I ~ Nuclear Physics A94 (1967) 476--480; (~) North-Holland Publishing Co., Amsterdam 1

Not to be reproduced by photoprint or microfilm without written permission from the publisher

I S O M E R I C C R O S S - S E C T I O N R A T I O S

F O R (n, 2n) R E A C T I O N S AT 14.8 M e V

R. PRASAD and D. C. SARKAR Department of Physics, Muslim University, Aligarh, India

Received 4 November 1966

Abstract: Isomeric cross-section ratios for (n, 2n) reactions at 14.8 MeV have been measured for the isomeric pairs aam,aaCl, 44m,448c, mm,91Mo and 114m,l14In. Using the compound nuclear mechan- ism and the spin distribution form due to Bethe and Bloch, theoretically calculated isomeric ratios have been compared with the measured values to find the probable value of the spin distribution parameter or. The parameter has also been calculated from the rigid moment of inertia of the nucleus.

E NUCLEAR REACTIONS 35C1, 4~Sc, 9~Mo, n~In, (n, 2n), E = 14.8 MeV;

measured isomeric cross-section ratios. Deduced spin distribution parameter c~. Natural targets.

1. Introduction

In a nuclear react ion where the residual nucleus has an excited level of measurable

half-life, the extent to which each isomer is popu la t ed in the reac t ion may be expressed

by the isomeric cross-sect ion rat io . Since isomers differ in their spin, it is possible

to calculate this cross-sect ion ra t io theoret ical ly using the spin densi ty re la t ion due to

Bethe 1) and Bloch z). This involves the spin d i s t r ibu t ion pa ramete r a. Many measure-

ments o f the pa rame te r 3-1o) a have been per formed, but the s i tua t ion is still far

f rom sat is factory due to the lack of data .

We have measured the isomeric cross-sect ion rat ios exper imenta l ly by fo l lowing

the activit ies p roduced in samples due to (n, 2n) react ions at 14.8 MeV. The experi-

menta l and the theoret ical values of the isomeric cross-sect ion rat ios were c o m p a r e d

to find the p robab le value o f the spin d is t r ibut ion pa ramete r a.

2. Measurements

Using the 130 keV deuteron beam of the C o c k c r o f t - W a l t o n type accelera tor of th is

l abora to ry , 14.8 MeV neutrons were ob ta ined f rom the t(d, n)4He react ion. Deta i l s

o f the i r r ad ia t ion technique have a l ready been descr ibed previously 1~'12). Cross

sections were measured with respect to the 56Fe(n, p)56Mn react ion. I r rad ia t ions were

carr ied out by placing the samples at the back of the t r i t ium target but in the fo rward

d i rec t ion where the spread in the energy of the neutrons fall ing on the sample was not

476

(n, 2n) REACTIONS 477

more than 0.5 MeV. The samples to be irradiated were generally available in powder form. They were uniformly spread in thin perspex rings and sandwiched between the cellulose tapes. Spectroscopically pure substances of chemical purity more than 99.9 % were used.

The residual nuclei in the reactions 35Cl(n, 2n)34mc1, 45Sc(n, 2n)44'Sc and 92Mo(n, 2n)91m'gMo decay partially through positon emission. Cross sections for these reactions have been found by following their activities by the end-window beta counter. For a check in the reaction 92Mo(n, 2n)gXmMo, the cross section has also been measured by following the decay of the 658 keV gamma ray arising from the isomeric transition of 91mMo. A 3.8 cm × 3.8 cm NaI(TI) crystal coupled to a photo- multiplier served as the gamma-ray detector. As the half-life of 9tmMo is short, the window width and the base line of the y-ray spectrometer were adjusted to include the 658 keV 7-~ay. The two values for the same cross section obtained in this way were found to agree well within the experimental errors. Necessary corrections have been applied for the contribution of the isomeric state to the decay rate of the ground state in molybdenum. The details of measurements for the reactions 35C1(n, 2n)34gC1 and 1 ~Sin(n ' 2n)114gln are given elsewhere l z).

3. Calculations

Isomeric ratios are theoretically calculated from the method developed by Vanden- bosch and Huizenga ls, 16). Calculations are carried out in three steps. First the normalized spin distribution Ps of the compound nuclear states has been determined from a ( J c, E ) , which is the cross section for the formation of a compound nucleus with spin Jc by the absorption of a neutron of energy E. This cross section a(J~, E )

for incident neutrons and target nuclei of spin I is given by

x+½ Jc+S (2 jc+ 1 ) a(J c, E) = 7r~ z Z Z TI(E), (1)

s= 11-½1 l= IJc-sl 2(2• + 1) and thus

Ps - a(Jc, E) (2)

Z (Jo, E)" all states

Transmission coefficients for neutrons are taken from ref. 17). Next the decay of the compound nucleus is considered. The relative probability

Psc ~ sf for a compound nucleus with spin Jo of emitting a neutron leading to a final state of spin Jf will depend on two factors. One is the density of levels with spin Jf and the second the angular momenta taken by the neutron. If the probability of de-exci- tation by a neutron of orbital angular momentum l is taken to be proportional to its barrier transmission coefficient, then

J r + ½ J c + S

Ps~-,s~ ~: P(Jf) Z Z TI(E.) . (3) S=lJf-½[ t=lJ=-Sl

478 n. PRASAD AND D. C. SARKAR

Bethe and Bloch 1,2) have predicted the following form for density of levels p(Jf) having the spin Jr:

p(Jf) = p(0)(2J~ + 1) exp [ - ½(Jr + ½)/a2], (4)

where p(0) is the density of levels with spirt zero and a a parameter characterizing the spin distribution. The absolute probability of populating a final state of spin Jr, by neutron emission is found by normalizing the partial probabilities for each final state of a given spin and summing over all the compound nuclear states. These calculations are repeated to include the emission of the second neutron. The average kinetic energy of the outgoing neutrons has been calculated from the nuclear temperature by using the following relations:

En = 2T, T = - l + [ l + a ( E c - B n ) ] - ~ - / a , (5)

where Ec and B n a r e the energy of the compound nucleus and the binding energy of the neutron.

In the third part of the calculations, the de-excitation through v-ray emission is considered. Each spin state population of the excited nucleus will redistribute itself among three spin states upon the emission of one dipole gamma ray. The probability of going from a state of spin Jf to a state of spin Jr_ 1 is then given by

Pj,._,j,. +, = P(Jf+ ' ) - - (6) P ( J f +1 ) -[- P ( J f ) AI- P ( J f - 1 )

Similarly

p(JO (7) Psf~Jf P ( J r + , ) + P ( J f ) + p ( J f - 1 )

P.t,.~J,_, = - P ( J e - , ) - - - . (S) P(Jf +1) + P(Jf) + P ( J f - l )

The average number of v-rays is given by

N =

With the emission of the last 7-ray only two states, namely the ground and the meta- stable states, will be available. It has been assumed that the emission of the last gamma ray populate either the high- or the low-spin state depending on which tran- sition has a small spin change.

The parameter a has also been calculated from the relation is)

a a = I T. (9) h:

Here I is the moment of inertia of the nucleus and T the nuclear temperature. At high excitation energies the moment of inertia can be replaced by its classical value Ir~g

2 9 / r i g = ~ m A R - ,

where the symbols have their usual meanings.

(n, 2n) REACTIONS 479

4. Results

In table 1 are given the observed cross sections and their half-lives. Isomeric ratios for these reactions are listed in table 2. Isomeric ratios for different values of o- are calculated in steps of 0.5. The best value of parameter o- is found by comparing the calculated values to those found experimentally. In chlorine and scandium, the prob- able value of o- is found to be 4_+ 1. In 115In and 92Mo, the value of o- is 6 .5+ 1 and

8.5_+ 1.5, which is higher than the general value 4_+ 1. In these calculations we have considered only the dipole emission. Bishop 9) has shown that the cross-section ratio is quite sensitive to the polarity of gamma rays. In the last column of table 2 are given arlg. It can be seen that there is some agreement between (Trig and O'prob.

TABLE 1

Activation cross sections for 14.8 MeV neutrons

Reaction Half-life Observed cross sections (mb)

35Cl(n, 2n)34mc1 33 min 12 ± 2 35C1(n, 2n)34gCl 1.7 sec 7.3 ± 1.5 45Sc(n, 2n)44mSc 2.4 d 150 ±11 a) 45Sc(n, 2n)4agSc 4.0 h 100 ±10 92Mo(n, 2n)91mMo 66 sec 51 ±10 92Mo(n, 2n)~lgMo 16 min 205 ±25 11~In(n, 2n)ll4mIn 50 d 1585 ±79 b) liSIn(n, 2n)l14gIn 72 sec 360 i 4 0

a) Ref. aa). b) Ref. 14).

TABLE 2

Isomeric ratios for (n, 2n) reactions

Isomeric pairs Spin Isomeric ratios Crprob Target Competing level high spin/total spin

O'rig

3~Cl(n, 2n)z4m, gc1 ~ 0 3 45Sc(n, 2n)a4m, gSc ~ 2 6 92Mo(n, 2n)91m, gMo 0 ½ xlBIn(n, 2n)iXm, gln ~ 1 5

0.64±0.02 2.5 :kl 2 0.60±0.01 4.5 ±0.5 2.25 0.80:k0.1 8.5 ±1.5 3.82 0.84±0.01 6.55~ 1 4.44

References

1) H. A. Bethe, Revs. Mod. Phys. 9 (1937) 84 2) C. Bloch, Phys. Rev. 93 (1954) 1094 3) S. K. Mangal and P. S. Gill, Nuclear Physics 41 (1963) 372 4) S. K. Mangal and P. S. Gill, Nuclear Physics 49 (1963) 510 5) J. H. Carver, G. E. Coote and T. R. Sherwood, Nuclear Physics 37 (1962) 449 6) A. C. Douglas and N. MacDonald, Nuclear Physics 13 (1958) 382 7) C. T. Hibdon, Bull. Am. Phys. Soc. 3 (1958) 48 8) S. K. Mangal and C. S. Khurana, Nuclear Physics 69 (1965) 158

480 R. PRASAD AND D.C. SARKAR

9) C. T. Bishop, ANL-6405 10) L. Katz, L. Peace and H. Moody, Can. J. Phys. 30 (1952) 476 l 1) R. Prasad, D. C. Sarkar and C. S. Khurana, Nuclear Physics 85 (1966) 476 12) R. Prasad, D. C. Sarkar and C. S. Khurana, Nuclear Physics 88 (1966) 349 13) L. A. Rayburn, Phys. Rev. 122 (1961) 168 14) J. R. Prestwood and B. P. Baythurst, Phys. Rev. 121 (1961) 1438 15) J. R. Huizenga and R. Vandenbosch, Phys. Rev. 120 (1960) 1305 16) R. Vandenbosch and J. R. Huizenga, Phys. Rev. 120 (1960) 1313 17) B. T. Field et al., Fast Neutron Data Project NYO-636 (1961) 18) T. Ericson, Nuclear Physics 11 (1959) 481