 (< 1) 132 (13 1) 1069 (< 1) 1159 (33 2) 2202 ( 1) 2130 i33 3j 3687 ( 2) 3304 (33 4) 3623 (13 2) 4289 ( 3) 4048 (13 3) 5134 ( 13 4) 5725 --- Emax = 7200 _-____------

25Na 25Mg(53) (51 1) O( 0) 0 (31 1) 975 (< 1) 1200 171 1) 1612 (< 1) 1730 i51 2j 1965 i< ii 2094 (71 2) 2738 (’ 1) 2980 (31 2) 2801 (< 1) 2908 --- Emax = 3833 _-----------

25A 1 25#g ( 5 1) ( 5 1 1) O( 0) 0 (31 1) 975 (< 1) 1200 iSt ij 1612 i< 1) 1730 (51 2) 1965 (’ 1) 2094 (71 2) 2738 (< 1) 2980 (31 2) 2801 (< 1) 2908 --- Emax = 4278 _--_--------

26Na 26Mg(64) (42 1) 1809 (< 1) 1928 (42 2) 2938 (< 1) 3153 (62 1) 3940 (< 1) 392 1 (82 1) 4318 (< 1) 4532


(W v4

10.100 ( 27) 4.400 ( 11) 0.400 ( 25)

0.250 2.130 I “t; 0.190 ( 36) O.OQOE-4i 33j O.OOQE-4( 44) 1.600E-4( 31) O.Q20E-4( 32) O.l70E-4( 35) O.O08E-4( 37) O.O04E-4( 50)

---------- Sum =

76.800 19.200 : 1:;

2.300 ( 21) 1.180 ( 25)

0.520 ( 28)

62.500 ( 3) 27.400 ( 1)

9.450 ( 2.1 0.440 ( 1) 3.000E-4(>99) 0.246 ( 2)

(W

Q.O84E-4 8.379E-4 0.288E-4 O . OOOE-4

101.684

11.295 3.497 0.227 0.008 1.980 0.294 1.633E-4

59.180E-4 0.043 0.014 0.025 6.538E-4 O.O96E-4

22.682E-4 O.O34E-4 0.053 O.O2lE-4 0.023 6.44lE-4 1.496E-4 0.481E-4 4.734E-4 O.lllE-4 O.O4lE-4 O.OOlE-4

17.470

71.106 23.461

3.603 0.630 0.189 0.876 0.100 0.035

100.000

63.337 27.736

8.337 0.261

196.150E-4 0.345

---------- Sum = 100.036

99.160 :‘1:; 99.198 0.047 0.067 0.794 ( 4) 0.735

22.000E-4(>99) 3.328E-4 46.000E-4(>99) 0.028E:4 ll.OOOE-4(>99) 3.72SE-4

---------- Sum = ,oo.oo,

88.100 (< 1) 85.746 0.200 0.237 t .600

:‘z; 1.404

0.540 ( 25) 0.218

374 Atomic Dala md Nudew DatX Tabh. Vol. 33, NO. 3. Novcmba 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller /3 Decay in .&Shell Nuclei

ITABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ft Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

bm WV/A) pew w (“4

-0.029 0.02 7.33 -0.180 0.02 9.63 -0.448 0.02 15.71 -0.819 0.01 31.07

-------------------

5.572 5.344 4.772 2.830 2.750 2.694 2.276 2.093 2.015 1 .608 1.541

0.266 0.154 3.035 3.876 3.762 3.261 2.976 2.802 2.423 2.313 2.283 1.904 1.935 1.196 1.020

0.503 0.356

-0.533 -0.878 -1.503

0.04 0.00 0.06 0.00 0.06 0.00 0.07 0.07 0.07 0.07 0.07 0.08 0.06 0.15 0.05 0.21 0.05 0.23 0.05 0.45 0.04 0.50 0.03 4.17 0.03 5.27 0.09 0.01 0.09 0.01 0.09 0.02 0.08 0.03 0.07 0.05 0.07 0.07 0.06 0.12 0.06 0.15 0.06 0.15 0.05 0.28 0.05 0.26 0.04 0.88 0.04 1.18 0.03 2.85 0.03 3.69 0.02 18.37 0.01 34.63 0.00 96.05 _--__-__-____--_-__

4.500 -0.25 4.201 -0.21 3.792 -0.16 3.099 -0.11 3.134 -0.11 2.737 -0.09 2.093 -0.07 1 .482 -0.05

-----------------_-

4.395 (0.031) 4.522 4.697 (0.056) 4.704 5.210 (0.103) 5.109 4.807 (0.124) 5.173

5.730 4.601 (0.142) 4.668

4.966 4.811

---------------------

3.261 -0.13 2.715 -0.10 2.241 -0.08 1.922 -0.06

0.974 -0.04 0.872 -0.04 -------------------

5.260 (0.015) 5.307 5.052 (0.009) 5.099 5.041 ~0.012) 5.147 6.054 (0.012) 6.332

a8.272 6.509 5.256 (0.015) 5.162 ------------------_-_

2.714 0.07 0.06 3.574 (0.001) 3.575 2.028 0.05 0.23 6.212 (0.056) 6.058 1.414 0.04 0.61 4.370 (0.019) 4.405 0.971 0.04 1.28 a6.485 7.306

-0.564 0.02 19.44 a4.629 7.841 -0.747 0.02 27.20 >5.066 5.539

_---____-___-----_- ------__----__-_-_--_

4.624 -0.29 4.294 -0.24 3.952 -0.19 3.007 -0.18

4.709 (0.007) 4.735 ~7.024 6.964

5.776 (0.055) 5.649 6.105 (0.113) 6.513

lo&t) Alos(fdl Wfd) ew ew th

5.271 5.155 6.351

11.210 ---------------------

5.681 (0.122) 5.915 (0.052) 6.264 (0.110) 4.546 iO.123) 3.536 (0.033) 4.530 (0.161) a.438 (0.146) 9.253 (0.194) 6.925 (0.137) 6.758 (0.143) 7.425 (0.154) 7.497 (0.164) 7.666 (0.216)

5.439 5.721 6.337 5.835 3.374 4.147 6.986

6.903 6.165 6.541 5.796 7.081 8.740 5.988 8.707 4.477 8.509 4.498 5.309 5.765 5.741 4.601 5.341 5.428 6.252

W-V AM(GT) NW WGT)

em ev th(eff) th(free)

0.546 0.721 0.624 0.849 0.157 0.207 0.001 0.007

----------------- w = 9.193

0.196 (0.027) 0.166 (0.010) 0.098 (0.012) 0.726 (0.103)

PO 0.739 (0.137) 0.008 (0.001) 0.003 (0.001) 0.047 (0.007) 0.057 (0.009) 0.026 (0.005) 0.024 (0.005) 0.020 (0.005)

0.259 0.300 0.188 0.205 0.092 0.120 0.165 0.215 1.358 1 .732 1.149 1.444

0.044 0.064

0.044 0.046 0.113 0.145 0.073 0.087 0.172 0.259 0.039 0.065 0.006 0.032 0.130 0.175 0.006 0.003 0.785 1.021 0.008 0.007 0.767 0.955 0.301 0.393 0.178 0.249 0.163 0.246 0.661 0.900 0.291 0.378 0.263 0.336 0.102 0.112

--__---__~-_-___- w = 5.308

0.705 (0.025) 0.609 0.498 (0.032) 0.494 0.276 (0.033) 0.310 0.439 (0.062) 0.288

0.151 0.442 (0.072) 0.515

0.365 0.437

_________̂ _______ w =

0.786 0.621 0.420 0.328 0.210 0.626 0.446 0.523 6.652

0.451 (0.008) 0.426 0.529 0.573 (0.006) 0.543 0,705 0.581 (0.000, 0.514 0.603 0.161 (0.002) 0.131 0.177

<0.014 0.107 0.146 0.453 (0.008) 0.505 0.674 ----------------- w = 9.193

1.971 (0.008) 1.966 2.497 0.151 (0.010~ 0.180 0.241 1.256 (0.028) 1.208 1.516

co.110 0.043 0.048 co.932 0.023 0.030 qO.562 0.327 0.442

_________̂ _______ w = 5.308

0.918 (0.008, 0.892 1.155 ~0.064 0.066 0.065

0.260 (0.017) 0.247 0.296 0.164 (0.024) 0.115 0.135

375 Atomk Dots and Nudwr Data Tables. Vol. 33. No. 3. Ncwm-nber 1955


TABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, 3 Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

AI 4 At Z 2J, 2T, 2J, 2T, nt

(42 3) (62 2) (42 4) (82 2) (42 5) (82 3) (82 4)

1:; x;

;:zz 573 (42 8)

IB”f :;

Edexp) Ah GM) BR(exP) ABWBR (exp) BR(th) WV) WV) WV) (%I (%I (“4

4332 (< 1) 4349 (< 1) 4834 (< 1) 4900 (< 1) 5290 (< 1) 5474 (< 1) 5715 (< 1) 6125 ( 1)

4540 4510 5000 4932 5403 5472 6000 6268 6646 6777 6043 7092 728 1 7410 7473 7602 7940 8004 839 1 0404 8413 8790 8958 9115

-----

1.700 ( 11) 1.973 2.700 ( 11) 5.153 2.700 ( 7) 2.046 0.300 ( 33) 0.089 0.200 (>99) 0.085 0.040 (>99) 0.194 0.700 ( 14) 1.126 1.700 ( 11) 1.430

0.038 0.042

94.573E-4 0.097 0.080

29.852E-4 0.042 0.016

17.343c-4 21.121E-4

3.217E-4 7.341E-4 0.857E-4 1.226E-4 O.l32E-4 O.OBlE-4

---------- Sum = 100.040

100.000 (< 1) 100.000 ---------- S”m = 100~000

i42 Bj (62 5) (82 7) (62 6) ( 4 2 10) (62 7) (82 8) (82 9) ( 8 2 10) (62 8) --- Emax =

26Alm 26Mg ( 0 2) ( 0 2 1) --- Emax =

2651 26A1 ( 0 2) ( 0 2 1) (20 1) (20 21 (20 3) (20 4) (20 5) (20 6) (20 7)

9325

0 ( 0) 81 4232 -___________

(20 8) --- Emax =

228 (< 1) 81 1058 (< 1) 818 1851 (< 1) 1737 2072 (< 1) 2003 2739 cc 1) 2899 3723 (< 1) 3685

4937 5154 5667

5064 __-------_--

27?4a 27M9 ( 5 5) ( 3 3 1) 985 (< 1) 895 (53 1) 1698 (< 1) 1667

75.030 (< 1) 74.302 21.890 ( 1) 22.871

2.726 2.403 0.290 0.307 0.062 ( 4) 0.035

13.000E-4(>99) O.B99E-4 O.O31E-4

---------- Sum = 99.998

( 2) 04.460 ( 15) 8.222 f 20) 1.106

84.000 13.000

1 .ooo 0.650 0.450 0.400 0.600

i53 (73

2) 1)

1940 cc 1) 1978 3109 (< 1) 3149 3420 1) 3490 I= 1)

3300 3162

4490 (< 1) 3632 4032 4201 4616 5101 5206 5226 5404 5454 548 1 5656

i 15j 0.386 ( 22) 1.503 (73

(33

133 (53 (53 (73 (53 (73 (33

2) 2)

1 ( 25) 0.105 ( 33)

0.879 3j 3) 39.138E-4

0.627 0.375 0.644 0.417

56.355E-4 0.096 0.504 0.056 0.077 0.142 0.083

24.480E-4 6.267E-4

52.816E-4 15.695E-4

0.029 0.024

4) 31 6) 4) 4)

i33 (53

5j 7) 5) 6) 6)

ii; 8)

(73 (33 (73 (33 (53 (33

5813 5887 6086 6428 6403 6640 6759 7230

9) 9)

(53 (33 (53 (33

10) 10)

-4- Emax = 8960 ___-----_---

27Yg 27Al(13)(ll 1) 844 (< 1) 912

---------- Sum = 100.100

71 .ooo (< 1) 71 .254

376 Ata,“k Oata Md Nuclew Data Tables. Vol. 33, NO. 3, N- 1335

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller (3 Decay in sd-Shell Nuclei


MOW AM(GT) M@T) MGT) th(eff) th(free)

0.349 0.459 0.568 0.716

0.558 0.079

0.452 0.098 0.118 0.197 0.549 0.009 0.194 0.228 0.115 0.460 0.531 0.112 0.450 0.324 0.167

W(W) Alog WfAt) em ew th

5.601 (0.052) 5.551 5.393 (0.049) 5.127 5.190 (0.034) 5.325 6.115 (0.145) 6.657

>6.110 6.494 B6.716 6.047

5.349 (0.063) 5.157 4.730 (0.053) 4.819

6.058 5.919 6.516 5.309 5.165 6.536 5.329 5.615 6.189 6.020 6.239 5.057 6.773 5.742 6.119 5.491

---------__----__----

WfA) W/A) WC) W) W)

-0.18 -0.10 -0.16 -0.16 -0.14 -0.13 -0.12 -0.11 -0.09 -0.09 -0.09 -0.00 -0.07 -0.07 -0.06 -0.06 -0.05 -0.05 -0.04 -0.04 -0.04 -0.03 -0.02 -0.02

ew em 3.602 3.795 3.591 3.562 3.381 3.290

0.329 (0.020) 0.418 (0.024) 0.528 (0.021) 0.182 (0.030)

CO.183 co.091

0.440 (0.032) 0.897 (0.055)

0.140 0.227 0.694 1.008

0.267 0.293 0.152 0.577 0.607 0.162 0.592 0.380

3.164 2.930 2.592 2.497 2.448 2.250 2.007 1.967 1.906 1.775 1.304 1.301

0.171 0.237 0.245

0.203 0.156 0.702

0.679 0.245 0.065 0.280 0.181 0.374

.-- w =

0.326 0.143 0.662

-0.214 -0.805 -1 .647

0.352 0.214 0.444

11.466

2.687 ------

0.07 0.00 3.489 (0.000) 3.491 ~___~~--__-__---___-- ________---_-__-_ w = 3.064

3.016 2.536 1 .944 1.743 0.900

-1.087 0.01 62.37 -3.340 0.00 100.00

0.00 0.06 0.07 0.13 0.06 0.33 0.05 0.46 0.04 1 .61

3.490 (0.004) 3.491 3.545 (0.009) 3.523 3.057 (0.012) 3.909 4.630 (0.017) 4.602 4.538 (0.018) 4.702

>4.148 5.305 4.507 4.754 4.521

-____--____-----_----

1.326 (0.013) 1 .361 0.926 (0.012) 0.872 0.380 (0.007) 0.393 0.423 (0.009) 0.319

CO.662 0.175 0.438 0.330 0.431

---------_----___ w =

1.729 1.166

0.518 0.440 0.213 0.596 0.443 0.570 3.064

1 .797 0.682 0.296 0.201 0.535 0.136

0.00 0.00

---c----_---_

4.301 (0.025) 4.303 4.920 (0.071) 5.124 5.966 (0.090) 5.926 5.785 (0.073) 6.016 5.833 (0.101) 5.314 5.861 (0.113) 6.440 5.284 (0.149)

4.745 4.554 4.406 4.118 4.006 3.903 3.502 3.931 3.775 3.706

-0.32 -0.28 -0.27

1.361 (0.039 1 .356 0.667 (0.055 0.520 0.200 (0.021) 0.210 0.246 (0.021) 0.189 0.233 (0.027) 0.424 0.226 (0.029) 0.115 0.439 (0.075)

0.353 0.028 0.387 0.368 0.371 0.630 0.539 0.063 0.292 0.691 0.233 0.309 0.466 0.376 0.075 0.050 0.152 0.096

-0.22 -0.20

3.526 3.479

-0.20 -0.16 -0.20 -0.18 -0.17 -0.15 -0.15 -0.14 -0.13 -0.13 -0.12 -0.12

3.294 3.240 3.230 3.135 3.107 3.092 -0.12 2.992 -0.12

5.472 7.660 5.394 5.437 5.430 4.970 5.105 6.964 5.639 4.890 5.633 5.509 5.231 5.419 6.821 7.173 6.206 6.604 5.243 4.003

---------------------

0.463 0.027 0.494 0.472 0.460 0.794 0.683 0.056 0.366 0.874 0.290 0.405

2.899 -0.11 0.616 0.472 2.653 -0.11

2.725 -0.10 0.090 2.465 2.444 2.315 2.224 1 .782

-----

-0.09 -0.09 -0.00 -0.00 -0.06

0.091 0.162 0.096

0.460 0.576 0.696 0.694

11 .866

1 .832 -0.07 4.735 (0.003) 4.670 0.477 (0.002) 0.509 0.639

377 Atomic Data end Nudaar Data Tables, Vol. 33. NO 3. November IS85




W) ("4 ("4

29.000 -------'s"~'

20.746 = 100.000

99.810 (< 1) 99.714 42.000E-4( 47) 772.644E-4

0.148 ( 41 0.161

Ai 4 At Zt 2J, 2T, 2Jf2Tf nl

(31 1) --- Emax =

E,(exp) Ah4 Wh)

WV) WV) WV)

1015 (< 1) 1264 2609 -----------_

27Si 27Al(51) (51 1) O( 0) 0 (31 1)

(51 2) (31 2) (31 3)

(71 1)

(51 3) (51 4)

--- Emax =

28Na 28#9 ( 2 6) ( 0 4 1) (44 1) to4 2)

2734

1015 (< 1)

(< 1) 2708

1264

2981

2211 (< 1)

(< 1)

2326

2780 3957 (< 1) 4027 4410 (< 1) 4139 4812 (< 1) 4939 4809 ------- ,-----

O( 0) 0 1474 (* 1) 1543 3863 (< 1)

lj 3802

4557 i< 4264 4878 (< 1) 4773

5402 6013 6187 4396 5412 6757 6855

0.013 ( 15j 0.016 0.023 ( 13) 0.030

l.l38E-4 0.382E-4

---------- Sum = 99.998

63.000 ( 11) 43.264 11.000 ( 54) 3.474 21.000 ( 14) 29.335

(44 2j (44 3) (44 4) (44 5)

5.000 1.999 1.000 0.086

0.163 2.680 0.213 7.262 5.510 1.793 0.642 0.689 0.252 0.439 1.120 0.214 0.833 0.031

---------- S"m = 100~000

95.000 ( 1) 90.606 5.000 ( 20) 1.394

---------- S"m = ,00~00l-J

(04 3) (24 1) (24 2) (44 6) (04 4) (24 3) (44 7) (24 4) (44 8) (04 5) (24 5) (04 6) --- Emax =

2%lg 28Al ( 0 4) ( 2 2 1) (22 2) (22 3) --- Emax =

28A 1 28Si ( 6 2) ( 4 0 1) --- Emax =

28P 28Si ( 6 2) ( 4 0 1) (80 1) (60 1) (80 2) (40 2) (40 3) (60 2) (40 4) (40 5)

I"" 3, 1

i (62 1; (42 1) ( (40 6;

6063 7330 7381 7420 7067 8229 8900

13890 ------------

1373 (< 1) 1364 1620 (< 1) 1746

2073 ,831 ------------

1779 (< 1) 1988 4643 _-__-___-___

1779 (< 1) 1988 4618 (< 1) 4659

100.000 (< 1) 100.000 ---------- Sum = 100~000

( ( 1:;

( 4) ('99) (>99) ( 30) ( 3) ( 7)

I 3; (>99) ('99) ( 3) ( 4)

I':';; ( 11) (>99) ( 13) (>99) (>99)

I'XZ

I'2 cc991

65.573 1.053

16.156 0.076 0.029 0.407 1.302 0.920 0.635 2.337

10.393 0.536

0.189

0.021

69.200 1.290 7.640 0.045 0.040 0.200 2.450 2.760 0.536 3.640 0.034 0.079

11.270 0.600 0.060 0.064 0.054 0.010 0.030 0.029 0.004 0.026 0.027 0.260 0.016 0.015

6276 i< lj 6167 6888 (< 1) 7037 7381 (< 1) 7523 7416 (< 1) 7906 7799 (< 1) 8140 7934 (< 1) 0457 8259 (< 1) 8668 8589 i< 1) 9812 8945 ( 2) 9164 ( 2) 9316 (< 1) 9588 9381 (< 1) 9446 9418 ( 2) 9479 (< 1) 9793 9796 ( 9497 i

1) 2)

10209 ( 2) 10312 ( 2) 10376 i 2j 10418 ( 2)

( I62 I (60 ) (40

Iti ;

(40 ; (80 3)

10515 ( 2) 10668 ic 1) 10805 ( 2) 11138 ( 2)

9493

378 AtOmk Data and Nudear Data Tables, Vol. 33, NO. 3. November 1935


I’ABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, .fl Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

Wfd

1.649 -------

3.002 2.394 1.327 0.598 0.136

-1.687 -2.348

W/A) cw

-0.06

P(W w

0.08 0.07 0.05 0.04 0.03 0.00 0.00

0.07 0.17 0.90 3.08 6.93

100.00 100.00

0.00

5.889 -0.70 5.657 -0.59 5.214 -0.44 5.067 -0.40 4.995 -0.38 4.872 -0.35 4.720 -0.32 4.674 -0.31 5.102 -0.41 4.070 -0.35 4.518 -0.28 4.490 -0.28 4.488 -0.28 4.348 -0.25 4.333 -0.25 4.321 -0.25 4.176 -0.23 4.052 -0.21 3.800 -0.10 ~~~--_--_--_--_--__

-0.438 -0.03 -1 .612 -0.02

2.744 -0.11 ---__--------------

5.260 0.10 0.00 4.674 0.12 0.01 4.239 0.12 0.01 4.053 0.12 0.02 3.891 0.11 0.02 3.879 0.11 0.02 3.743 0.11 0.03 3.693 0.11 0.03 3.567 0.11 0.04 3.432 0.10 0.04 3.276 0.10 0.05 3.173 0.10 0.06 3.099 0.09 0.07 3.067 0.09 0.07 3.048 0.09 0.08 3.017 0.09 0.00 2.047 0.09 0.10 3.007 0.09 0.08 2.602 0.08 0.15 2.536 0.08 0.17 2.495 0.08 0.10 2.467 0.00 0.19 2.401 0.00 0.21 2.292 0.07 0.24 2.190 0.07 0.28 1.910 0.06 0.44 3.009 0.09 0.08

log(W) AloS(fd) Wf At) exp ew th

4.941 (0.006) 4.809 -_____-____-__--_____

3.622 (0.002) 3.603 7.309 (0.207) 6.105 4.776 (0.021) 4.719 5.090 (0.068) 4.997 4.403 (0.060) 4.265

4.856 4.669 5.903

---------------------

4.574 (0.052) 4.952 0.702 (0.042) 0.455 5.100 (0.238) 5.815 0.384 (0.105) 0.168 4.377 (0.067) 4.446 0.002 (0.060) 0.014 4.852 (0.091) 5.465 0.510 (0.053) 0.252

>5.479 6.760 ~0.240 0.057 6.360 0.090 4.990 0.435 6.044 0.129 4.940 0.461 4.828 0.525 4.963 0.449 5.381 0.277 5.340 0.288 5.645 0.205 5.389 0.275 4.970 0.445 5.545 0.230 4.030 0.523 6.013 0.134

------------_________ __--__--___------ w =

4.461 (0.008) 4.150 0.462 (0.004) 0.655 4.566 (0.088) 4.034 0.410 (0.041) 0.301

4.352 0.524 _____--____~_----_~-- _-_-----___------ w =

4.872 (0.000) 4.037

4.852 (0.004) 5.995 (O.OSlj 4.787 (0.019)

>6.832 a6.721

6.010 (0.130) 4.786 (0.016) 4.604 (0.032) 5.270 (0.012) 4.303 (0.017)

>6.176 B5.707

3.479 (0.015) 4.720 (0.018)

a5.702 5.642 CO.0541 5.546 iO.048i

a6.439 5.454 (0.057)

a5.506 B5.002 .5.483 a5.401

4.309 (0.067) >5.417 a5.174

4.038 6.045 4.424 6.566 6.827 5.586 4.997 5.124 5.159 4.458

3.477 4.732

5.135

6.006

MGU AM(GT) MGV

ew ew th(eff)

0.376 (0.003) 0.399 ---------__------ w q

1.688 (0.014) 1.006 2.273 0.039 (0.009) 0.170 0.259

1.106 0.802

0.787 (0.019) 0.841 0.549 (0.043) 0.610 1.210 (0.083) 1.419

0.718 0.890 0.196

-~_~_--____---_-- w =

0.761 (0.000) 0.793 --------___------ w =

0.779 (0.004) 0.209 (0.015) 0.039 (0.019)

qO.080 <0.091

0.205 (0.031) 0.841 (0.016) 0.945 (0.034) 0.481 (0.007) 1.466 (0.028)

co. 170 co.291

0.597 (0.410) 0.907 (0.018)

co.293 0.314 (0.020) 0.350 (0.019)

co.125 0.390 (0.026)

~0.367 qO.656 <0.377 co.414

1.456 (0.112) ~0.406 co.538

WGT) th(free)

0.511 5.308

1.889 0.945 1.186 0.254 5.300

0.636 0.218 1.095 0.335 0.042 0.115 0.557 0.185 0.614 0.695 0.567 0.349 0.370 0.296 0.355 0.585 0.308 0.687 0.190 9.193

0.032 0.376 0.694 4.334

1.013 0.107

0.793 1.013 0.197 0.294 1.274 1.575

0.100 0.160 0.000 0.066 0.335 0.459 0.660 0.842 0.570 0.773 0.547 0.681 1.227 1.530

0.675 0.871 0.895 1 .084

0.563 0.755

0.108 0.247

379 Atomic Data and Nuclear Data Tables. Vol. 33, NO. 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller f3 Decay in s&hell Nuclei


44 Ar 21 ZJ, 2T, 2J, 2T, nf

(80 4) (62 2) (60 4) (60 5) (40 7)

El(exp) A4 Wh)

WV) WeV) WV)

9978 10423 10572 10661 10689 10980 10983 11059 11224 11530 11548 11552 11682 11730 11881 11882 11921 11971 12162 12206 12446 12507 12663 12694 12697 12920 12957 13070 13802

,433, ------------


("4 W) (W

is0 6j (42 2)

(40 9) (42 3) (80 7) (82 ‘1 ( 4 0 10) (80 8) (42 41 (60 6j (62 2) (80 9)

I:: i; (62 3) (60 9) (62 4) ( 8 0 10)

::j: ;;

: : ‘: ‘:; --- Emax =

2Qhlg 2gA1 ( 3 5) ( 5 3 1) (13 1) (33 1) i33 Pj (53 2) (53 3)

[ii :; (53 4) (33 4) (53 5) ( ‘3 3) (33 51 (53 6) ( ‘3 4) (33 6) (53 7) (‘3 5) (33 7) (53 8) ( 1 3 6) (33 81 i13 7j ( 1 3 8) ( ‘3 9) ---

2gA1 2gSi ( 5 3) ( 3

I: ( 5 ---

2QP 2gsi ( 1 1) ( 1

i: ( 1 ---

tmax =

O( 0) 0 ‘398 (< 1) 1214 2224 (< 1) 1959 2866 (< 1) 2735 3062 (< 1) 280 1 3184 (< 1) 3017 3433 (* 1) 3330

3578 3816 3976 4128 4229 4459 4501 4650 5064 5281 5470 5591 5648 5803 6113 6214 6482 7499

7470

1 1) 1273 1 1) 2028 1 2) 2426

1 2) 3067 Emax = 368 1

1 1) 1 1) 1 2) 1 2) Emax =

0 1273 2426 4840 4944

c< 11 1394 (< ‘1 2121 (< ‘1 2630 (< 1) 3513 ---e-e------

( 0) 0 (< 1) 1394 (< 1) 2630 (< 1) 4901 -e---v------

0.023 0.067 4.094E-4

13.693E-4 53.833E-4

0.264E-4 0.013 0.083

51.609E-4 ll.QllE-4 17.499E-4

39.516E-4 75.370E-4 11.401E-4

7.237E-4 1.410E-4

8.069E-4 2.134E-4 O.O03E-4 5.934E-4 O.OOlE-4 0.8606-4 O.O35E-4 O.O04E-4 O.O02E-4 O.O46E-4 0.736E-4 O.O12E-4 O.OOlE-4

---------- Sum = 100.002

36.000 (>QQ) 33.119 15.500 ( 12) 1.764 21 .ooo ( 23) 7.643

6.000 ( 25) 1.868 5.000 ( 20) 5.936

21 .500 ( 10) 10.968 3.155 1.912 0.237 2.050

41.755E-4 18.946E-4 13.144E-4

62.792E-4 0.110 0.113 0.024 0.028 8.832E-4 0.043

93.783E-4 47.3966-4

1.283E-4 15.799E-4

---------- Sum = 69.000

89.900 (< 1) 94.759 3.800

I :; 2.781

6.300 2.480 0.033

------‘s:~’ 0.012

= 100.033

98.291 I' ')

99.006 1.255 0.422 0.456 ( ii 0.574

O.lllE-4 ---------- Sum = 100.002

380 At- Dala and Nudear OWa Tables, Vd. 33. No. 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller fi Decay in s&Shell Nuclei

T’ABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ji Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

@l(L) PW rw

2.742 0.08 0.12 2.463 0.08 0.19 2.361 0.07 0.22 2.297 0.07 0.24 2.277 0.07 0.25 2.051 0.07 0.35 2.049 0.07 0.35 1.986 0.07 0.39 1 .841 0.06 0.49 1.544 0.06 0.80 1 .525 0.06 0.82 1 .520 0.06 0.83 1 .378 0.05 1.04 1 .323 0.05 1.14 1.138 0.05 1.55 1.137 0.05 1.55 1 .087 0.05 1 .69 1.020 0.05 1.86 0.743 0.04 3.01 0.674 0.04 3.39 0.249 0.03 7.09 0.126 0.03 8.81

-0.220 0.03 16.34 -0.294 0.02 18.67 -0.301 0.02 18.92 -0.866 0.01 51.83 -0.955 0.01 60.33 -1.182 0.00 85.69 -2.005 0.00 100.00

4.623 -0.32 4.204 -0.25 3.911 -0.21 3.652 -0.18 3.567 -0.17 3.511 -0.17 3.394 -0.16 3.322 -0.15 3.199 -0.14 3.113 -0.13 3.027 -0.13 2.967 -0.12 2.826 -0.11 2.800 -0.11 2.702 -0.11 2.402 -0.09 2.226 -0.08 2.060 -0.08 1 .946 -0.07 1 .890 -0.07 1 .729 -0.07 1 .362 -0.06 1.227 -0.05 0.813 -0.04

2.417 -0.10 1 .727 -0.07 1 .240 -0.06 0.042 -0.03 -------------------

3.063 0.09 0.07 2.297 0.07 0.24 1 .224 0.05 1.34

-3.429 0.00 100.00

log(M) Alog WfAt) ew ew th

5.773 5.033 7.143 6.555 5.940 8.024 5.345 4.461 5.523 5.862 5.676 5.318 4.895 5.660 5.673 6.382 5.574 6.085 8.640 5.295 8.648 5.586 6,625 7.487 7.816 5.862 4.572 6.131 6.51 1

---------------------

~5.163 5.052 5.110 (0.074) 5.907 4.686 (0.114) 4.978 4.971 (0.119) 5.331 4.964 (0.100) 4.743 4.276 (0.067) 4.421

4.845 4.991 5.774 4.751 7.356 7.640 7.657 6.951 5.611 5.300 5.789 5.569 6.949 5.201 5.706 5.636 7.068 5.564 5.589

~~~~~~~~~-----__-----

5.058 (0.006) 4.787 5.742 (0.013) 5.630 5.036 (0.016) 5.193 6.118 (0.067) 6.296 ~~____~~_--_---__----

3.686 (0.004) 3.700 0.741 (0.017) 0.664 0.827 4.813 (0.009) 5.304 0.435 (0.004) 0.248 0.285 4.179 (0.014) 4.097 0.904 (0.015) 0.994 1 .323

4.158 0.926 1 .224 ---------____-_------ ---------__------ w = 3.064

WGV AM(GT)

ew em

WGT) M(GV th(eff) th(free)

0.270 0.360 0.633 0.801 0.056 0.070 0.110 0.160 0.223 0.289 0.020 0.026 0.442 0.551 1.222 1 .600

0.360 0.474 0.244 0.319 0.302 0.306 0.456 0.597 0.742 0.940 0.307 0.404 0.303 0.408 0.134 0.185 0.339 0.433 0.188 0.273 0.010 0.016 0.468 0.608 0.010 0.012 0.335 0.430 0.101 0.127 0.037 0.047 0.026 0.034 0.244 0.323 1 .076 1,433

0.179 0.247 0.115 0.164 .- ----------_______ w = 8.10/

CO 0 0 0 0

.412 0.468

.437 (0.037) 0.175

.713 (0.094) 0.509 514 (0.071j

:518 (0.060) 0.339 0.668

1.144 (0.089) 0.968 0.594 0.502 0.204 0.662 0.033 0.024 0.023 0.053 0.246 0.352 0.200 0.258 0.053 0.394 0.220 0.239 0.046 0.259 0.252

__-_______----_-- w =

0.626 0.238 0.654 0.455 0.868 1 .244

0.705 0.651 0.272 0.872 0.032 0.032 0.016 0.085 0.316 0.424 0.269 0.311 0.095 0.519 0.282 0.308 0.062 0.322 0.326 9.690

0.569 (0.004) 0.777 1 .023 0.259 (0.004) 0.294 0.372 0.584 (0.011) 0.487 0.613 0.168 (0.013) 0.137 0.194 ---------__-_____ w = 9.193

381 Atomic Date and Nuckw Data Tabkd, Vol. 33, NO 3, November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller fi Decay in &Shell Nuclei


Ai 4 At Zr 2J, 2T, 2J, 2T, n, E,(exp) A& WV BWv) ABR/BR (exp) BR(th)

WV) WV) WV) w (“4 (W

0.500 11.900

3.900 4.000 0.180 0.160 0.800 0.300 0.300 0.710 0.300 0.260 1.080 0.330 0.250 0.082 0.230 0.690 1.010

18.300 1.140 0.140 0.430

1383 (< 1) 1954 (< 1) 2423 (< 1) 3106 (< 1) 4080 (< 1) 4954 (< 1) 5293 (< 1) 5826 ( 5) 5967 ( 3) 6074 ( 15) 6330 ( 6356 i

4) i5j

6505 ( 15) 6653 ( 15) 6832 ( 5) 7083 ( 20) 7148 ( ‘0) 7241 ( 20) 7366 ( 9) 7526 ( 5) 7759 ( 5) 8106 ( 9) 8231 i ilj 8381 ( 2) 8532 ( 9) 8787 ( 13)

1394 2121 2630 3513 4410 4917 5219 5881 6155

44.350 4.975

11.006 0.627 0.063

13.924 ( 7) 4.423 : ::; 0.078 1.391

( 12) ( 7) ( 13) ( 13)

: 9:;

(‘11)

I 1:;

( 16) ( 18) ( 17) ( 10)

i :53 1)

I ;

131 4; (71 4) (51 4)

15.837

: 2:; ( 1’)

0.322 1.632

0426

9390 ( 12) 6267 6389 6778 6862

l.O96E-4 0.090 (51 5)

(31 5) (31 6)

6901 7179

O.O00E-4 0.113 0.124 0.140 0.070 0.050 O.l54E-4 0.064

i71 5j (71 6)

7391 7526 7604 7634 7669 7875 7878 8268 8377 0401 8562 0841 9038

-----

i51 6, (31 7) (51 7) (51 8) (71 7) 0.172

0.241 (31 8) (31 9) (71 8) ( 3 1 10)

0.152 28.35lE-4

0.060 0.056

14.930E-4 99.972

75.272 7.660 0.023

(71 9) ( 7 1 10) --- Emax =

3oAl(06)(24 1)

(24 2) (24 3) (24 4) (24 5) (24 6)

--- Emax =

13790 -------

685 (< 1)

---------- Sum =

3OYg 493 2139

84.000 ( 14)

2538 2981 l.O95E-4

0.093 3185 3551

.----- 0.952

84.000

10.970 71.305

5.758 6.800 3.493 0.436 0.617 0.074 0.184

28.009E-4 5.583E-4

28.402E-4

---------- Sum =

17.100 ( 5) 67.300 ( 1)

5.700 ( 3)

6530 -_-----

2235 (< 1) 3499 ( 1) 4810 (< 1) 4830 (< 1) 5231 (* 1) 5279 (< 1) 5613 (< 1) 5950 (’ 1) 6357 (< 1) 6865 (< 1) 6915 (< 1)

30Al 30 Si(64) (42 1) (42 2) (42 3) (62 1) ifi2 2j (82 1) (42 4) (82 2) (42 5)

I:: i; (62 4)

2310 3550 5048 4961 5195 5506 6205 5913 6520

6.600 2.600 0.140 (>QQ) 0.300 ( 20) 0.160 ( 31)

7201 6967 7473

382 Atomic Data and Nudear Data TaMes. Vol. 33. NO. 3. November 1935

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller fl Decay in sd-Shell Nuclei


5.226 5.119 5.027 4.005 4.665 4.447 4.356 4.204 4.162 4.130 4.050 4.042 3.994 3.946 3.005 3.790 3.775 3.741 3.695 3.634 3.543 3.399 3.345 3.270 3.200 3.005 2.761 4.070 4.032 3.904 3.875 3.862 3.764 3.606 3.634 3.604 3.592 3.579 3.496 3.495 3.320 3.279 3.269 3.194 3.050 2.956

V/A) (%I

0.13 0.13 0.13 0.14 0.14 0.14 0.14 0.14 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.12 0.12 0.12 0.12 0.12 0.11 0.11 0.11 0.11 0.10 0.09 0.13 0.13 0.13 0.13 0.13 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.11 0.11 0.11 0.11 0.10 0.10

WC) bidfAt) Alog(ht) WM) MW) AM(GT) MGT) MGT) (“4 ev ev th ew em th(eff) th(free)

0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.04 0.04 0.05 0.06 0.06 0.07 0.07 0.09 0.15 0.02 0.02 0.03 0.03 0.03 0.03 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.06 0.07 0.07 0.00 0.09 0.11

a6.240 4.645 (0.022) 5.039 (0.030) 4.076 (0.047) 6.101 (0.052) 6.200 (0.057) 5.421 (0.030j 5.736 (0.060) 5.791 (0.061) 5.369 (0.042)

>5.603 5.657 (0.055) 5.015 CO.0351

4.787

5.269

5.630 5.193

6.400

6.296 7.072 4.511 4.918

co.146 0.915 (0.023)

0.702 (0.030) 0.502 (0.025)

0.156 (0.009)

5.497 io.057j 5.571 (0.073) 5.995 (0.002) 5.455 (0.079) 4.834 (0.050) 4.615 (0.065) 3.289 (0.0.29) 4.425 iO.OSSj 5.213 (0.097) 4.402 (0.060)

0.153 (0.010) 0.375 (0.016) 0.261 (0.010) 0.245 (0.017) 0.398 (0.019)

~0.277 0.205 (0.010) 0.590 (0.024) 0.343 (0.023) 0.315 (0.026) 0.194 (0.010) 0.360 (0.033)

0.777 1.023 0.294 0.372 0.407 0.613 0.137 0.194 0.056 0.091 1.060 1.333 0.669 0.000 0.446 0.544 0.111 0.116

3.207

0.736 iO.043j 0.948 (0.071) 1.023 (0.613) 1.179 (0.062)

0.476 (0.053) 1.211 (0.003)

1.076 1.369

5.771 5.027 9.072 6.129

11.142 5.917 5.800 5.697 5.920 6.090 9.590 5.096 5.460 5.155 5.306 7.025 5.624 5.515 6.991

0.250 0.317 0.590 0.663 0.006 0.019 0.166 0.208 0.001 0.081 0.212 0.237 0.242 0.301 0.272 0.349 0.211 0.220 0.172 0.216 0.003 0.024 0.217 0.200 0.355 0.434 0.509 0.602 0.427 0.541 0.059 0.086 0.297 0.394 0.336 0.444 0.061 0.075

----------------- w = 9.193

1.316 0.706 0.033 0.019 0.160 0.672 5.300

0.350 1.475

0.032 0.910 0.034 0.317 0.433 0.164 0.499 0.109 0.057 0.234

4.128 3.559 3.372

-0.24 3.715 (o.oal) 3.799 -0.17 4.223 -0.16 6.563 -0.14 8.652 -0.13 5.609 -0.12 4.376

.---- ----_-__ ---------------------

1.090 (0.102) 0.990 0.600 0.041 0.004 0.123 0.510

-------------____ w =

5.793 0.324 (0.010) 0.264 4.533 1.076 (0.023) 1.125 5.034 0.619 (0.019) 0.632 4.951 0.675 (0.020) 0.696 5.019 0.546 (0.026) 0.643 5.894 <0.131 0.235 5.537 0.243 (0.025) 0.354 6.227 0.232 (0.037) 0.160 5.511 0.365 6.045 0.079 7.491 0.037 6.047 0.197

3.143 3.020 2.806

4.291 -0.20 3.043 -0.21 3.251 -0.15 3.240 -0.15

5.614 (0.027) 4.572 (0.019) 5.052 (0.027) 4.977 (0.026) 5.160 (0.041)

>6.401 5.064 (0.091) 5.905 (0.139)

3.019 2.991

-0.14 -0.13

2.704 -0.12 2.553 -0.11 2.234 -0.09 1.750 -0.07 1.695 -0.07

0.950 -0.05

383 Atomic Data and Nudear Data Tabbs. Vol. 33. No. 3. November 1985



A( zi A( Zl 2J, 2T, 2J, 2T, nl

30P

(82 3)

lax ;;

(82 4)

le6X ;;

(82 6)

:ss: t; --- Cmax

ii ( 2 0) ( 0 2 1) (42 1)

=

3%

305

3499 (< 1) 3550 3770 (< 1) 4210

(02 2) 3788 (< 1) 4085 --- Emax = 4227 _____-_-----

30P (02)(20 1) O( 0) 0

(02 1) 677 (< 1) 693 (20 2) 709 (< 1) 644 (20 3) 3019 (< 1) 3131 (20 4) 3731 0 1) 3737 (22 1) 4501 i< 1 j 4903

IfX :; 4545 5712 .(< (< 1) 1) 4931 5896 (20 7) 8002 (< 1) 6085

(20 8) 7085 --- Emax = 6142 --_______-__

31Al 31Si ( 5 5) ( 3 3 1) O( 0) 0 (53 1) 1695 (< 1) 1606 (33 2) 2317 (< 1) 2295 (53 2) 2789 ( 1) 2871

(33 3) 3825 (33 4) 5129

5037 5398

(73 1) 3697 (73 2) 4711

(73 3) 5632

(33 5) 5709 (53 5) 5764

6074 6170

(33 6) 6215 (73 5) 8506 (73 6) 8555

(53 7) 8640 (53 8) 6884 (73 7) 7009 (53 9) 7198 (73 8) 7302 ( 5 3 10) 7414 --- Cmax = 7850 ---_--------

3’51

3’s

31P (33)(11 1) O( 0) 0 99.930 (< 1) 99.882 (31 ‘1 1268 (< 1) 1210 0.070 (>99) 0.048 --- Emax = ,490 ------------ ---------- Sum = 99.930

31P ( 11) ( 11 1) O( 0) 0 (31 1) 1266 (< 1) 1210 (1’ 2) 3134 (< 1) 3310 (31 2) 3508 (< 1) 3588 (31 3) 4261 (< 1) 458 1 (31 4) 4594 (< 1) 4732 (11 3) 5084 (31 5) 5783 (31 6) 61 17 --- Emax = 5395 ------------

El(exp) A& WN BWexp) ABR/BR (exp) BR(th)

WV) WV) WV) WI (“4 rw

7223 (< 1) 6997 7256 (< 1) 7307 7827 (< 1) 744 1

805 1 8195 8606 8696 8757 8933

8539 ------------

O( 0) 0 2235 (< 1) 2310

0.111 0.217E-4 7.793E-4

44.072E-4 10.871E-4

--------- - Sum = 99.760

99.940 (< 1) 99.923

l:%E-4: 4, 0.072

9) l:830E-4( 19)

23.164E-4 0.817E-4

33.900E-4( 8) 33.118E-4 ---------- Sum = 100.000

21.310 : :;

20.845 76.110 75.668

0.293 (<23) 1.736 2.283 ( 2) 1.727 0.011 (‘99) 0.015

73.000E-4(>99) 2.153E-4 73.000E-4(>99) 38.547E-4

0.943E-4 O.O41E-4

---------- Sum = 99.996

65.000 I 1:;

84.167 11.500 8.826 23.500 ( 14) 25.849

1 .ooo ( 40) 0.310 0.749 0.031 0.011 0.032 0.137 0.113 0.109 0.017 0.535 0.036 0.015

75.754E-4 0.042

94.932E-4 0.600E-4

16.755E-4 22.880E-4

0.599E-4 O.O35E-4 O.l46E-4

---------- Sum = ‘0’~(-)00

98.860 (< 1) 99.108 1 a097 0.844 0.033 0.032 0.012 ( 8) 0.017 2.800E-4(>99) 0.326E-4 2.5OOE-4(,99) 0.337E-4

O.O85E-4

---------- Sum = 100.002

384 Atomic Data and Nuclew Data Tab&.. Vol. 33. No. 3. November 1985



Wf A) WV/A) WC) (“4 (“4

1.323 -0.06 1.270 -0.06

0.693 -0.04 -0.323 -0.03 -0.664 -0.03

2.667 0.08 0.14 4.043 (0.002) 4.812 0.440 0.04 5.01 5.882 (0.021) 5.738

-1.728 0.00 100.00 5.255 (0.042) 5.052 -2.133 0.00 100.00 5.780 (0.086) 6.099 -2.169 0.00 100.00 4.477 (0.036) 4.456

-----------________ _-__-----_-----_-__-_

3.507 0.12 0.04 3.303 0.11 0.06 3.269 0.11 0.07 1.847 0.07 0.60 1.079 0.05 2.11

-0.278 0.03 22.24 -0.302 0.02 26.77 -2.097 0.00 100.00 -3.081 0.00 100.00

0.00

------me_---____-__

4.735 -0.37 4.243 -0.27 4.029 -0.24 3.852 -0.22 3.400 -0.17 2.647 -0.11 2.710 -0.12 2.451 -0.10 3.461 -0.16 2.919 -0.13 2.264 -0.09 2.196 -0.09 2.151 -0.09 1.857 -0.08 1.756 -0.07 1.706 -0.07 1.360 -0.06 1.295 -0.06 1.176 -0.06

0.790 -0.05 0.556 -0.04 0.139 -0.04

-0.140 -0.03 -0.500 -0.03

1.557 -1.479

------_

3.271 2.598 0.873 0.253

-1.248 -1.554 -2.379

-0.07 -0.02

0.11 0.07 0.09 0.19 0.05 2.99 0.04 8.69 0.00 99.26 0.00 100.00 0.00 100.00

0.00 0.00

.---- -------_

WAfd) Alog WfAt) em ew th

4.821 8.485 6.344 4.575 4.642 6.437 7.699 7.536 7.264

-------------------__

4.330 (0.010) 4.334 3.493 (0.004) 3.491 5.893 (0.102) 5.116 3.560 (0.011) 3.677

>5.109 4.960 B3.931 5.456 >3.027 4.099

3.995 4.370 4.591

--____-__--_-___--___

4.731 (0.045) 4.740 4.991 (0.071) 5.109 4.467 (0.074j 4.429 5.661 (0.179) 6.173

5.336 5.967 6.469 5.756 6.137 5.679 5.039 5.772 4.234 5.113 5.394 5.640 4.552 5.129 7.210 5.378 5.010 6.174 7.122 6.148

~~~~~~------_---_____

5.532 (0.001) 5.382 a5.651 5.667

~_--_-__---__-_--_-__

3.685 (0.002) 3.695 0.743 (0.010) 0.703 0.066 4.966 CO.0131 5.091 0.365 (0.006) 0.317 0.386 4.768 (0.022) 4.793 0.455 (O.OllY 0.446 0.589 4.579 (0.036) 4.434 0.571 (0.024) 0.674 0.922

>4.713 5.650 x0.489 0.165 0.204 >4.456 5.337 ~0.657 0.238 0.314

5.108 0.310 0.386 5.051 0.331 0.444 6.185 0.090 0.113

--------------------- --------------___ w = 3.064

WV AM(GT) WW WW

ew ew th(eff) th(free)

0.807 1.000 0.012 0.029 0.140 0.186

1.072 1.399 0.992 1.257 0.126 0.103 0.029 0.040 0.035 0.043 0.049 0.060

---____--__--_-__ w = ,, 466

0.516 (0.001) 0.535 0.665 0.156 (0.004) 0.184 0.226 0.321 (0.015) 0.405 0.529 0.175 (0.017) 0.121 0.140 0.786 (0.034) 0.804 1.037 ----------------- w = 3.064

0.537 (0.006) 0.535 0.665

0.089 (0.010) 0.217 1.303 (0.017) 1.140

co.219 0.260 CO.851 0.147 co.959 0.701

0.790 0.513 0.398

----___---_-__-__ w =

0.830 co.0431 0.821 0 .615 (0.050) 0.537 1 124 (0.096) 1.175 0 :284 (0.059) 0.156

0.412 0.200 0.112 0.255 0.164 0.278 0.581 0.250 1.469 0.534 0.386 0.291 1.018 0.524 0.040 0.394 0.601 0.157 0.053 0.162

-_--___---_----__ w =

1.118 0.729 1.559 0.194 0.528 0.268 0.150 0.336 0.166 0.365 0.755 0.319 1.895

0.690 0.469 0.344 1.364

0.661 0.094 0.466 0.705 0.199 0.052 0.226

11.868

0.269 (0.000) 0.320 ~0.235 0.230

----------------- w =

0.221 1.515 0.331 0.184 0.946 1.058 0.680 0.547 3.064

0.402 0.320 7.506

385 Atomic Data and Nuclear Data Tables. Vol. 33, NO 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller j3 Decay in &Shell Nuclei


4 z Af ZI 2J, 2T, 2Jr 2T, nf Edexp) A% Wh)

WV) VW WV)

BR(exp) ABFVBR (exp) BR(th)

W) rw (“4

100.000 ----‘;“;)

100.000 = 100.000

100.000 (< 1) 100.000 ---------- Sum = ‘00~000

1 .ooo I “:;

0.114 60.000 60.768

2.600 ( 30) 1.247 3.100 ( 12) 0.422 6.000 ( 11) 6.752 4.100 ( 12) 2.549 1 .a00 ( 27) 2.705

32si 32P (04)(22 1) --- Emax =

S2P 32s ( 2 2) ( 0 0 1) --- Emax =

32Cl 32s ( 2 2) ( 0 0 1) (40 1) (00 2) (40 2) (20 1) (40 3) (40 4) (22 1) (42 1) (20 2) --- Emax =

33P 33s (13)(31 1) --- Emax =

O( 0) 5 213 ____________

O( 0) 0 ,710 ------------

0 2230 3779 4282 4695 5549 6666 7003 7116

0 2148 3748

(< 1) 4353 (< 1) 4705 (< 1) 5490 (< 1) 6695 i< li 7057 (< 1) 7052

20.500 ( 9i 25.763 0.500 ( 40) 0.762 0.900 ( 11) 0.218

---------- Sum = ,0,*300 7190 (< 1) 7125

12687 -----------_

100.000 0 1) 100.000 ---------- Sum = ‘00*000

98.580 (< 1) 98.801 33C 335 (3,)(3

::

1 1) 1 1) 1 1)

0 779

1896 2174 2839 3899

840 i< lj 1966 (< 1)

0.479 ( 13j 0.570 0.460 ( 13) 0.160

1 2j 1 1 2 1 3) 1 2) 1 4) 1 3)

2313 2866 3832 3935 4053 4144 4375 4424 4746

(< 1) (< 1) (< 1)

0.035 0.029 0.443 0.416 9.200E-4(>99) 19.665E-4

i< lj 3667 7.000E-4(>99) O.O72E-4

(< 1) 3063 4.700E-4( 31) 2.413E-4

(< 1) (< 1) (< 1) (< 1)

4185 4206

2.600E-4(>99) O.O30E-4 4.400E-4(>99) 2.158E-4 5.700E-4(>99) 4.lOOE-4( 29)

1 .567E-4 2.406E-4 O.O30E-4 O.O03E-4 O.OOlE-4

---------- Sum = 99.998

13.619

4697 4607 5076 5145 5561

v---m

l 4) 1 5) 1 6) 1 5) 1 4) Emax = 5582

O( 0) 0 811 (< 1) 779

2352 (< 1) 2174 3972 ( 1) 3667

3063

33Ar 33Cl ( 1 3) ( 3 1 1) (11 1) (31 2) (3, 3) (11 2)

i3’ 4, 1

47.529 3.933

0.400

0.430 2.500 0.047 0.310 0.081 0.570

27.000 0.550 0.370 0.230 0.027 0.017 0.580 0.041 0.290 0.250 0.010 0.230 0.140 0.017

( ‘0) 0.366 0.022

( 11) 0.440 ( 12) ( 17) ( 12) ( 16) ( ‘0)

: 1:: 29.230

( 10) ( 43) ( 25) ( 41) ( ‘0) ( ‘9) ( 10) ( 12) ( 30)

I ;:; ( 23)

4113 ( 1) 4165 4463 ( 2) 4720 ( 35) 4832 ( 3) 5105 ( 2) 5450 ( 4) 5544 ( 1) 5191 5675 5763 5682 6034 6125 6254

( 17) ( 23) ( 3,) ( 25)

I fZ 7228 i 25j 7475 ( ‘8) 7595 ( 22) 7767 ( 40) 8084 ( 17) 8183 ( 25) 8310 8609 8969 ( 30)

4286

0.017 ( 23) 30.000E-4( 50)

2.763

386 Atomic Data and Nudear Data Table% Vol. 33. NO. 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller j3 Decay in s&Shell Nuclei

TABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ft Values, and Gamow-Teller Matrix Elements

See page 362 for Explanation of Tables

Wf A) W/A) w-3 log(f,t) AlOg @lW) MW) AM(GT) M(GT) WGT) W) (“4 ew ew th ew exp th(eff) th(free)

-1.592 -0.02 -------------------

7.927 (0.053) 7.535 ---------------------

0.009 (0.001) 0.013 ----------------- w =

0.009 4.334

1.816 -0.08 7.907 (0.001) 7.720 ------------------- ---------------------

0.015 (0.000) 0.019 0.009 ----------------- w = 5.308

5.269 0.14 0.00 6.743 (0.174) 7.720 4.828 0.16 0.01 4.524 (0.029) 4.553 4.458 0.16 0.01 5.517 (0.134) 5.871 4.323 0.15 0.02 5.306 (0.056) 6.206

4.205 0.15 0.02 4.846 (0.051) 4.884 3.939 0.15 0.03 4.800 (0.053) 5.041 3.531 0.13 0.06 4.750 (0.121) 4.608 3.391 0.13 0.07 3.554 (0.043) 3.489 3.343 0.13 0.07 5.118 (0.174) 4.969

3.310 0.12 0.00 4.830 (0.049) 5.480 ------------------- ---------------------

0.056 (0.012) 0.019 0.744 (0.025) 0.720 0.237 (0.037) 0.158 0.303 (0.020) 0.107 0.513 (0.030) 0.491 0.542 (0.033) 0.410 0.573 (0.080) 0.675

>O 0.046 0.376 (0.075) 0.446 0.523 (0.029) 0.247 ------_---___-_-_ w =

0.009 0.916 0.164 0.154 0.607 0.491 0.927 0.026 0.561 0.310 5.308

-1.306 -0.03 5.034 (0.012) 5.138 ------------------- ---------------------

0.338 (0.005) 0.300 0.379 --------------_-_ w = 5.308

3.348 0.13 0.07 3.754 (0.001) 3.750 2.944 0.11 0.14 5.663 (0.056) 5.586 2.242 0.09 0.40 4.979 (0.057) 5.384 1 .968 0.08 0.61 5.820 (0.059) 5.910

1.437 0.07 1.43 4.190 (0.057) 4.216 -0.026 0.03 17.28 B5.410 5.078 -0.251 0.03 25.67 B5.304 7.290 -0.519 0.02 41.05 5.209 (0.139) 5.496 -0.721 0.01 57.80 ~5.264 7.197 -1.094 0.00 96.18 >4.662 4.969 -1.142 0.00 98.77 a4.502 -1.431 0.00 100.00 4.356 (0.127) -1 .381 0.00 100.00 4.821 -1.497 0.00 100.00 4.519 -1.868 0.00 100.00 5.954 -1 .996 0.00 100.00 6.947 -4.703 0.00 100.00 4.721

------------------- ---------------------

0.598 0.232 0.509 0.193 1 .261

<0.310 co.350

0.391 <0.367 <0.733 CO.881

1.043

(0.014) 0.629

I:% 0.253

(0:013) 0.319 0.174

(0.083) 1.226 0.454 0.036

(0.062) 0.281 0.040 0.515

0.820 0.303 0.387 0.221 1 .676

0.613 0.036 0.393 0.047 0.660

(0.153) 0.611 0.864 0.166 0.053 0.685

.----------- w =

0.777 1.171

0.230 0.050 0.932 4.334

5.061 0.18 0.01 4.896 0.18 0.01 4.542 0.18 0.02 4.093 0.17 0.03 4.126 0.17 0.03 4.049 0.16 0.03 3.936 0.16 0.04 3.850 0.16 0.04 3.811 0.16 0.05 3.713 0.15 0.05 3.582 0.15 0.06 3.545 0.15 0.07 3.492 0.14 0.07 3.456 0.14 0.08 3.406 0.14 0.08 3.341 0.14 0.09 3.300 0.14 0.10 3.242 0.13 0.11 2.740 0.11 0.22 2.591 0.11 0.28 2.515 0.10 0.32 2.401 0.10 0.38 2.172 0.09 0.54 2.095 0.09 0.61 1.992 0.09 0.71 1 .727 0.08 1.09 1.355 0.07 1.98 3.994 0.16 0.03

5.729 (0.045)

5.654 (0.052) 4.777 (0.053) 6.416 (0.076) 5.557 (0.057) 6.042 (0.071) 5.064 (0.047) 3.352 (0.014) 4.990 (0.050) 5.126 (0.050) 5.282 (0.190) 6.147 (0.114) 6.308 (0.180) 4.717 (0.048) 5.366 (0.088) 4.367 (0.050) 4.355 (0.058) 5.639 (0.135) 4.048 (0.191) 4.187 (0.312) 5.000 (0.108) 4.734 (0.109) 5.116 (0.222)

5.138 4.430 5.158 5.741 7.002 5.617

3.290

4.764

0.152 (0.008)

0.165 (0.010) 0.454 (0.028) 0.069 (0.006) 0.185 (0.012) 0.106 (0.009) 0.326 (0.018)

>o 0.355 (0.020) 0.304 (0.017) 0.254 (0.055) 0.094 (0.012) 0.078 (0.016) 0.487 (0.027) 0.231 (0.023) 0.728 (0.042) 0.738 (0.049) 0.168 (0.026) 1.051 (0.231)

0.896 (0.322) 0.351 (0.044) 0.477 (0.060) 0.307 (0.079)

0.300 0.379 0.677 0.859 0.293 0.416 0.150 0.161 0.035 0.002 0.173 0.194

0.572 0.719

0.461 0.596

387 Atomic Data end Nudsar Data T&es. Vol. 33. No. 3. November 1985

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller 0 Decay in s&Shell Nuclei

rABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios,ft Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

AI Z A1 zt 2J, 2T, 2J, 2T, ni

3%

s4c I

34Clm

-Ar

35P

35s

35Ar

(31 5)

iu 6, 7) 11' 4) (31 8) (11 5) (31 9) (33 1)

I : : lo) ( 3 1 1:;

E 2, ( 3 1 1:; (1' 6) ( 3 1 13) (33 3) ( 3 1 14)

(11 9) ( 3 1 15) ( 3 1 16) ( 1 1 10) ( 3 1 17) ( 3 1 la) ( 1 1 11) --- Emax =

34s ( 2 4) ( 0 2 1) (42 1) (42 2) (02 2) (22 1) (42 3) (42 4) --- Emax =

34s (02);;; 1) 1)

(22 2) --- Emax =

34S ( 6 0) ( 4 2 1) (42 21 (42 3) (82 1) (62 1) (42 4) --- Emax =

34Cl ( 0 2) ( 0 2 1) (20 1) (20 2) (20 3) (20 4) (20 5) (20 6)

--- Emax =

355 (15)(33 1) (13 1) (33 2) --- Emax =

35 Cl ( 3 3) ( 3 1 1) --- Emax =

35C1(31) (31 1) (11 1) (51 1)

E,(exp) AEt WV

WV) WV) WV)

4807 5076 5309 5561 6553 6003 6630 6722 7091 7273 7491 7637 7940 7983 8155 6231 8797 6802 6815 8964 9098 9377 9379 9489 9775

11618 ---_-_-__-__


rw ("4 W)

0.176 0.235 0.267 0.256 0.014 0.538

44.255E-4 78.985E-4

0.053 0.048 0.181 0.043

97.934E-4 0.081 0.141 1.277E-4 3.780E-4 8.247E-4

42.339E-4 11.629E-4

0.015 22.405E-4 32.358E-4 36.197E-4

1.687E-4 ---------- Sum = 100.010

O( 0) 0 84.600 ( 2) 67.731 2127 (< 1) 2201 14.900 ( 13) 31.225 3304 (< 1) 3138 0.040 ('99) 0.051 3914 (< 1) 3906 0.045 ( 35) 0.056 4074 (< 1) 3951 0.110 ( 18) 0.259 4115 (< 1) 4302 0.330 ( 18) 0.660 4889 (< 1) 4651 0.030 ('99) 0.003 5380 ------------ ---------- Sum = 99.985

O( 0) 0 4074 (< 1) 3951

5558 549, --------_---

100.000 (< 1) 100.000 7.800E-4('99) 1.045E-4

---------- Sum = 100.000

2127 (< 1) 2201 28.530 I

1) 10.103 3304 (< 1) 3138 26.420 4115 (c 1) 4302 0.458 ( :;

44.676 0.596

4686 (< 1) 4896 0.034 ( 8) 0.040 4875 (< 1) 4774 0.038 ( 15) 0.054 4689 (< 1) 4651 13.000E-4('99) 106.803E-4 5638 --_--------- ---------- Sum = 55.480

O( 0) 0 94.440 (< 1) 96.507 461 (< 1) 184 0.910 ( 17) 0.098

666 (< 1) 528 2.490 ( 4) 2.032 2581 (< 1) 2389 0.060 ( 11) 0.645 3128 ( 2) 3117 1.300 ( 6) 0.716

3740 3.296E-4 4843 8.165E-4

6059 -_---------- ---------- Sum = 100.000

O( 0) 0 1.000 (>QQ) 0.769 1572 (< 1) 1557 100.000 ( 10) 98.752 2939 ( 3) 2600 8.000 (>99) 0.479 3910 ------------ ---------- sum = 100~000

O( 0) 0 100.000 (< 1) 100.000 167 __-----_-_-- ---------- Sum = 100.00(,

O( 0) 0 1219 (< 1) 1244 1763 (< 1) 1760

98.235 i' :;

98.362 1.228 1.099

0.272 ( 3) 0.311

At,,,,,,c Data and Nuclear Data Tables. Vol. 33, NO. 3, November 1935 388


TABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ji Values,

Wf A) W/A) (“4

3.820 0.16 3.723 0.15 3.636 0.15 3.538 0.14 3.100 0.13 3.354 0.14 3.062 0.13 3.016 0.12 2.818 0.12 2.714 0.11 2.581 0.11 2.352 0.10 2.273 0.10 2.246 0.10 2.117 0.09 2.057 0.09 1.541 0.07 1.536 0.07 1.522 0.07 1 .360 0.07 1 .203 0.06 0.632 0.05 0.629 0.05 0.663 0.05 0.164 0.04

w3 log(Lt) ~IogW) log&t) VW dM(GT) WGT) WGT) (“4 exp ev th ew w th(eff) thlfreeb

0.05 0.05 0.06 0.07 0.13 0.09 0.14 0.15 0.20 0.23 0.29 0.41 0.46 0.48 0.59 0.64 1.47 1.48 1.51 1.97 2.55 4.73 4.75 6.30

14.90

5.781 0.143 5.563 0.184 5.390 0.224 5.337 0.238 6.176 0.091 4.834 0.425 6.627 0.054 6.329 0.076 5.306 0.247 5.244 0.265 4.535 0.601 4.933 0.380 5.494 0.199 4.553 0.588 4.181 0.903 7.162 0.029 6.175 0.091 5.831 0.135 5.107 0.311 5.499 0.198 4.225 0.857 4.692 0.501 4.531 0.603 4.316 0.772 5.148 0.296

--------------_----__ --------------_-- w =

0.212 0.252 0.277 0.306 0.127 0.538 0.072 0.076 0.341 0.341 0.814 0.507 0.274 0.801 1.223

0.042 0.129 0.189 0.431 0.256 1.164

0.681 0.817 1.059 0.388 5.308

3.997 -0.27 5.164 (0.018) 5.380 3.012 -0.16 4.933 (0.063) 4.732 2.169 -0.10 >6.661 6.672 1.541 -0.08 5.982 (0.162) 6.007 1 .338 -0.07 5.392 (0.095) 5.13s 1 .284 -0.07 4.860 (0.096) 4.678

-0.278 -0.04 '4.339 5.523 -_-_-_____-----____ -------------------__

3.307 0.13 0.08 3.491 (0.001) 3.490 -0.765 0.01 62.10 >4.527 5.152

0.00 5.384 ---------___-__-___ ___---______-------__

2. 162 0.09 0.45 5.990 (0.008) 6.677 0.210 (0.002) 0.095 0.971 0.06 3.10 4.832 (0.005) 4.840 0.797 (0.004) 0.790

-0.533 0.02 42.06 5.089 (0.009) 5.211 0.593 (0.007) 0.515 -1 .320 0.00 100.00 5.437 (0.038) 5.597 0.397 (0.017) 0.331 -1.511 0.00 100.00 5.190 (0.068) 5.274 0.528 (0.041) 0.480 -1 .528 0.00 100.00 >6.642 5.963 <0.099 0.217

---__-__-___-_-____ ------________--_____ __-----___-__--_- w =

3.53s 0.15 0.07 3.490 (0.002) 3.490 3.347 0.14 0.09 5.314 (0.076) 6.290 3.255 0.13 0.10 4.786 (0.021) 4.883 2.129 0.09 0.58 4.121 (0.051) 4.256 1 .652 0.08 1 .23 3.464 (0.030) 3.733

0.932 0.06 4.00 6.350 -1 .oos 0.00 96.44 4.015

__-______-------___ ------______--__-____

3.368 -0.19 >7.043 7.164 2.388 -0.12 4.063 (0.071) 4.076 0.830 -0.06 >3.602 4.832 -----------__-_--_- ------_-----_--___-__

-1 .857 -0.03

3.501 0.15 0.07 2.937 0.12 0.17 2.628 0.11 0.27

and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

5.021 (0.002) 5.113 -------_____---_____-

3.758 (0.001) 3.750 5.097 (0.012) 5.138 5.442 (0.016) 5.377

389

0.356 (0.007) 0.278 0.465 (0.034) 0.566

~0.064 0.063 0.139 (0.026) 0.135 0.274 (0.030) 0.367 0.506 (0.056) 0.623

co.921 0.236 ----------------- w =

CO.428 0.208 0.160

----------------- w =

0.173 (0.015) 0.056 0.318 (0.008, 0.284 0.683 (0.040) 0.585 1.455 (0.051) 1 .069

0.053 0.772

-------__ _----__ w =

qo.033 0.029 1.033 (0.084) 1 .018

Cl .757 0.426 ------- - ._-- ---__- w =

0.119 0.375 0.757 1.457

0.077 1.073 3.064

0.008 1 .325

0.589 6.852

0.485 (0.001) 0.436 ----------------- w =

0.589 7.506

0.561 (0.015) 0.622 0.820 0.444 (0.006) 0.423 0.536 0.298 (0.006) 0.322 0.414

Atomic Data and Nuclear Data Tables. Vol. 33. NO. 3. November 1985

0.399 0.777 0.090 0.214 0.500 0.753 0.333 7.506

0.263 0.225 5.308

0.142 1 .006 0.723 0.435 0.643 0.277 6.852

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller p Decay in &Shell Nuclei

TABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, j Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

44 Atz 2J, 2T, 2J, 2T, nf El(exp) AEt WV) WV)

2694 (< 1) 3003 (< 1) 3916 (< 1) 3968 (< 1) 4624 (' 1)

Wh) WV)

2672 3146 3962 4088

4788 4595 5089

-----

BWexp) ABRPR (exp) BR(th)

W) (%I W)

0.161 ( 4) 0.155 0.090 ( 3) 0.062

79.000E-4( 6) 65.265E-4 74.400E-4( 11) 52.453E-4

4.4OOE-4(>99) 0.792E-4 Q.O94E-4 O.l25E-4

---------- Sum = l(Jo.001

(31 2) (51 2) (31 3) ('1 2) ( (31 4;

(51 3) (11 3)

--- Ernax q

35K 35Ar(33) (31 1) ('1 1) (51 1) (31 2)

5964 - - - a - - -

0( 0)

1184 (< 1) 18.683

0.032 8.725 0.406

21.730 1.306

0.001

2.046

42.239

1.016 1.528 1.162 0.338 0.035 0.117 0.057 0.013 0.055

15.064E-4 32.32lE-4

0.190 0.128 O.O67E-4 0.040 0.013 0.039 0.013 a.043

28.896E-4 1.255E-4

99.962

40.823 10.465

43.324

0.641

1.789 0.723

0.005 0.146

0.059 1.219 0.163 0.224 0.126 a.019 a.134 9.410E-4

0 1244 1780 2672 3146 4088 3962

5089

5957

2.200 ( 31) 11.900 ( 7)

0.400 (>99) 26.000 ( '1)

0.550 I 54)

1751 i< ij 2638 (< 1) 2983 (< 1) 3884 ( 1) 4065 (< 1) 4528 (< 1) 4726 (< 1) 4786 ( 1) 5537 (< 1)

7510 ( 20) 8395 ( 20)

is.1 2j (1’ 2) (31 3)

111 3;

( [33 1;

1 ( 1

0.700 i 57j 2.100 ( 19) 1.000 ( 40)

36.000 ( 8) 0.150 ( 40) 0.062 ( 41)

(51 3) (31 4) (51 4) (31 5) (51 5) (51 6) (31 6) i51 7) ('1 4) (11 5) (13 1) (31 7) (31 8)

(1 1 6) (5' 8) (31 9)

4595 4788 5536 5677 5879 6394 6932 7050 7206 7404 7514

_--..-__-----

7577 7979 8203 8377 8429 8447 8637 8760 8622 9295

--- Emax = 11880

(51 9) (53 1) ( 5 I 10) ( 3 1 10) ('1 7) - ---------- Sum =

( 10) ( '0) (pQ9)

I 1:;

I :x; ( '0) ( 10) ( '0) ( '0)

: 2; ( la) ( 10)

36K 36Ar(42) (40 1) (40 2) (40 (42 1; (40 1 ( 1

1970 (< 1) 4441 (< 1) 4951 (< 1) 6612 i< lj 6730 ( 2)

1927 4410

6657

43.700 8.300 0.200

42.000 0.900

a.400 0.700 0.800 1.900

0.500 0.200 0.100 0.200 Ct.100 0.200

6867 (< 1) 7140 (< 1) 7178 (< 1) 7338 (< 1) 7710 (< 1) 7971 (< 1) 8133 (< 1) 6556 i< lj 9220 ( 1) 9502 (< 1)

7248

7462 7858

8192 8661

Y” ‘) 1 (62 1) (22 1) ( 1 (22 2) (42 2)

7099 7174

(40 5) (42 2) (42 3) (22 3) (20 2)

8093 8265 8661 9103 9120 9314

390 Atcmk Data and Nuclear Data Tables. Vol. 33. No. 3. November 1995



lW(fA) W/A) ww WW) Alog elm (“4 W) ew ew th

1 .961 0.09 0.75 5.005 (0.018) 5.014 1 .682 0.08 1.17 4.977 (0.016) 5.133

0.530 0.05 7.90 4.882 (0.029) 4.958 0.445 0.05 9.15 4.823 (0.051) 4.968

-0.851 0.01 81.44 a4.755 -1.047 0.00 98.46 5.297 -0.804 0.01 76.30 6.467 -1.311 0.00 100.00 5.834

---__-------------- _--_--_-_-~--_--___--

5.104 0.20 0.01 4.865 0.20 0.01 4.740 0.20 0.01 4.528 0.20 0.02 4.440 0.19 0.02 4.191 0.19 0.03 4.137 0.18 0.03 3.993 0.18 0.04 3.929 0.18 0.05 3.909 0.18 0.05 3.642 0.16 0.07 2.721 0.12 0.27 2. 127 0.10 0.68 3.972 0.18 0.04 3.908 0.18 0.05 3.642 0.16 0.07 3.588 0.16 0.07 3.508 0.16 0.08 3.290 0.15 0.12 3.034 0.14 0.17 2.974 0.13 0.19 2.891 0.13 0.21 2.782 0.13 0.25 2.719 0.12 0.27 2.681 0.12 0.29 2.427 0.11 0.43 2.271 0.10 0.55 2.141 0.10 0.67 2.100 0.10 0.71 2.086 0.10 0.73 1.930 0.09 0.93 1.804 0.09 1.14 1 .765 0.09 1.21 1.274 0.07 2.68 -------------------

5.801 (0.154) 4.943 (0.076)

b6.205 4.304 (0.085)

5.675 (0.247) 5.427 (0.257) 4.885 (0.108) 5.188 (0.187) 3.364 (0.078) 4.824 (0.188) 4.613 (0.196)

5.113 7.637 5.079 6.200 4.383 5.355 8.548

4.898

3.296

5.245 5.004 4.857 5.339 6.239 5.503 5.556 6.149 5.430 6.884 6.489 4.682 4.600 8.727 4.820 5.258 4.777 5.095 4.451 5.585 6.456

4.894 0.20 0.01 4.296 0.19 0.03 4.149 0.19 0.03 3.584 0.16 0.08 3.538 0.16 0.08 3.482 0.16 0.09 3.368 0.15 0.10 3.351 0.15 0.11 3.281 0.15 0.12 3.108 0.14 0.15 2.976 0.13 0.19 2.891 0.13 0.21 2.649 0.12 0.31 2.203 0.10 0.61 1 .980 0.09 0.86 3.386 0.15 0.10 3.353 0.15 0.11 2.912 0.13 0.21 2.818 0.13 0.24 2.584 0.12 0.34 2.289 0.11 0.53 2.276 0.11 0.54 2.131 0.10 0.68

4.788 4.911

~6.382 3.495 5.118 5.415 5.057 4.982 4.536 4.943 5.209 5.425 4.882 4.737 4.213

(0.043) (0.044)

(0.044) (0.044) (0.044) (0.044) (0.044) (0.044) (0.044) (0.044) (0.044) io.044j (0.044) (0.044)

4.822 4.815

3.486

5.100 0.520 (0.026) 0.495 0.691

4.567 4.787

0.567 (0.028) 0.947 (0.048) 0.914 1.218

6.714 5.023

0.947

0.053 0.733

0.593 (0.030) 0.709 0.437 (0.022) 0.341 (0.017) 0.077 0.636 (0.032) 0.541 0.752 (0.038) 1.374 (0.070)

0.147 0.694 0.422 0.551 0.541 0.292 0.794 0.079

6.156 4.806 5.239 5.006 5.023 5.560 4.690 6.697

391 AtMnicDataandN-DalaTeblea.Vol.33.No.3.November1085

M&W AM(GT)

w w

0.494 (0.010) 0.510 (0.009) 0.569 (0.019) 0.609 (0.036)

~0.658

0.198 (0.035) 0.531 (0.047)

<O. 124 1.107 (0.108)

0.228 (0.065) 0.304 (0.090) 0.567 (0.070) 0.400 (0.086)

>o 0.609 (0.131) 0.776 (0.175)

W’W M(GT1 th(eff) th(free)

0.489 0.632 0.426 0.580 0.522 0.734 0.516 0.709

0.353 0.501 0.092 0.122 0.190 0.243

-- w = 4.334

0.436 0.589 0.024 0.019 0.454 0.630 0.125 0.157 1.011 1.393 0.330 0.405 0.008 0.077

0.559 0.748

0.705 0.937

0.375 0.470 0.494 0.600 0.585 0.786 0.336 0.417 0.119 0.222 0.278 0.384 0.262 0.362 0.132 0.144 0.303 0.414 0.057 0.089 0.089 0.157 0.716 0.954 0.787 1.066 0.007 0.011 0.611 0.817 0.369 0.507 0.642 0.889 0.445 0.622 0.935 1.274 0.253 0.344 0.093 0.108

----------------- w = 7.506

0.709 (0.036) 0.682 0.935 0.615 (0.031) 0.687 0.879

co.113 ‘0 0.290 0.388

0.485 (0.024) 0.345 (0.017)

0.163 0.972 0.570 0.762 0.733 0.449 1.075

0.110

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller /3 Decay in &Shell Nuclei

T’ABLE II. Experimental and Theoretical Final-State Excitation Energies, Branching Ratios, ft Values, and Gamow-Teller Matrix Elements See page 362 for Explanation of Tables

Ai Z 4 Z

3’Ar

3'K

3’Cl

3’Ar

3’Ca 3’u

38K

38Km

3*Ctl

3gCa

3*Ar

3*Ar

38K

3%

2J,2T, 2Jf2Tf nf E,(exp) AEI WV

WV) WV) WV)

(60 2) 9485 (62 2) 9508 (40 6) 9538 --- Emax = 12805 ---_---_-_--

(31) (33 1) O( 0) --- Emax = 813 --.v--m-e-"

1 1) O( 0) 0 1 1) 1410 (< 1) 1586 1 1) 2796 (< 1) 2884 1 2) 3171 ( 1) 3112 1 2) 3602 (< 1) 3539 1 2) 4620 1 3) 5091 1

:; 5665

1 5965 1 4) 6128 1 4) 6881 Emax = 6148 __-_-____-__

(33)(31 1) (11 1) (51 1) (51 2) (31 2)

I ; (11 21 i j

i33 1; (11 3) ( 1 ( ) ( (31 3; (51 3) (51 4) (13 1) --- Emax =

O( 0) 1368 (< 1) 2750 ( 1) 2970 ( 1) 3617 ( 8) 3840 ( 7) 4417 .( 5) 4509 ( 5) 4665 ( 8) 5023 ( 6) 5047 ( 3) 5122 ( 6) 5319 ( 6) 5448 ( 6) 6016 ( 8)

1,636 -------

0 1586 2884 3112 3539

4620

4883 5665

509 1 5965 6128 6721

_----

(60)(42 1) 2168 (< 1) 2013 99.849 99.972 (42 2) 3937 (< 1) 4489 0.151 :' :: 0.028

(42 (42 ;

4565 (< 1) 30.000E-4(>99) 5157 (< 1) 40.000E-4(>99)

--- Emax = 5912 ------------ ---------- S"m = 100.000

(02)(02 1) O( 0) 311 100.000 (< 1) 100.000 --- Emax = 6042 ____________ ---------- Sum = 100.000

(02)(02 1) 130 (< 1) 311 (20 1) 459 (< 1) 635 ~~00 i; 3342 1698 i< (< 1) 1) 4143 1721

--- Eman = 6742 --_----_----

76.100 ( 2) 83.145 2.660 ( 13) 2.412

21.000 : 13,'

13.176 0.291 1.318

---------- Sum = 100.051

(31) (31 1) O( 0) 0 (11 1) 2523 (< 1) 2730 (51 1) 7418 --- Emax = 6524 -------o--e-

100.000 (< 1) 100.000 23.300E-4( 25) 26.375E-4

---------- Sum 5 1()0.002

392 Atomk Data and Nucbaf Data T&b% Vol. 33. No. 3. NwembW 1985


(W v4 ("4

0.047 0.094 1.219E-4

---------- Sum = 100.000

100.000 ---------';";~

100.000 = 100.000

98.200 (< 1) 98.127 0.020

1'7:; 0.000

1.800 1.831 60.000E-4(>99) 481.728E-4

0.019 ( 15) 0.012 0.819E-4 l.l22E-4

0.365E-4 O.l56E-4 O.OOOE-4

---------- S"m = ,oo.(),g

18.872 8.400 ( 29) 4.052 6.400 ( 10) 14.118

3.922 4.020 ( 9) 4.521 4.480 1.150 I 12; 2.080 ( 11) 6.846 1.150 ( 40) 1.900 ( 31)

44.318 5.900

: 2:; 1.775

1.050 0.510 0.650 I 2;

1.519 0.034 0.040 0.012

_*-------- Sum = 100.030

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller p Decay in s&hell Nuclei


Wf A) W/A) pw (“4 t-4

1.994 0.10 0.84 1.975 0.09 0.87 1.952 0.09 0.90 _____-_------------

log(w) ilWfAV WfAt) ew em th

4.860 4.543 7.405

---------------------

M&W AM(GT) M&W

ev ew th(eff)

0.653 0.940 0.035

_---------------- w =

WV th(free)

0.924 1 .328

0.055 6.852

-1.375 0.00 100.00 5.106 (0.001) 4.994 _-__--------------- ---------------------

0.440 (0.000) 0.500 0.673 ----------------- w = 4.334

3.567 0.16 0.08 3.663 (0.003) 3.664 1.169 (0.016) 1.162 1 .560 2.926 0.13 0.20 a6.714 8.786 CO.069 0.006 0.041 2.021 0.10 0.81 3.854 (0.072) 3.848 1.858 CO.1551 1 .873 2.605 1 .689 0.09 1.37 B5.999 5.096 co. 157 0.445 0.648 1.228 0.07 2.89 5.038 (0.069) 5.227 0.475 (0.038) 0.383 0.563

-0.466 0.02 51 .46 5.710 0.219 0.294 -1.075 0.00 100.00 4.964 0.518 0.694 -1.759 0.00 100.00 4.769 0.648 0.888 -2.610 0.00 100.00 4.287 1.130 1 .546 -4.651 0.00 100.00 6.155 0.131 0.141

0.00 5.140 0.423 0.572 _____-------------- ____-_--------------- ----------------- w = 4.334

5.050 0.22 0.01 4.763 0.22 0.02 4.430 0.21 0.03 4.371 0.21 0.03 4.190 0.20 0.04 4.124 0.20 0.04 3.943 0.19 0.05 3.912 0.19 0.06 3.860 0.19 0.06 3.734 0.18 0.07 3.725 0.18 0.07 3.698 0.18 0.08 3.624 0.18 0.08 3.575 0.18 0.09 3.341 0.16 0.13 3.709 0.18 0.07 3.363 0.16 0.12 3.292 0.16 0.14 3.010 0.15 0.21 ------------------- -----__----______ w = 7.506

2.319 0.11 0.51 4.981 (0.001) 4.875 0.672 (0.001) 0.759 0.987 0.407 0.05 11 .52 5.889 (0.035) 6.519 0.236 (0.009) 0.114 0.237

-0.785 0.01 83.30 >6.399 co. 131 -1 .369 0.00 100.00 >5.690 co.297

_____-------------- __------------------- _______---------- w = 6.852

3.525 0.16 0.08 _-_----------------

3.491 (0.000) 3.490 ----------------- w = 3.064

3.734 0.18 0.07 3.491 (0.014) 3.490 3.611 0. 18 0.09 4.825 (0.058) 4.905 3.075 0.15 0.19 3.391 to.0351 3.631 2.052 0.11 0.92 4.227 (0.058) 3.609 ------------------- ---------------------

0.304 (0.020) 0.277 0.436 1.583 (0.063) 1.201 1 .655

0.805 CO.0401 1.233 1 .693 ----------------- w = 3.064

3.702 0.18 0.08 3.636 CO.0021 3.612 1.308 (0.011) 1 .425 1 ,938 2.486 0.12 0.47 7.053 (0.110) 6.975 0.047 (0.006) 0.051 0.000

0.00 3.515 2.745 3.876 ___-_-------------- ___------------------ ____-_----------- I& = 4.334

5.082 CO.1301 4.866 (0.049)

4.829 CO.0441 4.716 (0.034) 5.125 (0.055) 4.837 (0.052) 5.042 (0.174) 4.698 (0.138)

4.170 (0.040) 4.846 (0.113) 5.110 (0.163) 4.771 (0.063)

4.994 5.376 4.500 4.998 4.755

4.297

3.299 4.669

4.748 6.046 5.906 6.161

0.452 (0.068) 0.579 co.0331

0.605 (0.031) 0.689 (0.027) 0.430 (0.027) 0.599 CO.0361 0.473 (0.095) 0.703 (0.112)

1.291 (0.060) 0.593 co.0771 0.438 (0.082) 0.646 (0.047)

0.500 0.673 0.322 0.462 0.884 1.200 0.498 0.623 0.658 0.990

1.116 1 .496

0.640 0.868 0.727 0.984

0.664 0.907 0.149 0.163 0.175 0.211 0.130 0.151

393 Atomic Data and Nuclear Data Tables. Vol. 33. NO. 3. November 1985

4 z

“F

‘0F

‘*Ne

‘90

1 QNe

200

20F

2ONi3

2’0

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller 0 Decay in s&Shell Nuclei

TABLE III. Theoretical Multiparticle Transition Amplitudes See page 362 for Explanation of Tables

At Zt 2J, 2T, 2Jf 2T, nf

"0 ( 5 1) (5 1 1) (31 1)

‘60 ( 2 0) ( 0 2 1)

‘6F (02)(20 1) (20 2)

‘9F (53)(5l 1)

K ‘) (31 :;

‘QF ( 1 1) ( 1 l 1) (31 1)

20F (O4)(22 1) 1048 (22 2) 3348 (22 3) 4882 !22 4) 5211

2oNe(42) (40 1) 1776

20Ne(42) (40 1) (40 2) (60 1) (42 1) (40 3) (40 4) (62 1) (22 1) (60 2) (20 1) (42 2) (62 2) (40 5) (62 3) (60 3) (40 6) (22 2) (60 4) (42 3) (40 7)

2’F (55)(53 1) (33 1) (33 2) (53 2) (73 1) (33 3) (53 3) (73 2) (33 4) (53 4) (73 3) (33 5) (73 4) (73 5) i53 5) (53 6) (33 6) (53 7) (53 0) (73 6) (53 9) ( 5 3 10)

(73 7) (33 7)

El WV)

0 5595

0

0 4108

99 1698

487 1 6627

0 1698

1776 7316

10230 10148 10437 10737 10746 11196 11437 12234 12243 12346 12955 13044 ‘3060 13307 13496 13509 13510 13561

0 1853 3512 3681 3611 4097 4269 4427 4660 5122 5283 4892 5602 5720 5956 6284 6534 6562 6790 6956 7313 7435 7459 7660

AU’)

5-5 5-3 l-l l-3 3-5 3-l 3-3

1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ?.OOO 0.000 0.000

0.274 -0.223 0.217 -0.042 0.075 0.019 0.000

0.274 -0.075 0.217 -0.019 0.223 0.042 0.000 -0.373 -0.007 0.197 -0.055 0.021 0.124 0.011

-0.485 0.008 0.102 -0.052 0.261 -0.002 -0.022 0.450 -0.047 0.147 0.046 -0.230 0.019 0.042

-0.638 0.185 -0.112 -0.011 -0.047 0.021 0.002 -0.174 0.046 -0.019 0.084 0.021 0.009 -0.016

-0.241 0.105 -0.408 0.013 -0.105 -0.013 0.012 -0.149 -0.057 0.019 -0.123 0.102 0.264 0.038

0.550 -0.061 -0.006 0.080 -0,.222 -0.019 0.046 0.090 -0.092 0.319 -0.056 0.110 0.055 0.004 0.167 -0.092 -0.063 -0.048 0.071 -0.154 0.005

-0.054 0.116 0.032 0.037 -0.230 -0.190 0.031

-0.278 0.066 -0.036 -0.100 0.161 0.029 -0.031

-0.278 0.066 -0.036 -0.100 0.161 0.029 -0.031 0.252 -0.193 0.043 -0.068 -0.047 -0.001 -0.023 0.067 -0.084 -0.040 -0.120 0.070 0.035 0.036 0.064 0.073 -0.323

-0.225 0.155 -0.111 0.205 0.305

-0.609 -0.327 -0.263

0.156 -0.535

0.071 0.268 0.099 0.015 0.057 0.154 0.051 0.032 0.357 0.133 -0.051 -0.043 0.010 -0.035 0.008

-0.081 -0.033 -0.052 0.139 -0.029 0.054 -0.077 -0.027 -0.101 0.016 -0.097 0.167 0.030 -0.080

0.048 0.045 0.070 0.013 0.140 0.058 0.004 -0.202 0.040 0.139 0.140 -0.053 -0.012 0.006

0.076 0.007 -0.019 -0.005 -0.121 -0.073 -0.025

0.207 0.031 0.394 -0.041

-0.605 0.000 -0.630 0.086

-0.034 -0.055 0.006 -0.037 0.073 -0.229

-0.110 0.048 -0.004 -0.052

0.013 -0.036 -0.207 -0.047

0.062 0.131

0.002 -0.073 -0.002 0.022 0.001 -0.248 -0.029 -0.001

-0.030 0.147 0.024 0.001 0.076 0.089 -0.109 0.012

-0.025 -0.159 0.040 0.016 0.035 0.077 -0.063 0.053 -0.194 -0.061 0.109 -0.020 -0.120

-0.072 0.005 0.138 -0.030 0.073 0.047

-0.012 -0.008 -0.158 0.005 -0.006 -0.235 0.028 -0.036 0.304 0.060 0.000 0.274

0.002 0.060

-0 .a,! 3 0.025

-0.005

-0.010 -0.009 0.001 0.001 0.003 -0.022 0.022 -0.012

0.109 -0.052 0.022 0.025 -0.103 -0.058 0.035 0.530 -0.029 0.135 0.016 -0.305 -0.011 0.014 0.620 0.055 -0.090 0.067 -0.325 0.029 -0.013 0.308 -0.097 -0.120 0.012 -0.142 -0.021 -0.001 0.326 0.017 0.011 -0.011 -O:194 0.007 0.036

-0.059 0.031 0. 1.61 -0.043 0.000 0.035 -0.001 0.069 -0.040 -0.117 0.00’ -0.300 -0.112 0.060

-0.243 0.025 -0.000 -0.076 0.145 -0.074 0.009 -0.440 0.091 -0.135 -0.058 0.152 -0.056 -0.029

0.506 0.001 0.166 0.050 -0.273 -0.033 0.017 -0.090 0.065 -0.032 -0.004 0.055 0.020 0.007

0.349 -0.111 0.226 -0.111 -0.039 0.054 0.013 -i:iO+ -0.066 -0.162 -0.032 0.145 0.040 -0.010 -0.343 0.001 0.145 -0.000 0.225 0.069 0.044 -0.263 0.060 -0.113 0.043 0.115 0.131 0.024 -0.054 -0.193 0.064 -0.073 0.197 0.036 -0.043

0.160 -0.013 -0.182 0.050 0.055 -0.082 -0.030 -0.313 -0.015 -0.043 -0.020 0.126 0.023 -0.006

O.006 0.049 0.002 -0.044 -0.132 -0.020 0.026 -0.334 -0.090 0.183 0.009 0.177 0.026 -0.038

394 Atombz Data and Nuclear Data TabcM. Vol. 33. No. 3. November 1885

Ai z At Zr 2J, 2T, 2J, 2Tf n,

21,

*‘NE4

2’MQ

**F

**Na

**tdg

*3Ne

23MQ

24Ne


TABLE III. Theoretical Multiparticie Transition Amplitudes See page 362 for Explanation of Tables

(73 5) 7945 (33 0) ala2 (73 9) 6245

*‘Ne ( 5 3) ( 3 1 1) (51 1) (71 1) (51 2)

0 247

1795 3731 4575 4709 5377

(51 3) (31 2) (71 2)

*‘Ne ( 3 1) ( 3 1 1) 0 (51 1) 247 (11 1) 2870

*‘Na ( 5 3) ( 3 1 1) (51 1) (71 1) (51 2)

0 247

1795 3731 4575 4789 5690 5377 578 i 6287 6439 6974 7275 7379 7560 7667 a092 a308 a592 8600 0697

**NC3

(51 3) (31 2) (53 1) (71 2) (31 3) (71 3) (31 4) (71 4) (5’ 4) (71 5,) (31 5) (51 5) (51 6) (31 6) (71 61 (5’ 7) (31 7)

(es)(an 1) (a2 2) (62 1) (a2 3) (62 2) (a2 4) (62 3) il0 2 1) (62 4) (10 2 2)

**Ne ( 6 0) ( 4 2 1)

**Na(O2) (20 1) (20 2)

‘(‘,“o 3, 4)

23Na(53) (31 1) (51 1) (71 1) (31 2) (51 2) (71 2)

3378 -0.047 -0.045 - 0.043 0.074 0.068 0.005 0.063 5480 0.556 -0.189 0.062 -0.014 -0.370 0.001 0.039 5635 0.379 -0.108 0.019 0.019 -0.233 0.006 0.006 6430 -0.619 -0.052 0.029 -0.004 0.333 0.023 0.013 6519 0.399 0.020 0.060 0.010 -0.266 -0.010 0.040 6992 0.162 -0,096 0.119 -0.026 -0.060 -0.026 0.013 7741 -0.054 -0.027 - .O.l67 -0.023 0.056 -0.034 0.001 7461 -0.757 0.001 0.006 -0.133 0.302 0.056 - -0.066 a435 -0.095 0.021 0.011 -0.034 0.064 0.045 - -0.022 0696 0.707 0.095 0.065 0.150 -0.305 -0.077 - -0.009

1368

391 2024 3985 5673

0 411

2131 2747 3893 4636

23Na ( 3 1) ( 3 1 1) 0 (51 1) 411 (11 1) 2323 (31 2) 2747

24Na(04) (22 1) 448

6 WV) 5-5 5-3 l-l l-3 3-5 3-l 3-3

-0.197 -0.037 0.069 -0.014 0.254 0.108 -0.011 -0.657 -0.075 -0.090 0.018 0.243 0.016 0.004

0.114 0.052 -0.179 0.008 -0. i 15 0.092 0.027

0.120 -0.060 0.064 0.001 -0.108 0.019 0.012 0.404 -0.109 0.057 0.076 -0.240 0.014 0.072

-0.549 0.000 0.040 -0.152 0.203 0.090 -0.061 0.116 0.100 -0.019 0.046 -0.058 0.022 0.024

-0.111 0.066 -0.200 -0.034 0.026 0.007 0.030 -0.112 0.153 -0.169 0.027 0.020 -0.042 -0.006

0.201 0.002 0.002 -0.030 -0.078 -0.107 0.028

0.359 -0.100 -0.069 0.009 0.100 -0.009 0.025 -0.106 0.112 0.010 -0.007 -0.076 0.065 -0.030

0.173 -0.053 -0.033 -0.152 0.032 0.007 -0.013

0.120 -0.060 0.064 0.001 -0.108 0.019 0.012 0.404 -0.109 0.057 0.076 -0.240 0.014 0.072

-0.549 0.000 0.040 -0.152 0.203 0.090 -0.061 0.116 0.100 -0.019 0.046 -0.050 0.022 0.024

-0.111 0.066 -0.200 -0.034 0.026 0.007 0.030 -0.112 0.153 -0.169 0.027 0.020 -0.042 -0.006 -0.523 0.055 -0.200 -0.082 -0.050 0.082 0.021

0.201 0.002 0.002 -0.030 -0.078 -0.107 0.025 0. iaa -0.170 -0.141 0.042 0.060 -0.044 0.008 0.212 0.006 0.051 -0.064 -0.039 -0.081 0.029 0.171 -0.105 -0.008 -0.006 0.006 -0.005 - .O.OlQ

-0.177 -0.045 0.050 -0.170 0.169 0.200 0.027 -0.110 0.097 0.047 0.050 -0.073 -0.006 0 .QO2 -0.092 0.01’ 0.064 0.062 -0.046 0.153 - .o .045

0.415 -0.046 0.044 0.127 -0.004 -0.038 0.038 -0.177 0.164 0.057 0.050 -0.191 -0.040 0.054

0.337 0.232 -0.149 -0.033 -0.220 -0.003 0.094 -0.204 0.059 -0.015 0.037 -0.079 0.003 0.017

0.504 -0.056 -0.032 -0.106 0.352 0.099 -0.002 -0.216 0.055 -0.175 0.035 -0.320 -0.086 0.056 -0.370 0.032 -0.129 0.012 -0.209 -0.002 -0.022

-0.050 -0.033 -0.015 -0.021 0.024 0.017 -0.020

0.292 -0.062 -0.030 0.033 0.142 -0.040 0.021 0.048 -0.072 0.031 -0.081 0.247 0.076 -0.065

-0.230 -0.135 -0.117 -0.016 -0.053 0.008 -0.010 -0.260 -0.031 0.136 0.019 0.102 0.035 0.032

-0.409 -0.020 -0.066 0.032 0.255 0.022 -0.013 -0.340 -0.002 -0.046 0.047 0.243 0.021 0.021 r;.;W; -0.052 -0.030 0.032 0.115 -0.016 -0.001

0.021 -01023 -0.019

0.009 0.024 -0.007 -0.007 0.034 0.005 -0.026 0.022 0.014 -0.010

0.042 -0.004 0.015 -0.004 0.016 0.065 -0.043

-0.292 0.099 0.097 -0.072 -0.099 0.072 -0.031 -0.225 0.060 0.010 0.002 -0.076 0.088 -0.031

0.136 0.165 0.026 0.096 -0.170 -0.057 0.006 0.044 -0.095 0.009 -0.013 0.194 0.066 -0.100

-0.370 -0.034 -0.129 0.051 0.232 0.046 -0.009

395 Atomic Data and Nudear Data Tables. Vol. 33. No. 3. November 1995

396 B. A. BROWN and B. H. WILDENTHAL Gamow-Teller fi Decay in &Shell Nuclei


A, zl At Zt 2J, 2T, 2J, 2Tf n,

(22 2)

24NZ3 24M9(82) (80 1)

(60 1)

24A 1 24M9(82) (eo 1)

(60 1) (80 2) (10 0 1) (80 3) I00 4) !;; 2j

1) (10 0 2) (62 1) (60 3) is0 5) (10 2 1) (62 2) (60 4) (80 6) (60 5) (62 3) (80 7) (82 2) (00 8) (62 4) (10 0 3) (82 3)

24Alm 24Mg ( 2 2) ( 0 0 1) (40 1) (40 2) (20 2) (22 1) (42 1) (00 4) (00 2) (40 3) (20 1) (40 4) (00 3) (40 5) is0 6j (22 2) (42 2) (42 3) (40 7) (40 8) (40 9) ( 4 0 10) (42 4) (22 3) (02 1) (22 4)

0 1510

4123 9987 9991

10131 10679

7562 7443 7764 894 1 9561 9077

10479 10635 10676 11146 11110 11820 11956 12289 12369 12753 12872 13142

=Ne 25Na(15) (33 1) 132 (13 1) 1159 (33 2) 2130 (33 31 3304 (33 4) 3623 (13 2) 4048 (13 3) 5134 ( 13 4) 5725

25NCI 25Mg(53) (51 1) (31 1) (71 1) (51 2)

Et WV) 1092

4379 5097

4379 5097 5935 7864 8374 9640 9596 9543

IO565 10917 10804 11039 11092 11294 11224 11378 11580 11723 11746 12103 12128 12192 12296 12426

0 1200 1730 2094

5-5 5-3 l-l l-3 3-5 3-l 3-3

-0.107 0.030 -0.055 0.004 -0.037 -0.002 -0.009

0.120 -0.000 0.049 0.000 -0.070 -0.028 0.011 -0.028 0.052 0.042 0.035 0.011 0.004 0.056

0.120 -0.000 0.049 0.008 -0.070 -0.028 0.011 -0.020 0.052 0.042 0.035 0.011 0.004 0,056

0.120 -0.002 -0.003 0.004 -0.069 0.021 -0.044 0.011 -0.009 0.026 0.007 -0.016 0.040 -0.030

-0.920 0.000 0.026 -0.001 0.076 0.135 0.021 -0.260 0.044 0.052 -0.047 -0.050 0.001 0.005 -0.075 -0.073 -0.054 -0.030 0.000 0.021 -0.019

0.351 0.172 0.110 -0.094 -0. 172 0.094 -0,072 0,540 0.097 0.022 -0.032 0.045 -0.040 0.001

-0.344 -0.088 -0.103 -0.126 -0.005 0.021 -0.006 -0.172 -0.111 -0.071 0.001 0.139 0.042 -0.033 -0,071 0.058 0.082 -0.040 -0.094 -0.023 0.010 -0.603 -0.303 -0.064 -0.083 0.102 -0.090 0.015

0.202 0.062 0.006 -0.039 -0.000 -0.043 0.032 -0.097 -0.128 0.047 -0.031 0.192 0.052 -0.006 -0.186 0.004 0.026 0.026 -0.127 0.035 -0.026 -0.049 -0.021 -0.009 -0.020 0.044 -0.002 -0.019

0.140 0.078 -0.031 0.000 -0.100 -0.040 0.041 0.059 -0.032 -0.052 0.069 0.075 0.029 0.006 0.182 0.126 0.135 0.017 -0.033 -0.010 0.‘1319

-0.033 0.033 -0.024 0.061 -0.115 -0.003 -0.025 0.197 0.249 -0.039 0.115 -0.155 -0.06c 0.118

-0.026 -0.013 0.004 0.019 -0.045 -0.022 0.001 -0.064 -0.040 -0.037 0.105 0.053 -0.012 0.005

-0.240 0.011 -0.051 0.048 0.168 0.047 -0.021 -0.216 -0.056 -0.068 0.025 0.150 0.017 0.007

0.028 0.046 -0.030 0.031 0.024 0.055 0.024 -0.015 0.002 -0.027 0.010 -0.017 -0.033 0.002

0.592 -0.057 -0.045 0.076 0.057 -0.076 0.002 -0.653 -0.045 0.010 -0.060 0.023 0.132 -0.016 -0.069 -0.017 -0.062 -0.023 -0.031 -0.003

0.072 0.025 0.177 0.126

-0.035 -0.028 -0.157 -0.081

0.029 -0.005 0.029 0.013

-0.232 0.060 0.003 -0.011

-0.325 -0.120 -0.029 0.013

0.074 0.053 0.052 -0.027

-0.076 0.090 0.097 0.007

-0.007 -0.009 -0.154 -0.068

-0.002 0.015

-0.020 -0.002

0.009 -0.044

0.036 -0.015

0.015 0.065

-0.017 -0.082 -0.031

0.033 -0.001

0.057 -0.013

0.130 -0.025 0.015 -0.009 -0.026 0.079

0.023 0.074 -0.040 0.026

0.018 0.021 -0.003 -0.027

0.014 -0.092 0.024 0.054

-0.037 0.044 0.006 0.007

-0.014 -0.032 0.023 -0.120

-0.025 0.003 0.028 -0.001 0.010 -0.025

-0.032 -0.099 -0.042 0.026

0.032 -0.171 -0.020 0.077

-0.082 0.007

-0.081 0.039

-0.038 0.051 0.025

-0.045 0.000

-0.022 0.001 0.012 0.020 -0.008

-0.052 0.024 0.018 0.016 0.015 -0.047

-0.030 0.081 0.018 0.023

-0.052 -0.006 0.011 0.074

0.016 0.029 0.032

-0.016 0.044

-0.003 0.001

-0.035 -0.015

0.053

0.296 -0.143 -0.032 0.074 -0.101 0.204 0.014 0.236 0.024 -0.601 -0.013 0.125 -0.012 0.020 0.147 0.004 0.027 -0.009 0.018 0.507 0.039 0.383 -0.011 0.070 -0.005 -0.279 -0.160 0.052

-01053 -0.042 -0.015 0.001 0.093 0.028 -0.007 0.196 0.054 0.412 -0.031 -0.232 -0.005 -0.010 0.259 0.021 0.000 -0.016 -0.139 -0.014 -0.023

-0.321 -0.093 -0.197 -0.006 0.206 0.010 0.068

0.245 -0.064 0.062 -0.023 -0.166 -0.047 0.040 0:051 -0.069 0.124 0.006 -0.004 0.071 0.000

-0.441 -0.091 -0.155 0.021 0.255 0.070 -0.010 0.106 -0.024 -0.115 0.015 0.025 0.000 0.009

AtOmk Data and Nudmr Data Tab&s. Vol. 33. No. 3. November 1985



AI 2, A, Zf 2J, 2T, 2J, 2T, nf

25A I

(71 2) (31 2)

*%lg ( 5 1) ( 5 1 1) (31 1) (71 1) (51 2) (71 2) (31 2)

*6N, ‘%9(64)(42 1) (42 2) (62 1) (82 1) (42 3j (62 2) (42 4) (82 2) (42 5) (82 3) (82 4) (62 3) (42 6) (82 5) (42 7) (42 8) (62 4) (82 6) 142 9) (62 5) (82 7) (62 6) ( 4 2 10) (62 7) (82 8) (82 9) ( 8 2 10) (62 8)

1928 3153 3921 4532 4540 4510 5000 4932 5403 5472 6008 6268 6646 6777 6843 7092 7281 7410 7473 7602 7940 8004 8391 8404 8413 8790 8958 9115

26Si 26A1 (02) (20 1) 818 (20 2) 1737 (20 3) 2003 (20 4) 2899 (20 5) 3685 (20 6) 4937 (20 7) 5154 (20 81 5667

*7NL?? *7Mg (55)(33 1) (53 1)

IX *) 1) (73 2) (33 2) (33 3) (53 3) (53 4) (73 3) (53 5)

i5: 6, (33 a; (33 5) (53 7) (73 5) (33 6) (73 6) (33 71 (53 8j (33 8)

El WeV) 2980 2908

0 1200 1730 2094 2980 2908

895 1667 1970

3149 3300 3162 3632 4032 4201 4616 4719 5101 5206 5226 5404 5454 548 1 5656 5813 5807 6086 6428

4’)

5-5 5-3 l-l I-3 3-5 3-l 3-3

-0.031 -0.031 -0.019 0.028 0.069 -0.031 0.024 0.039 -0.164 -0.083 -0.055 0.039 -0.061 -0.054

0.700 0.032 0.045 0.028 -0.032 -0.028 -0.035 -0.005 -0.024 0.000 0.037 0.050 0.016 0.015

0.532 0.153 0.028 0.048 0.020 0.012 -0.010 -0.027 -0.010 -0.058 0.079 0.045 0.024 -0.007

0.006 0.005 -0.015 0.016 0.020 -0.016 0.034 0.009 -0.045 -0.029 -0.050 0.097 -0.018 0.027

-0.015 -0.202 0.487 -0.050 -0.201 0.176 -0.026 -0.081 0.002 0.188 -0.029 -0.054 0.044 -0.022

0.222 -0.046 0.040 -0.009 -0.166 -0.090 0.042 -0.158 -0.038 -0.036 0.030 0.077 -0.042 -0.034

0.159 -0.097 -0.099 0.013 -0.017 0.000 -0.004 -0.021 0.006 -0.425 -0.121 0.114 -0.155 -0.018 -0.247 0.020 0.768 -0.088 -0.159 -0.088 0.006

0.101 -0.054 0.002 0.214 -0.152 -0.562 -0.057 0.086 0.037 0.110 -0.022 -0.083 0.091 0.000

-0.295 -0.059 -0.097 0.139 0.200 -0.065 -0.038 0.437 0.033 0.037 0.076 -0.138 0.433 0.072 0.282 0.015 0.434 0.056 -0.245 0.164 0.023 0.019 -0.108 -0.124 -0.029 0.045 -0.066 -0.032 0.067 -0.034 -0.023 0.107 0.023 -0.035 0.008

-0.053 0.011 0.127 -0.018 0.005 0.099 -0.013 0.232 0.041 0.158 -0.001 -0.140 0.235 -0.064 0.101 0.005 -0,430 0,024 0.045 -0.196 0.046

-0.033 -0 026 -0.026 0.042 -0.032 -0.354 -0 008 -0.144 -0 087 0.285 -0.023 0.015 -0.003 -0 010

0.263 0 126 0.192 0.057 -0.157 0.099 -0 023 0.212 0 092 0.096 -0.039 -0.154 -0.320 -0 056 0.001 0 060 0.294 0.001 -0.088 -0.087 -0 003 0.236 0 117 -0.004 0.059 -0.167 -0.048 0 031 0.223 0 065 -0.102 -0.059 0.018 0.338 -0 054

-0.013 -0.065 0.002 0.069 -0.110 -0.579 -0.016 0.154 0.047 0.071 0.071 -0.061 0.227 -0.049 0.257 0.093 0.058 0.072 -0.090 0.237 0 064

-0.170 -0.035 -0.208 -0.050 0.143 0.220 0 006

0.443 0 080 0.101 0.045 0.016 -0.030 -0 029 0.039 0 021 -0.164 0.085 -0.212 -0.104 -0 051

-0.050 -0 007 0.098 0.012 0.079 -0.010 -0 048 0.037 0 077 0.086 -0.034 -0.148 0.073 -0 017

-0.077 -0 072 -0.121 0.053 0.022 -0.042 -0 038 -0,032 0 011 0.069 0.064 -0.123 -0.124 0 091 -0.160 -0.011 0.171 0.051 -0.105 -0.045 0.012

0.012 -0.007 -0.003 0.050 0.148 -0.087 0.031

-0.033 0 509 -0.335 0 061 0.179 -0.215 0 0.551 -0 172 -0.280 -0 052 -0.164 0.110 0 0.065 -0 079 -0.183 0 017 0.085 0.179 -0

-0.499 -0 071 0.010 0 105 0. 26.7 0.065 -0 -0.247 0 101 0.041 -0 228 0.120 -0.034 0

0.079 0 092 0.150 0 000 -0.040 0.110 0 -0.110 0.036 -0.135 0.187 0.078 -0.131 0 002 -0.107 0.002 0.127 0.077 -0.040 -0.077 -0 102 -0.163 0.022 -0.146 0.013 0.068 -0.064 -0 085

0.082 0.004 0.150 -0.016 -0.030 0.029 -0 021 0.112 0.040 -0.363 0.040 0.058 -0.034 0 022

-0.062 -0.028 -0.511 -0.114 0.110 --0.120 -0 068 0.077 -0.089 -0.642 0.240 0.111 --0.034 0 027 0.197 -0.123 -0.566 -0.038 0.094 -0.027 -0 049 0.070 -0.068 -0.427 0.137 0.075 -0.067 0 011

-0.205 -0 035 -0.428 0.037 0.120 -0.084 -0 113 0.095 0 018 0.001 0.135 -0.028 -0.018 -CI 125 0.245 -0 096 -0.192 0.163 -0.019 0.148 0 013

-0.257 -0.053 -0.120 0.270 0.018 -0.375 -0.078

061 106 056 095 032 021

0.032 0 015 0.332 -0.130 -0.116 -0.042 -0 021 0.089 -0 032 -0.075 0.177 0.011 0.122 0 064

-0.041 0.002 -0.057 -0.333 0.081 0.060 -0.076

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller (3 Decay in s&Shell Nuclei


4ii’) 4 4 AI Z 2J, 2T, 2J, 2T, n,

(53 9) (33 9) ( 5 3 10) ( 3 3 10)

2’Mg 27A1 ( 1 3) ( 1 1 1) 912 (31 1) 1264

2’si 27A1 (51)(51 1)

(31 1) (71 1) (51 2) (31 2) (31 3) (51 3) (51 4)

28Ni3 28M9(26) (OS 1)

(44 1) (04 2) (44 2) (44 3) (44 4) (44 5)

Ii:: 3, (24 :; (44 6) (04 4) (24 3) i44 7j (24 4) (44 8) (04 5) (24 5) (04 6)

%g 2*Al(04)(22 1) 1364 (22 2) 1746 (22 3) 2073

28A 1 28Si ( 6 2) ( 4 0 1)

2fJP 28Si ( 6 2) ( 4 0 1) (80 1) (60 1) (80 2) (40 2) is0 3) (60 2) (40 4) is0 5) (60 3) (62 1) (42 1) (40 6) (80 3) (80 4) (62 2) (60 4) (80 5) (40 7) (40 8) (42 2) (60 5) (80 6) (40 9) (42 3) (80 7)

El WV) 5-5 5-3 l-l l-3 3-5 3-l 3-3

6483 6648 6759 7230

-0.352 -0.073 0.068 -0.069 0.182 -0.003 0.073 0.331 0.158 0.084 -0.144 -0.190 0.215 -0.015

-0.014 0.073 -0.208 -0.356 0.068 0.035 0.055 0.260 -0.010 0.218 0.048 -0.077 0.236 0.046

0.079 -0.021 -0.480 0.002 0.092 0.001 -0.005 -0.175 0.038 0.001 -0.159 0.032 -0.126 -0.032

0 1264 2326 2708 2780 4027 4139 4939

-0.680 -0.111 -0.202 -0.099 0.111 0.099 0.027 0.093 0.124 0.137 0.060 -0.106 0.068 0.063 0.094 -0.006 -0.032 0.169 0.147 0.080 -0.138 0.077 -0.006 -0.254 0.136 -0.073 0.067 0.023 0.037 0.073 -0.253 -0.010 -0.259 -0.139 -0.021 0.007 -0.003 -0.223 0.002 -0.101 -0.086 -0.047 0.132 0.024 -0.014 -0.078 0.232 0.042 0.029 0.226 0.026 -0.162 -0.135 -0.001 -0.018 -0.018

0 1543

3802 4264 4773 5402 6013 6187 4396 5412 6757 6855 6863 7330 738 1 7420 7867 8229 8900

0.072 0.545 0.218 0.143 0.106 0.202 0.103 0.103 0.167 -0.082 -0.164 0.088 0.093 0.078 0.073 -0.467 0.033 -0.048 -0.138 0.136 -0.016 0.177 -0.075 -0.070 -0.182 -0.065 0.045 -0.024 0.484 0.089 -0.281 0.106 -0.182 0.064 -0.151

-0.148 -0.007 -0.124 0.575 0.108 0.187 -0.152 -0.187 0.194 -0.170 0.245 0.207 0.246 -0.155

0.050 0.164 0.103 0.027 -0.003 0.073 0.067 -0.105 0.185 -0.012 0.078 0.061 -0.092 0.061

0.232 -0.233 -0.180 0.121 -0.071 0.101 -0.076 0.000 0.115 -0.438 -0.117 0.174 0.003 -0.128

-0.025 -0.076 0.192 0.248 -0.084 -0.002 -0.035 0.217 0.141 -0.317 -0.420 0.062 -0.079 0.039

-0.020 -0.041 -0.186 0.011 0.063 0.369 -0.357 iI: -0.048 0.252 -0.029 -0.083 0.115 0.123

-0.203 0.086 -0.035 0.062 0.087 -0.204 0.028 0.000 0.135 0.052 -0.043 -0.009 0.095 0.037 0.273 0.018 0.071 -0.097 -0.056 0.416 -0.066

-0.002 -0.072 0.098 0.035 0.048 0.227 0.242

0.019 0.089 0.542 -0.070 -0.071 0.073 0.019 0.132 -0.066 -0.031 0.364 -0.025 0.004 0.029 0.317 0.044 -0,034 -0.196 0.014 0.310 0.018

1988 0.095 0.069 -0.566 -0.065 0.145 -0.104 -0.042

1988 4659 6167 7037 7523 7906 8140 8457 8668 9812 9588 9446 9793 9493 9978

10423 10572 10661 10689 10980 10983 11059 11224 11530 11548 11552

0.095 0.069 -0.566 -0.056 -0.051 -0.014 -0.506 -0.200 -0.521

0.021 0.066 0.004

-0.042 0.067 0.016

-0.038 -0.104 -0.256 -0.037 -0.069 0.021

-0.065 0.145 -0.104 0.209 -0.030 -0.497 0.016 0.287 -0.217 0.095 0.088 0.520

-0.027 0.112 -0.014 -0.027 0.060 0.035 -0.038 -0.043 0.013 -0.022 -0.097 -0.139 -0.021 0.073 0.163

0.017 -0.108 -0.352

0.126 0.036 0.201 0.079 0.080 -0.155

-0.012 -0.031 -0.276 0.311 0.091 0.330

-0.679 0.086 0.596 0.291 0.236 0.719 0.096 0.071 -0.172

0.003 -0.010 -0.016 -0.038 -0.051

0.102 -0.082

-0.012 0.005 -0.011 0.030 0.004 -0.021

-0.208 -0.086 0.208 0.087 -0.264 -0.194

-0.044 -0.088 -0.054 -0.020 -0.001 -0.031

0.055 0.049 0.094 -0.054 -0.009 0.651

0.016 -0.010 -0.239

-0.037 -0.149 -0.023

0.076 -0.074

-0.084 0.078 -0.067 -0.030 -0.060 -0.073

0.004 -0.021 -0.012 0.045 0.019 -0.141

0.006 -0.011 -0.298 -0.041 -0.024 0.029

iiii25 0.019 -0.046 -0.156 -0.179 -0.399

0.147 0.028 0.197 -0.068 0.044 0.069 -0.002 0.012 -0.049 -0.033 -0.080 -0.289

0.092 -0.020 -0.033

-0.003 0.001 0.039 -0.036 0.056 -0.259 -0.111 0.122 -0.030

0.045 -0.025 0.118 0.016 -0.002 0.001

-0.017 -0.002 -0.175 -0.059 0.049 -0.126

0.149 -0.033

0.090 -0.075 -0.048 -0.052 -0.051

0.089 0.056

-0.083 -0.051

398 Atomic Data md NucWr Data Tables, Vd. 33, No. 3, November 1985



AM’) AI Zi A, & 25, 2T, 2J, 2T, n,

(02 1) ( 4 0 10)

Iti rt; (60 Sj (82 2) (80 9) (60 7) (60 6) (62 3) (60 9) i62 4j ( 8 0 10) (62 5) (02 3) ( 6 0 10) (02 4)

2QMg

294,l

2QAl(35)(53 1) Cl3 1) (33 1) (33 2) (53 2) (53 3) (13 2)

29Si

(33 3j (53 4) (33 4) (53 5) (13 3) (33 5) (53 6) (13 4) (33 6) (53 7) ( 13 5) (33 7) (53 0) ( 1 3 6) (33 8) (13 7) (13 0) ( 13 9)

(53)(31 1) (51 1) (31 2) (51 2)

2QP 29Si ( 1 1) ( 1 1 1) (31 1) (31 2) (11 2)

2gs 29p (53)(3l 1) (51 li (31 2)

I:: 2, (51 A; (71 2) (71 3) (31 31 (53 lj (31 4) (71 4) (51 4j (51 5) (31 5)

El WV)

11682 11730 11081 11882 11921 11971 12162 12206 12446 12507 12663 12694 12697 12920 12957 13070 13802

0 1214 1959 2735 2801 3017 3330 3578 3816 3976 4128 4229 4459 450 1 4650 5064 528 1 5470 559 1 5648 5803 6113 6214 6482 7499

1394 2121 2630 3513

0 1394 2630 490 1

1394 2121 2630 3513 4410 4917 5219 5881 6155 8426 6267 6389 6778 6862 690 1

5-5 5-3 l-l l-3 3-5 3-l 3-3

-0.154 0.063 0.016 -0.172 -0.120 0.796 0.057 -0.014 -0.008 -0.085 0.018 -0.050 -0.002 -0.035

0.036 0.012 -0.043 0.003 0.074 0.151 -0.087 0.098 0.051 -0.063 0.025 -0.065 0.060 -0.012 0.037 -0.013 -0.171 -0.052 0.001 0.032 0.051 0.007 0.053 0.011 0.123 0.107 0.656 -0.059 0.012 -0.001 -0.035 0.023 0.001 0.052 -0.036

-0.104 -0.041 -0.092 0.072 -0.039 0.002 -0.022 0.046 0.002 -0.039 0.019 -0.007 0.077 0.013

-0.113 -0.016 0.274 -0.081 0.032 -0.119 0.000 -0.062 -0.011 0.027 -0.018 -0.019 0.046 -0.023

0.068 -0.007 -0.114 0.013 0.007 0.028 O.‘OOS -0.006 -0.013 0.001 0.005 -0.031 0.044 -0.062

0.087 -0.024 -0.067 -0.060 0.040 -0.061 -0.050 -0.244 -0.038 0.052 0.208 -0.268 -0.093 0.210 -0.017 -0.006 -0.001 0.024 0.096 0.022 0.043

0.021 -0.028 0.015 -0.020 -0.046 -0.250 0.147

0.097 -0.187 0 002 0.003 -0.037 0.044 0.027 -0.215 -0.002 -0 000 0.764 0.096 0.168 -0.045 -0.134 0.099 -0 349 0.247 0.141 0.170 -0.240 -0.050 -0.006 -0 006 -0.007 -0.063 0.265 -0.550

0.087 0.162 -0 470 -0.111 0.134 -0.059 -0.002 0.145 0.093 -0 914 -0.115 0.220 -0.201 -0.012

-0.226 -0.067 -0 192 0.189 0.095 -0.575 0.171 -0.040 0.012 -0 ,202 -0.003 0.108 -0.154 0.257 -0.059 -0.006 0 230 -0.051 0.008 0.109 0.082

0.053 0.007 0.446 0.007 -0.028 0.471 0.098 0.063 -0.059 -0.150 0.095 0.035 0.131 0.080

-0.207 0.099 0.385 -0.435 0.002 -0.151 0.005 -0.153 -0.020 0.216 0.101 -0.027 -0.227 0.031 -0.167 -0.040 0,004 0.125 0.024 -0.525 -0.117 -0.104 0.035 -0.022 -0.142 0.025 -0.063 -0.019 -0.033 -0.030 -0.342 -0.137 0.114 0.207 -0.004

0.317 -0.004 -0.355 0.197 0.006 0.220 0.014 -0.018 0.001 0.292 0.289 -0.076 - .0.031 0.047

0.027 0.037 -0.100 -0.350 0.064 0.139 -0. 124 -0.071 -0,029 0.255 0.095 0.040 0.073 0.028

0.102 0.045 0.113 -0.117 -0.056 0.078 -0.037 0.049 0.013 0.170 0.127 -0.020 0.228 0.068 0.212 -0.051 -0.308 0.176 0.025 - -0.015 0.105

-0.190 -0.090 -0.307 0.296 0.160 - -0.141 -0.106 0.019 0.025 -0.120 -0.022 -0.003 0.107 0.027

0.005 -0.118 0,275 0.042 -0.030 0.109 -0.006 0.449 -0.029 -0.319 0.202 -0.047 0.151 0.078

-0.054 -0.019 0.440 0.234 -0.072 0.069 0.123 0.031 0.044 0.073 -0.408 -0.012 0.055 -0.055

0.111 0.186 0.553 -0.014 -0.186 0.014 -0.088 0.040 -0.069 -0.024 0.089 -0.031 -0.637 -0.034

-0.131 0.036 0.039 0.132 -0.113 0.059 0.201 -0.097 0.043 0.383 0.027 0.195 0.007 0.097

0.005 -0.118 0.275 0.042 -0.038 0.109 -0.006 0.449 -0.029 -0,319 0.202 -0.047 0.151 0.070

-0.054 -0,019 0.440 0.234 -0.072 0.069 0.123 0.031 0.044 0.073 -0.408 -0.012 0.055 -0.055

-0.020 0.040 0.128 -0.179 -0.090 -0.170 -0.040 -0.437 -0.237 -0.636 0.255 0.255 -0.214 -0.045 -0.134 -0.159 -0.272 0.221 0.038 -0.521 0.239

0.093 0.192 0.402 0.002 -0.113 0.216 0.001 0.063 0.160 0.259 -0.009 -0.086 0.167 -0.034

-0.840 -0.119 -01057 -0.020 0.119 0.020 0.105 0.032 0.099 0.269 -0.043 -0.031 0.204 0.035 0.107 0.113 0,416 0.303 -0.328 -0.561 -0.419

-0.078 -0.095 -0.050 0.065 0.070 -0.157 0.091 0.153 -0.182 -0.461 0.331 0.061 -0.511 -0.079 0.111 0.132 0.192 0.177 -0.264 -0.327 -0.233

399 Atomic Data and Nuckir Data Tables. Vol. 33. No. 3. November 1995

Ai Zc AI zi 2J, 2T, 2J, 2Tf nl

(31 6) (71 5) (71 6) (51 6) (31 7) (51 7) (51 8) (71 7)

30#Q

(31 8) (31 9) (71 8)

: $ : ‘t; ( 7 1 10)

3oA1 (06) (24 1) (24 2) (24 3) (24 4) (24 5) (24 6)

3oA 1 3oSi ( 6 4) ( 4 2 1) (42 i)

(42 3) (62 1)

(82 2) (42 5) (62 3) (42 6) (62 4) (82 3) (42 7) (42 8)

:z 2;

(82 5) (82 6) (62 6) (82 7)

3OP

30s

30 Si ( 2 0) ( 0 2 1) 0 -0.057 -0.115 -0.504 0.235 0.188 -0.118 0.045

(42 1) 2310 -0.010 -0.110 -0.180 0.093 0.061 -0.658 -0.077 (42 2) 3550 -0.067 0.032 0.121 0.042 -0.057 0.329 0.159

(22 1) 4210 -0.050 0.024 -0.060 -0.003 0.001 0.289 -0.162 (02 2) 4085 0.043 0.089 0.368 -0.150 0.017 -0.108 -0.017

30P (02)(20 1) (20 2) (20 3) (20 4)



Nil’)

i22 1) (20 5) (20 6) (20 7) (20 8)

3lA1 31Si ( 5 5) { g ; ;;

(33 2) i53 2) (33 3) (33 4) (53 3) (53 4) (73 1)

El WV) 5-5 5-3 l-l l-3 3-5 3-1 3-3

7179 7391 7526 7604 7634 7669 7875 7878 8268 8377 8401 8562 8841 9038

-0.014 -0.084 -0.229 -0.023 0.155 0.326

0.027 -0.095 -0.419 0.006 0.066 0.250 0.039 0.039 0.081

-0.006 0.031 0.055 -0.139 -0.037 0.216

0.028 0.053 0.334 0.032 -0.014 0.019

-0.164 -0.088 -0.014 0.004 -0.048 -0.031 0.012 -0.029 -0.128

0.090 0.283

-0.191 -0.258

0.042

-0.077 0.135 0.101 -0.003 0.069 -0.003 0.117 -0.124 0.058 0.000

-0.059 -0.106 0.095 0.013

-0.103 -0.035 -0.075 0.055

0.015 0.048 0.019 0.049

-0.121 -0.102

-0.138 -0.075

0.193 -0.021 -0.219 -0.111 -0.004 -0.182

0.015 0.145

-0.180 0.268 0.102

-0.092

-0.294 0.074

-0.053 -0.046 -0.115

-0.028 -0.057 0.115 -0.001 0.095 -0.217 0.170 -0.018 -0.045 -0.081 0.031 0.026 -0.064 0.024

493 2139 2538 298 1 3185 355 1

2310 3550 5048 496 1 5195 5506 6205 5913 6520 7201 6967 7473 6997 7307 7441 8051 8195 8606 8696 8757 8933

-0.136 0.194 -0.476 0.474 0.144 -0.118 -0.072 -0.258 -0.115 0.659 0.555 -0.081 0.286 0.005 -0.146 0.140 0.573 -0.403 -0.123 -0.157 0.081 -0.042 0.075 -0.080 -0.156 0.046 0.416 -0.280

0.029 -0.048 -0.011 0.067 -0.044 0.024 -0.082 0.297 0.108 0.170 -0,146 -0.137 0.743 -0.195

0.044 -0.020 0.159 -0.418 -0.115 -0.036 -0.089 0.172 -0.175 0.515 -0.409 -0.273 0.111 -0.042 0.089 0.094 -0.432 -0.073 0.045 -0.132 -0.058

-0.281 -0.075 0.700 -0.091 -0.123 0.054 -0.121 0.092 -0.051 0.131 0.697 -0.086 0.633 -0.248 0.147 0.014 -0.430 0.105 0.034 -0.237 -0.153 0.116 0.018 -0.488 -0.433 0.103 -0.096 -0.096

-0.013 0.029 0.058 0.000 -0.158 -0.566 -0.416 -0.099 -0.058 0.231 -0.185 -0.031 -0.563 0.569 -0.036 -0.113 -0.074 0.300 0.046 -0.214 0.206

0.062 0.022 -0.008 0.050 -0.010 0.011 0.075 -0.175 0.114 0.030 -0.422 0.025 0.164 -0.303 -0.166 -0.026 -0.522 -0.270 0.264 0.005 0.110 -0.135 0.005 0.028 -0.100 -0.003 0.085 -0.245 -0.089 -0.044 0.122 -0.006 0.000 -0.067 -0.010

0.140 0.123 0.626 0.029 -0.083 0.673 -0.092 0.314 0.219 0.921 -0.478 -0.298 0.390 0.172

-0.013 -0.064 -0.439 -0.198 0.167 0.349 -0.187 0.053 0.033 -0.030 -01160 -0.015 0.167 -0.076 0.174 0.151 0.149 -0.380 -0.091 0.285 0.049

-0.016 -0.041 -0.078 0.001 0.034 -0.137 0.038

0 -0.057 -0.188 -0.504 0.118 0.115 -0.235 0.045 644 -0.046 -0.037 -0.152 -0.192 0.151 0.361 0.161

3131 -0.093 0.019 -0.061 0.016 -0.166 0.075 0.143

3737 -0.054 -0.002 0.238 0.126 0.098 -0.174 0.304

4903 0.029 -0.070 -0.025 -0.280 -0.042 -0.550 -0.064 493 1 -0.076 0.009 0.172 -0.004 0.149 0.104 -0.077

5896 -0.150 -0.039 0.026 0.040 -0.194 -0.022 -0.004 6085 -0.018 0.019 0.136 -0.025 0.119 -0.095 0.028 7085 -0.033 -0.012 0.039 0.038 -0.143 -0.062 0.020

0 1606 2295 2871 3825 5129 5037 5398 3697

0.037 -0.156

0.047 -0.724 -0.058 -0.066

-0.395 0.109 0.343

-0.055 -0.089

0.041 -0.093 -0.015

0.045

0.067 -0.176 -0.108 0.033 -0.067 -0.156 0.749 0.126 0.042 0.027 -0.663 -0.071 0.174 -0.207 -0.160

0.516 0.129 0.078 -0.122 -0.130 -0.457 0.372 0.160 -0.082 0.054

0.295 -0 _ 420 -0.068 0.016 -0.071

-0.100 0.202 0.079

-_--- -0.076 61742 0.044 0.367 -0.142 -0.455 0.230 0.104 -0.093 0.141 -0.183 -0.485 0.074 0.123 0.054

400 Atcmk Data and Nudear Data Tables. Vol. 33, NO. 3, November 1995

AI Z A, & 2J, 2Ti 2Jf 2T, nf

31Si

3's

32Si

32P

3*c1

33P

33c 1

33Ar



(73 2) (73 3) (33 5) (53 5) (53 6) (73 4) (33 6) (73 5) (73 6) (53 7) (53 8) (73 7) (53 9) (73 8) ( 5 3 10)

3’P (33)(11 1) (31 1)

3’P ( 1 1) ( 1 1 1) (31 1) (11 2) (31 2) (31 3) (31 4) (11 3) (31 5) (31 6)

32P (04)(22 1)

32s ( 2 2) ( 0 0 1)

32s ( 2 2) ( 0 0 1)

(40 1) (00 2) (40 2) (20 1) (40 3) (40 4) (22 1) (42 1) (20 2)

335 (13)(31 1)

33s ( 3 1) ( 3 1 1) (‘1 1) (51 1) (31 2) (51 2) (51 3) (31 3) (11 2) (31 4) (11 3) (51 4) (31 5) (31 6) (51 5) (11 4)

33Cl ( 1 3) ( 3 1 1) (‘1 1) (31 2) (31 3) (‘1 2) (31 4) 113 1)

Et VW

--

4711 5632 5709 5764 6074 6170 6215 6506 6555 6640 6004 7009 7190 7302 7414

5-5 5-3 1-I l-3 3-5 3-l 3-3

0.032 0.002 0.652 -0.975 -0.124 -0.173 0.413 0.002 -0.070 -0.630 -0.094 0.076 -0.406 -0.133 0.032 0.003 0.159 0.194 -0.015 0.085 0.043

-0.431 -0.104 -0.766 -0.275 0.264 -0.792 0.101 -0.111 -0.232 -0.752 0.037 0.200 -0.245 -0.027 -0.074 -0.060 -0.507 -0.276 0.059 0.040 -0.360

0.000 -0.030 -0.471 -0.203 0.121 0.119 -0.160 0,004 0.149 0.499 -0.049 -0.069 1.169 -0.404 0.027 0.067 0.415 -0.020 -0.136 -0.066 -0.101

0 1210

0. 040 -0.024 -0.227 -0.055 -0.026 0 550 -0.343 0. 071 -0.009 0.392 0.304 -0.107 0 030 0.201

-0. 114 -0.042 -0.392 -0.296 0.337 0 609 0.440

-0. 200 -0.019 0.012 -0.011 0.057 -0 134 -0.073 -0. 005 0.000 -0.225 -0.151 -0.024 0 100 -0.391

0. 014 0.077 -0.114 -0.020 -0.071 -0 047 -0.205

-0.040 0.007 0.003 -0.690 -0.046 -0.230 0.040 -0.042 0.019 -0.166 0.005 -0.022 0.224 -0.614

0 -0.051 - -0.159 -0.549 0.011 0.159 -0.011 0.121 1210 0.000 - -0.052 -0.036 0.211 0.005 -0.444 - .o. 129

3310 -0.021 0.000 0.305 0.131 0.006 0.205 0.152 3586 0.067 0.016 -0.037 - .0.031 0.120 0.273 - -0.202 458 1 -0.017 0.040 0.011 0.070 0.014 0.363 0.021 4732 -0.002 0.020 0.000 0.151 0.012 0.191 0.155 5004 -0.051 - -0.013 -0.095 0.133 0.033 0.325 0.046 5763 0.033 0.022 0.076 - -0.011 0.151 -0.100 0.210 61 ‘7 -0.040 0.004 0.000 - -0.045 -0.047 0.129 - -0.105

5

0

-0.009 0.072 0.260 -0.605 -0.046 -0.090 0.176

-a.001 -0.052 0.086 -0.575 -0.008 -0.109 0.065

0 -0.001 -0.052 0.006 -0.575 - 0.000 -0.109 0 065 2140 0.030 0.040 0.434 -0.006 - ,o. 101 0.062 -0 157 3740 -0.025 -0.005 -0.042 -0.446 0.025 0.169 0 030 4353 0.026 0.031 0.056 -0.133 0.006 0.160 0 007 4705 0.011 -0.119 -0.256 -0.001 0.117 0.005 0 404 5490 -0.011 -0.059 -0.220 -0.075 0.009 0.322 0 101 6695 0.000 -0.002 0.220 -0.025 0.054 0.402 -0 006 7057 0.026 -0.020 0.270 0.320 0.020 -0.320 0 550 7052 -0.041 -0.141 -0.679 0.253 0.157 -0,151 -0 146 7125 -0.015 -0.055 -0.117 -0.036 0.036 -0.013 0 129

0 -0.000 0.033 0.014 -0.612 -0.019 -0.131 0.130

0 779

1896 2174 2839 3099 3667 3863 4105 4286 4697 4807 5076 5145 5561

0.003 -0.101 -0.040 0.079 0.101 -0.079 0.756 0.045 -0.042 -0.024 0.296 0.001 -0.295 -0.022

-0.017 -0.029 -0.130 0.060 0.054 0.304 0.120 0.021 -0.000 -0.149 -0.062 -0.010 -0.401 -0.154

-0.046 -0.005 -0.221 -0.096 -0.250 -0.409 -0.077 -0.029 0.104 0.136 0.002 -0.099 0.446 0.070

0.021 0.010 0.093 0.099 0.033 -0.024 0.199 -0.016 -0.046 -0.072 0.031 -0.064 -0.200 0.022

0.002 -0.020 -0.053 -0.094 -0.015 -0.239 -0.070 -0.039 -0.034 -0.097 0.130 -0.061 0.202 0.068

0.057 0.013 0.157 -0.167 -0.025 -0 520 -0.121 0.044 0.061 0.101 -0.087 0.187 0 066 -0.109

-0.006 0.036 0.045 0.042 -0.057 0 115 -0.000 0.005 0.002 0.006 -0.062 0.005 -0 324 0.125

-0.058 -0.041 -0.037 0.090 -0.150 -0 055 0.094

0 779

2174 3667 3063 4105 5191

-0.000 0.033 0.014 -0.612 -0.019 -0.131 0.130 0.030 0.067 0.579 -0.003 -0.150 0.056 0.041

-0.000 -0.024 -0.006 0.201 0.050 -0.419 0.371 -0.023 0.050 0.002 -0.304 0.057 0.362 0.069 -0.020 -0.042 0.119 0.053 0.140 0.347 0.466

0.032 -0.070 -0.010 -0.003 0.196 0.132 0.690 -0.056 -0.177 -0.759 0.010 0.177 -0.010 0.003

401 Atomic Data and Nuclear Data Tables, Vol. 33, NO. 3. November 1995

402 B. A. BROWN and B. H. WILDENTHAL Gamow-Teller fi Decay in s&Shell Nuclei


4 4 4 ZI 2J, 2T, 2J, 2T, n, El WV)

(11 3) (31 5) (31 6) (31 7) (11 4) (31 8) (11 5) (31 9) (33 1) ( 3 1 10) (1 1 6) t 3 1 11) (33 2)

(11 7) ( 3 1 12) (11 8) ( 3 1 13) (33 3) ( 3 1 14) (11 9) ( 3 1 15) i 3 1 16) ( 1 1 10) ( 3 1 17) ( 3 1 18) ( 1 1 11)

124)(02 1) (42 1) (42 2) (02 2) (22 1) (42 3) (42 4)

4286 4807 5076 5309 5561 6553 6003 6630 6722 7091 7273 7491 7837 7948 7983 8155 623 1 8797 8802 8815 8964 9098 9377 9379 9489 97’5

0 2201 3138 3906 395 1 4302 4851

(02)(22 1) (22 2)

3951

5558

(60)(42 1) 2201 (42 2) 3138

(42 3) 4302 (82 1) 4896

(62 1) 4774 (42 4) 4851

(02)(20 1) 184 (20 2) 528 (20 3) 2389 (20 4) 3117 (20 5) 3748 (20 6) 4843

‘15’;;~ ;;

(33 2)

(33)(3l 1)

( 3 1) ( 3 1 1) (11 1) (51 1) (31 2) (51 2) (31 3) (11 2) (31 4) (51 3) (11 3)

(33)(3l 1) (11 1)

0 1557 2800

0

0 1244 1780 2672 3146 3962 4088 4788 4595 5089

0 1244

5-5 5-3 l-l l-3 3-5 3-l 3-3

-0.012 0.135 0.314 -0.032 -0.006

0.046 0.016 0.029 0.001

-0.045 .0.057 -0.006 0.059 0.028 0.061

-0.039 .0.030 0.010 -0.011 -0.070 -0.023 -0.016 -0.010 -0.001 -0.017

-0.076 0.261 0.054 0.329 0.043 -0.054

0.001 0.048

-0.017 0.045 0.021

0.043 0.493 -0.035 0.124

0.036 0.016 .0.227 -0.064

0.001 0.047 0.019 -0.155 0.086 -0.012

-0.303 -0.015

0.021 0.158 0.015 0.064

-0.158 -0.010

0.005 0.257

-0.011 -0.061 0.004 0.389

-0.035 0.078 -0.002 0.683 -0.006 -0.137

0.034 -0.004 0.056 -0.099 -0.056 -0.164 -0.15; -0.054 0.016 0.031 0.182 -0.087 0.125 0.227 -0.050 0.022 0.028 0.163 -0.077 0.300 0.233 -0.019 0.014 0.044 -0.041 -0.002 -0.154 0.164 -0.039 0.021 0.010 -0.050 -0.147 -0.041 0.081

0.006 -0.015

0.010 0.025 0.021

-0.037 0.017 0.007

-0.070

-0.203 0.026 0.027 -0.039

-0.154 0.035 -0.042 -0.009 -0.016 0.070

0.043 0.053 -0.025 -0.016

0.00s 0.03n

-0.053 0.041

-0.025 0.013 0.005

-0.029 0.170 0.003

-0.019

0.023 0.013

-0.012 -0.030

0.066 0.036 -0.074 -0.003

0.003 0.010

-0.021 -0.031

0.022 -0.001 -0.011

0.051 0.253 -0.022 -0.038

0.122 0.040 0.034 -0.098

-0.241 -0.046 0.098 0.055

0.028 -0.038

0.088 0.035 0.018 -0.002 0.024 0.007 0.137 -0.006

-0.122 0.027 0.271 0.027 0.022 -0.147

-0.009 -0.175 0.072 -0.664 -0.133 -0.167 -0.086 0.013 -0.066 0.491 -0.875 -0.273 -0.261 -0.131

-0.017 0.017 -0.154 0.478 0.067 0.139 -0.li5 -0.001 -0.085 -0.016 -0.355 0.033 0.063 0.067

0.007 0.035 0.010 -0.027 0.057 -0.248 0.405 0.015 0.028 0.624 0.650 -0.195 -0.069 0.066

-0.024 -0.004 0.016 -0.029 -0.060 0.432 -0.352

34P 345

34Cl 34s

34Clnl 34s

34Ar s4c 1

35p 355

355 3% 1

35Ar 3561

-0.009 0.030 0.009 0.239 -0.023 0.681 0.066 0.012 0.034 0.009 0.242 0.100 0.378 0.005

0.020 -0.060 -0.018 0.079 0.047 -0.357 0.296 0.030 0.028 -0.010 -0.003 0.043 -0.793 -0.450

-0.028 0.069 -0.015 -0.378 0.049 0.149 -0.489 -0.021 0.039 0.009 0.073 -0.028 0.311 0.065 -0.014 0.074 0.074 0.085 -0.109 0.472 0.057

0.034 0.019 0.071 -0.046 -0.005 -0.120 -0.016

-0.004 0.024 0.092 -0.091 0.139 0.396 0.305 -0.016 0.093 0.075 -0.126 -0.101 0.228 -0.492

0.037 0.031 0.228 0.078 0.047 -0.172 0.070 -0.048 0.017 -0.006 0.058 -0.185 0.005 0.250

0.018 0.007 0.008 -0.009 -0.060 0.051 -0.047 0.014 -0.007 -0.028 0.038 0.259 0.114 -0.041

0.012 0.012 0.008 1.271 0.073 0.158 0.163 -0.018 0.059 -1.018 0.031 0.246 -0.141 -0.304

0.015 0.053 0.001 -0.075 0.109 -0.535 0.570

-0.013 -0.021 -0.003 0.074 -0.066 0.211 -0.469

-0.686 -0.101

0.444 0.088

-0.072 -0.117 -0.442

0.024 0.377 0.151

-0.013 -0.021 -0.003 0.074 -0.066 0.211 -0.469 0.005 0.019 0.005 0.164 -0.024 0.035 -0.079

-0.003 0.019 0.011

-0.036 -0.018

0.012 -0.002 -0.008

0.003 0.032

0.071 -0.042 -0.059

0.017 -0.017 -0.016

0.011 0.020 0.040

-0.035 0,063 0.122

-0.071 0.035 -0.584

0.162 0.609 0.221 0.333 0.089

-0.606 -0.132

0.229

0.042 0.059

0.048 0.083

0.065 -0.033 -0.037 -0.122 -0.174

0.018 0.152

-0.047 -0.102

0.132 0.025

0.044 0.019

-0.079 -0.023 -0.050

-0.053 -0.102 -0.10s

0.082 0.063 -0.076 -0.005

35K 35Ar

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller (3 Decay in d-Shell Nuclei 403


A1 z AI & 2J, 2T, 2J, 2T, n,

(51 1) (31 2) (51 2) (11 2) (31 3) (11 3) (33 1) (51 3) (31 4) (51 4) (31 5) (51 5) (51 6) (31 6) (51 7) (11 4) (11 5) (13 1) (31 7) (31 8) (1 1 6) (51 8) (31 9) (51 9j

(53 1) ( 5 1 10) ( 3 1 10) (11 7)

36K 36At-(42)(40 1) (40 2) (42 1) (60 1) (62 1) (22 1) (22 2) (42 2) (20 1) (40 3) (40 4) (40 5) (42 2j (42 3) (22 3) (20 2) (60 2) (62 2) (40 6)

37Af- 37c1 (31)(33 1)

37K 37Ar ( 3 1) ( 3 1 1) (11 1) (51 1) (51 2) (31 2) (11 2) (31 3) (11 3) (51 3) (51 4) (31 4)

37Ca 37K (33)(3l 1) (11 1) (51 1) (51 2j (31 2) (11 2)

El WV) 5-5 5-3 l-l l-3 3-5

1780 2672 3146 4088 3962 5089 5957 4595 4788 5536 5677 5879 6394 6932 7050 7208 7404 7514 7577 7979 8203 8377 8429 8447 8637 8780 8822 9295

-0.027 -0.010 0.006 -0.018 -0.090 0.493 -0.677 0.024 0.000 0.064 0.152 -0.011 0.056 0.031

-0.016 0.081 -0.201 0.090 -0.071 0.368 0.180 -0.008 -0.041 0.063 -0.039 0.209 0.146 0.827

-0.039 -0.044 -0.023 -0.024 0

0.024 -0.020 -0.041 0.236 -0.120

044 -0.014

-0.003 0.082 0.121 -0.056 -0.059

0.056 -0.066 -0.151 -0 250 0.007 0.014 0.089 -0.204 0 055

-0.018 0.084 0.026 -0.089 -0 029 -0.011 -0.001 -0.158 -0.051 -0 022

0.003 0.022 0.017 -0.057 -0 153 -0.012 -0.036 -0.129 -0.059 -0 ,011 -0.007 -0.008 0.033 0.015 0.065

0.003 -0.045 -0.165 -0.009 0.085 -0.001 -0.030 -0.098 -0.044 -0.065 -0.014 0.027 0.003 0.027 0.020

0.007 -0.041 -0.030 0.074 -0. 12.5 0.033 -0.049 0.071 0.072 0.126

-0.033 -0.001 -0.165 -0.033 -0.150 -0.006 -0.019 -0.125 -0.049 0.041 -0.027 0.027 -0.083 0.040 -0.080 -0.003 0.005 -0.051 -0.027 -0.116

0.002 -0.046 -0.051 -0.092 0.178 0.004 -0.058 0.011 -0.071 0.156

-0.039 0.035 -0.059 0.011 -0.171 0.001 -0.007 0.014 0.056 0.070 0.001 0.006 0.051 -0.017 -0.039

1927 4410 6657 7248 7462 7858 8192 8661 7099 7174 8093 8265 8661 9103 9120 9314 9485 9508 9536

-0.014 -0.025 -0 006 0.001 -0.096 0.021 0.021 0 021 0.040 -0.096

-0.031 0.061 -0 020 -0.139 -0.061 -0.016 0.053 -0 079 -0.132 -0.097 -0.012 -0.053 -0 028 0.040 0.092 -0.003 -0.077 -0 039 0.016 0.055 -0.018 -0.002 0 027 -0.107 0.071 -0.001 -0.004 -0.094 0.080 -0.155

0.014 -0.035 -0.035 0.036 0.014 0.013 -0.047 -0 002 -0.012 0 106 0.012 0.031 -0 037 0.092 -0 071 0.025 -0.016 0 045 0.081 0 107

-0.001 -0.004 -0 094 0.080 -0 155 -0.014 0.055 0 084 -0.062 0 209

0.014 0.053 -0 016 -0.154 0 129 -0.016 0.009 -0 014 0.014 -0 011

0.002 0.050 0.044 -0.075 -0.195 -0.026 0.083 -0.083 -0.010 -0.317

0

0 1586 2884 3112 3539 4620 509 1 5665 5965 6128 688 1

0.022 0.021 0.046 0.081 0.022

0.004 -0.097 0.001 0.146 -0.016

-0.032 0.012 -0.034 -0.076 -0.012 -0.006 -0.007 0.024 -0.085 0.094 -0.021 0.055 -0.106 0.051 -0.336

0.026 -0.055 0.081 0.132 0.250 -0.019 0.040 -0.009 -0.209 0.138

0.000 0.041 -0.035 -0.041 -0.048 0.025 0.029 0.166 -0.011 0.141

-0.005 -0.092 -0.122 -0.008 -0.140 0.032 -0.068 -0.003 -0.019 0.324

-0.007 0.001 -0.065 0.175 -0.006 0.005 0.015 0.050 -0.076 0.128

0 -0.004 -0.016 -0.001 0.032 -0.097 1586 0.008 0.024 0.010 -0.019 0.070 2884 0.001 0.007 -0.014 0.000 0.073 3112 -0.009 -0.036 0.027 -0.141 0.254 3539 0.003 -0.064 0.093 -0.111 0.210 4620 -0.002 -0.027 -0.012 -0.081 -0.052

3-l 3-3

0.024 0.949 -0.158 -1.021

-0.710 -0.174

0.060 -0.170 0.138 0.251

0.279 -0.545

0.483 -0.064 -0.773 -0.185 -0.380 0.053

0.068 -0.029 0.214 0.091

-0.170 0.020 0.255 -0.090

-0.778 -0.055 -0.342 -0.045 -0.019 0.014

0.087 -0.095 0.246 0.090

-0.012 -0.025 -0.111 -0.159

0.174 -0.133 0.027 0.181

-0.027 -0.028 -0.186 -0.073

0.377 -0.661 -0.383 -0.616

0.139 -0.050 -0.265 -0.097 -0.005 1.112 -0.113 0.889

0.817 0.194 0.231 0.083

-0.591 -0.017 0.254 -0.175 0.257 0.054 0.177 -0.027 0.231 0.083 0.850 0.087

-0.203 -0.632 -0.032 -0.037 -0.217 0.060 -0.582 -0.011

0.245 0.088

0.032 0.571

0.076 0.641 0.454 0.209

-0.332 0.354 0.268 0.452 0.250 -0.144 0.075 -0.384

.o. 197 0.176

.O. 176 0.158 ,0.512 0.042 0.671 -0.056

.0.256 0.019

0.146 -0.571 -0.556 0.398 .0.253 0.827 0.136 0.976 1.095 0.109

.0.239 -0.965

B. A. BROWN and B. H. WILDENTHAL Gamow-Teller @ Decay in &Shell Nuclei


At Zt 2J, 2T, 2J, 2Tf n,

(33 1) i I I 3j

::: x;

(51 4) (13 1)

36Ar ( 6 0) ( 4 2 1)

(42 2)

36K (02)(20 1) (20 2) (20 3)

39K ( 3 1) ( 3 1 1) (11 1) (51 1)

Et WV) 4663 5665 509 1 5965 6126 6721

2013 4489

635 1721

4143

0 2730 7416

5-5

-0.011 -0.007

0.009 0.012 0.005 0.010

0.011 0.005

-0.001 -0.005 -0.019

0.000 0.000 0.000

5-3 l-l

0.054 0.010 0.003 -0.066

-0.029 0.07% -0.021 0.092

0.004 0.056 -0.015 -0.004

0.134 0.001 -0.045 0.001

0.029 -0.049 0.012 -0.032 0.046 -0.006

0.000 0.000 0.000 0.000 0.000 0.000

l-3 3-5 3-l 3-3

-0.141 -0.054 0.141 -1.037 0.060 -0.053 0.105 0.355 0.025 0.140 -0.061 -0.064 0.124 -0.064 -0.362 -0.014

-0.110 -0.050 -0.394 -0.135 0.063 0.042 -0.710 -0.017

0.000 -0.015 -0.293 -0.766 0.000 -0.010 -1.254 0.204

0.008 -0.197 -0.359 -0.307 0.044 -0.080 -0.181 0.612

-0.066 -0.307 0.260 -0.002

0.000 0.000 0.000 -1.000 0.000 0.000 1 .ooo 0.000 0.000 1.000 0.000 0.000

404 Atomk Data and Nuclear Data Tebles, Vol. 33, No. 3, Novambef 1985

atomic data and nuclear data tables 33,347-404 (1985

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