chapter motivation behind the high-spin study of mass 60 - 70...

Chapter 2

Motivation behind the High-Spin Study of Mass 60 - 70 Region

2.1 Introduction

The nuclei in the mass range 60:::; A :::; 70 have been studied during the last decade

with increasing interest from both experimentalists and theoreticians. Although the

term "high-spin" in this region of the periodic table applies already to spins around

1017,, it is the richness of nuclear phenomena occurring in these nuclei which makes

the studies particularly attractive.

The single-particle level density in the A ::::: 60 nuclei is noticeably lower than

that ih e.g. the A ::::: 160 mass region. Indeed, with the number of single-particle

states per unit energy about a factor of two smaller, the single-particle energy gaps

and, more generally, the shell structure effects manifest themselves in the A ::::: 60

nuclei in a comparatively dramatic way. In particular, they give rise to a strong shape

variation as a function of both particle number and spin and lead to pronounced

shape-coexistence effects.

The microscopic structure of the nuclei in the A ::::: 60 mass region is primarily

determined by the 1g9; 2 , 2p1; 2 , 1f5;2 and 2p3; 2 orbitals (see Fig. 2.1). The structure

of the proton and neutron single-particle spectra is very similar and the relevant

single-particle properties can be sufficiently well illustrated by showing diagrams of

one kind of nucleon only. The proton and neutron number of the nucleus in this fpg

25

CHAPTER 2. SCIENTIFIC MOTIVATION 26

-8

-10 .

-1J

> (])

~ -14

aJ

-16

-18

-20

Figure 2.1: Neutron single-particle levels in this mass region A '::::: 60 as functions of qu?-drupole deformation {32 , calculated using the Woods-Saxon potential. At each value of {32 the liquid-drop-model energy has been minimized with respect to {34 as described in the Ref. [1]. Since the effective potential wells for protons and neutrons are similar, the resulting single-particle diagrams are similar for both kind of particles. Although the wavefunctions are strongly mixed in many cases, the asymptotic quantum numbers [NnzAS1] are given to simplify the identification of individual levels. The spherical quantum numbers are also given, since they are the most appropriate ones for small deformations.


shell lie between the two spherical magic gaps 28 and 50. So spherical shapes are

expected for the light nuclei, having proton number, N, close to 28 (e.g. Ni, Cu

isotopes) and for the heavy nuclei for which neutron number, N, approaches 50 (e.g.

]t/[ o isotopes). But as the Fermi surface approaches the middle of this shell, one finds

that g9; 2 orbitals get occupied and that the nuclei start showing interesting shape

features. In particular, the nuclei with N, Z ;:::::;; 29 - 40 exhibit a wide variety of

behavior which makes this region ideal testing ground for many theoretical models.

Various nuclear shape properties and excitation modes are established in this mass

region, which otherwise are distributed over different regions of the periodic table.

Besides spherical shapes, one finds here very large prolate as well as oblate and

triaxial deformations at low excitation energy. Moreover, the high spin states are

also interesting as one finds alignments of quasi-particles and resulting shape changes

due to such alignment. Shape variations and associated interesting features have

been reviewed by various authors [2, 3, 4, 5] for this mass region. Now some of the

general features of this mass region would be described to look into the systematics

in this region.

2. 2 Basic Features of Nuclei in Mass 60 - 70 Re-. g1on

2.2.1 High-Spin Shell-Model States near 56Ni

The spectroscopy of doubly magic nuclei and their near immediate neighbors pro

vides vital ingredients for the understanding of nuclear structure, as the single

particle energies and two-body residual interactions observed in these systems form

the building blocks of large basis shell model calculations. On the other hand they

put the most severe constraints on the outcome of such calculations and, conse

quently, define and relate the effective nuclear forces. Nuclei in the vicinity of

self-conjugate, doubly magic nuclei are of particular interest since the protons and

neutrons occupy the same orbitals giving rise to increased proton-neutron corre

lations. Much recent interest has focussed on excited states in nuclei around the

N = Z = 50 shell gap at 100Sn [6, 7, 8, 9]. However, the very neutron deficient


nature of these systems means that production cross-sections for fusion-evaporation

reactions are small and, as a result, only a few states can be identified. Of the four

doubly magic, self-conjugate nuclei with A>4 (160, 4°Ca, 56 Ni, and 100 Sn), high

spin states are most accessible in nuclei near 56 Ni via fusion evaporation reactions

induced by stable beams [10, 11] . As such, nuclei in the mass 60- 70 region provide

an opportunity for a so-called "complete" spectroscopic study. Further information

on high spin states in these nuclei complements the information obtained in studies

of nonyrast states, and allow us to build a full picture of the variety of excitation

modes in the rather restricted fpg single-particle basis between the N = Z = 28

and 50 shell closures. In particular, it also allows us to examine how collective ex

citations are generated with increasing nucleon numbers away from the, nominally

inert, ·56 Ni core.

The mechanism for the generation of high angular momentum states in the

restricted valence space around the 56 Ni core is of particular interest. Energetically

speaking, the first three shell model orbitals above the N = 28 closed shell are the

negative parity p3; 2 , ] 5; 2 , and p1; 2 orbitals. The three lowest lying states in 57 Ni

all have negative parity and respective spins of ~-, ~-, and ~-, corresponding to a

single neutron in these three shell model orbitals [12]. To generate a high spin value

requires the breaking of theN= Z = 28 core and/or the promotion of neutrons into

the positive parity "intruder" g9; 2 orbital. These higher spin states are of particular

interest for A rv 60 systems in light of both theoretical predictions [13, 14] and the

recent experimental evidence [15, 16] of a change at higher spins from a spherical to

a highly collective, superdeformed prolate shape. The question of which mechanism

is energetically preferred is one of the main motivations of this work. In addition

to the general interest in the build up of high spin configurations outlined above, a

detailed and careful study of the medium spin, near yrast states in these nuclei is

important for reliable assignments of spins and parities to states in superdeformed

bands [15, 16] in this mass region. Also, the observation of direct proton decay

from excited states in Cu nuclei [10] makes it important to determine the excitation

energies, spins, and parities of the levels populated in both the parent and daughter

(Ni) nuclei in order to provide a complete characterization of the proton-decaying


states.

A very recent study with the AYEBALL+FMA configuration [18] has identified

the high spin states of the nuclei 61 Cu and 61 Zn. The resulting level schemes have

been compared with shell model calculations using both a simple fP9 basis with no

core breaking, and a full jp basis which allowed no excitations into the 99/2 orbital.

In general, reasonable agreement has been obtained at low excitation energy between

experiment and theory, suggesting that the low-lying yrast excited states in these

nuclei correspond predominantly to valence particle excitations into the ] 5; 2 , p3; 2 ,

and p1; 2 orbitals. However, higher energy and spin states are fairly well accounted

for by allowing only excitations into the positive parity 99; 2 orbital, with no core

breaking.

Another in-beam 1-ray spectroscopy study of high-spin states of 62 ,64 Zn have

been performed by K. Furutaka et al. [19], where they have carried out a shell-model

calculation in the k ::; 3 model space with (0]5;2 1p3; 2 1p1; 2 )A-56-k(099; 2 )k. The

calculation reproduces the yrast levels quite well, including the negative parity levels.

The c.rossing of level sequences with different (k) configurations are established by

the calculation, which seems obvious because the energy increase with I are slower

for the higher k configuration. This crossing structure accounts for the parity change

in the experimental yrast sequences. By this study it is established that the low

lying states of these nuclei may be described as spherical vibration or excitation of

a few nucleons to the higher-lying orbits including 99; 2 , but for higher spins 99; 2

orbits must be included in order to explain the yrast structures of this mass region.

The unique feature of these medium mass nuclei is that the number of valence

particle is not prohibitively large for the new generation of shell-model calculations

and, at the same time, is large enough to create substantial collectivity. Thus

these systems provide a testing ground to confront the large scale spherical shell

model [20], as well as various collective models like, cranked shell-model, cluster

model, or interacting Boson Fermion Fermion model [19, 20, 21, 22, 23].


2.2.2 Shape Transition and Smooth Band Termination

This region of the mass 60 - 70 nuclei has lately become a region stimulating much

activity, both in experimental and theoretical investigations. Recent developments

in nuclear structure have brought a considerable focusing on the problems of shape

evolution and shape coexistence phenomena. Current emphasis is not only on the

geometrical shapes in terms of various forms of the nuclear surface, but maybe more

importantly, with an understanding of the underlying microscopic forces from the

different single-particle configurations. This feature influences in a dramatic way,

the changes in nuclear global properties. One of the reasons centered around a

basic prediction [1] of the cranked shell model ( CSM) which indicates that when the

Fermi surface is raised to the g9; 2 shell, the triaxial deformation-driving effects of the

quasi particles is toward the non-collective asymmetry sector ( +1). The implication

is that the collectivity in the s band, following the rotation alignment of a pair of

g9; 2 neutrons (or protons), should drastically reduce compared to that of ground (g)

band.

In recent years it has become possible to observe rotational bands in heavy nuclei

which gradually exhaust the angular momentum content of their single-particle con

figurations. Such bands were first predicted and observed in nuclei around 158 Er [24].

More recently, rotational bands which either reach or approach their terminating

states have been observed over extended spin ranges in 109Sb [25, 26] and neighbour

ing nuclei, and bands approaching terminations have been identified in a few A rv

80 nuclei and three in mass 60- 70 nuclei [16, 27, 2S]. These smoothly terminating

bands are predicted to show a continuous transition from states of high collectivity

at intermediate spins to a pure particle-hole (noncollective) state of maximum spin

in which the angular momenta of all the valence particles and holes are quantized

along one axis. Such bands provide a unique opportunity to study the interplay

between collective and single-particle degrees of freedom within a single nuclear

configuration. Although transition quadrupole moment measurements up to termi

nation would provide a crucial test of the predicted loss of collectivity inherent in

the present interpretation of smoothly terminating bands, such measurements have

only been possible for 62 Zn [16].

CHAPTER 2. SCIENTIFIC MOTIVATION

.. ·····n·· ' .''

, Macro8copic prolate conective rotort created by ehcitations 'across the z:;;. 28 magic shell gap, smoothly change.~ \\(idi·increasing: spirno an oblate non-collective slut~;

• The nucleus cbttngestbe mechaill:sm .by"which>it gen.enltes a.ngtdat momenbtm; ' . . . . . ~ .

from ooUective t'Q~ation·to.sitJg}e .. patticle alignment I

31

Figure 2.2: Theoretical calculations predict that as the available valence nucleons outside of the Z = N = 28 double shell closure align, the nuclear shape gradually traces a path from a collective prolate shape ( '"Y = 0°) through triaxial shapes to a noncollective oblate shape ( 1 = +60°) over many transitions. This feature called "smooth band termination" is illustrated here, where the potential energy surface is plotted for the yrast configuration in 62 Zn as a function of shape and spin [16].


Recently an interesting study by Svensson et al. [16] has revealed the first obser

vation of terminating states of rotational bands in the A= 60- 70 mass region. Also

the evidence from quadrupole moment measurements indicates that these bands of 62 Zn do indeed lose collectivity as they approach termination. This investigation

has played a most significant role in establishing a novel form of band termination

in nuclei near mass A = 60 - 70. The structures of interest involve particle-hole

excitations across the Z = 28 shell gap into specific high-j g9; 2 orbitals to create

prolate collective rotational sequences or bands. As the rotational frequency and

spin increases the Coriolis interaction forces the valence particles to gradually align

their individual angular momenta along a common spin axis resulting in character

istic decreasing dynamic moments of inertia ( J(2)). The calculated potential energy

surfaces show characteristic shape behavior which are different for each configura

tion. These properties are illustrated in Fig. 2.2 for the yrast band in 62 Zn. It is

the ability to observe a specific configuration over such an extended range of spin

values without interruption that is so special in this mass region.

Another study by Galindo-Uribarri et al. [27] has discovered a high-spin rota

tional band in 64 Zn, which is seen as two signature partners connected by strong

.1\11 transitions. Nilsson-Strunsky cranking calculations give evidence that this yrast

band is triaxial (! "" 30°) at intermediate spin values, while with increasing spin,

the collectivity is gradually lost and the two signatures end up in non-collective

terminating states (! rv 60°) at spin values around 25-11. Similar kind of feature is

also o.bserved in 69 As [29], where the nucleus is predicted (by total routhian surface

calculations) to change its shape from an oblate (! rv -55°) to a triaxial prolate

(r "" 20°) shape at intermediate spin. Self-conjugate 62 Ga [30], and 68Ge [31] nuclei

also show features of smooth band termination. Recently some highly deformed

rotational bands in 62 Cu and 63 Zn are also reported [32] to have shown a continu

ous decrease in their moments of inertia - an indicative of band termination, the

detailed results of which are still awaited. This has established a sets of examples of

the existence of collective bands [coming close to termination] in this mass region.

Further studies of smoothly terminating bands in this mass region will undoubt

edly lead to a more detailed understanding of the gradual loss of collectivity. These


nuclei are also of particular interest because they are just at the limits of modern

large scale shell model calculations. Further studies of this transition from collec

tive rotation to noncollective terminating states in these light nuclei should provide

unique opportunities to compare the mean-field cranking models of rotational nuclei

with the microscopic shell model.

The nuclei from the 60 - 70 mass region have been known for many years to

exhibit various signatures of shape coexistence. Among doubly-even nuclei the best

examples are 68 ,70 ,72 Se [33, 34], where an oblate ground state coexists with a well

deformed prolate structure which becomes yrast at higher angular momentum. In

odd-A nuclei experimental information for coexisting oblate and prolate bands has

been found in 69 ,71 Se [35, 36]. All these nuclei belong to the lower half of the g9; 2

subshell.

2.2.3 Band-Crossings and Alignments

An interesting aspect of this mass region A = 60 - 70 is the fact that some nuclei

exhibit backbending phenomenon. In the region between 10 to 20 units of angular

momentum, an anomaly is observed in the yrast band of many nuclei. It can be

most easily demonstrated if one plots the kinematic moment of inertia ( 1 1) as a

function of rotational frequency ( w). In lowest order of rotational model this should

give a straight line. The deviation from a constant is then a measure of the validity

of the I(I + 1) law. Figure 2.3 gives an example for such curves, measured by

Gammasphere group [37]. This figure shows that the rotational excitations in 156Dy

can be split into three distinct angular momentum groups. The low moment of

inertia class (spin I= 0- 16h) corresponds to the ground-state rotational band and

vibrational structures. Here the nucleus displays superfiuid properties with nucleons

teaming up in time-reversed orbits, or "Cooper pairs". But collective rotation of

the nucleus tries to break these correlated fermions apart (the Coriolis-antipairing

effect). This leads to the second class of states (I = 18- 38h) where one, then two,

then three specific pairs of nucleons have been broken apart by the Coriolis field

(back bending). With increasing rotational frequency and spin, it is thought that a

transition may occur from a superfiuid to a normal phase in a manner analogous to


> Q)

~ 80

'i ro ·-e Q) 60 c:

0 c Q)

E 0 ~

40

20

0.0

I= 40--760h

0.2 0.4 0.6 0.8 1.0

Rotational Frequency (MeV) 1.2

Figure 2.3: Typical backbending plot: the observed rotational states in 156 Dy [37] can be grouped into three major classes, reflecting the dramatic changes in shape and · structure that occur with increasing spin. How the Coriolis force tries to break apart pairs of correlated nucleons moving in time reversed orbits in a rotating nucleus is shown schematically.

the quenching of superconductivity in metals by a sufficiently high magnetic field.

The third class of states (I = 40 - 601i) indicates another structure change occurs,

most likely associated with a prolate to oblate shape change of the nucleus, but which

also may involve the transition to a region where the pairing field is significantly

weakened. Indeed, calculations which assume that pairing correlations are quenched

provide an excellent description of this high-spin change in structure. However,

such a comparison while indicative, cannot be taken alone as conclusive proof of the

long sought pairing phase transition. If, where, and exactly how the superfluid to

normal phase transition occurs in the finite system of the atomic nucleus remains

an important and unfinished task. Such a phenomenon can be easily reproduced

as an· effect due to the crossing of two bands with different moments of inertia.

Because of the residual interaction, such a crossing does not take place (the 'no

crossing rule') and this means we have an increasing J(l} with decreasing w, while

the properties of the bands exchanged. On the other hand, it is also clear that the

strange backbending behavior has its origin in the fact that we follow the yrast line


in the critical region, that is, we switch over to the crossing band of different internal

structure. Now it is well understood that the reduction of the pairing correlations

is only responsible for the slow change of the moment of inertia at low spin values,

but that sudden effects are due to alignment of a single high j pair of nucleons.

The alignment (ix) is, in fact, a measure of the aligned spin of the broken pair

of particles at a first band-crossing between the 9 and s bands. If the interaction

strength between the two crossing bands is weak, a sharp backbending is observed

but if it is strong a gradual up-bend over a wide range of spin and frequency values

occurs. The third type of band-crossing with moderate interaction is called a vertical

up-bend. In practice, alignment plots are good indicators of these different types of

band-crossing, which will be described later in Chapter 6.

An interesting study on N = Z 68 Se by Fischer et al. [33] establishes an excited

prolate band that has a moment of inertia always larger than the ground state oblate

band and that that has a sharp backbend at nw = 0.57 MeV. This nucleus is well

known for oblate ground state deformation. The alignment partially matches the

predictions of Ref. [1] and cranked calculations for a prolate configuration. A gain

in alignment, about 4n, similar to that measured for (99; 2)2 aligned configurations

measured in neighbouring nuclei, but half that which would be expected for simul

taneous alignment of protons and neutrons, is found. However, there seem to be

other inconsistencies in high-spin alignment in prolate selenium and krypton nuclei

which need to be resolved as a separate issue. At high spin, above the alignment

region, 68,70

,72Se [33, 34] show similar characteristics, with rather constant moments

of inertia, which increase with mass faster than the expected A 513 dependence. This

is consistent with the predicted increase in deformation with mass of {3 = +0.27,

0.30, and 0.32 driven increasingly strong by prolate shell gap at N = 38. Similarly

in 67,69

,71 As isotopes backbends are observed for the 99; 2 bands [29]. Particularly in

69 As [29], it is evident that there is a gain in alignment of rv 7n at a frequency of

0.511 MeV and this is interpreted as the alignment of a pair of 99; 2 neutrons. Con

sideration of the spin projection for this configuration provides evidence of shape

changes in this nucleus from an oblate shape to a triaxial prolate shape at intermedi

ate spin where the nucleus is stabilized by quasiparticle alignment. 68 Ge is another


candidate for showing a band-crossing phenomenon [31], where it is consistent with

the prediction that for the neutron aligned yrast band, the contribution of the g9; 2

neutrons and protons to the total angular momentum should be nearly equal [38].

Recent studies [15, 27, 39, 40, 41, 42] of superdeformed (SD) and highly deformed

bands in 60 - 65 ,68 Zn have allowed systematic analyses of strongly deformed shapes

and configurations in the A = 60 - 70 mass region. In the study [39] of 60 Zn, a

rise in dynamical moments of inertia ( J(2)) of the SD band was interpreted as the

simultaneous alignment of the g9; 2 protons and neutrons. However, the absence of

such an alignment in 61 Zn raises questions [40] of whether or not the T = 0 pairing

is responsible for such an alignment. Similarly for the highly deformed bands in 63 ,65 Zn [41, 43], it is indicated that the normal nn, pp pairing alone can not be the

only cause for the observed alignments. The np interactions are supposed to be

most likely the main cause for the rise, and such interactions appear to exist only

when the occupation of the g9; 2 intruder orbitals is identical for valence protons and

neutrons. 62 Cu is also recently reported to have exhibited a sharp backbend for a

highly deformed rotational band [32]. To understand the true cause of the band

crossing and the associated alignment and more, to gain insight into the question of

the possible T = 0 pairing, more experimental data are needed for the neighbouring

nuclei

2.2.4 Superdeformation and Other Features

Superdeformed nuclei are beautiful examples of quantum rotors. They have been

referred to as "nuclear pulsars" and indeed close analogies have been found between

the fast rotation of the nucleus and that of a neutron star. Additionally the stun

ning discovery is that superdeformed nuclei are the best example of single-nucleonic

motion in a deformed potential. Thus the physics of superdeformation involves a

fascinating interplay between the microscopic (shell structure) and the macroscopic

(e.g. surface and Coulomb energies) properties of the nucleus. Consequently, they

provide a unique laboratory for testing nuclear models. Many superdeformed rota

tional bands have been observed throughout the nuclear chart and they cover the

full range of possible spins, from I = On right up to I = 70n close to the fission limit.


The observation of superdeformed states constitutes an important confirmation of

the shell structure of the nucleus. Quantum-mechanically, the remarkable stability

of SD states can be attributed to strong shell effects that are present in the average

nuclear potential at very elongated shapes. The structure of single-particle states

around the Fermi level in SD nuclei is significantly different from the pattern at nor

mal d·eformations. Indeed, the SD shells consist of states originating from spherical

shells having different principal quantum numbers, and hence having very different

spatial character. This unusual situation produces new effects in nuclear structure.

SD states have been discovered in mass 60 - 70 region quite recently. Because

of the limited number of valence particles in these nuclei and their proximity to the

N = Z line, SD in this mass region is of particular interest. Based on calculations of

large SD shell gaps in the single-particle energy levels for particle numbers N, Z :::

30 - 32, SD bands have been predicted in this region. The SD nuclei which are up

to date known in this mass region are 62 Cu, 60 - 65 ,68 Zn, and 68 Ge. The observation

of first SD band in this region is that of 62 Zn, where a cascade of six 1 rays is

found to form a rotational band over an estimated spin range of I = 18 - 301i. The

scaled J(2) moment of inertia of this band is comparable to those of SD bands in

other mass regions, and the measured quadrupole deformation of /32 = 0.45~8:5~

is in excellent agreement with theoretical calculations. This result establishes a

new region of superdeformation in mass 60 - 70 region. A systematic study of

SD bands in this mass region is clearly required to define the limits of this newest

region of superdeformation and to extract detailed information about the single

particle energies at large deformation for these light nuclei. Because of a number

of experimental difficulties, searches for these bands have been unsuccessful with

our experimental facilities at Nuclear Science Centre, so we would refrain ourselves

from describing the detailed features of this SD nuclei. The various consequences

of the SD bands in this mass region are described in detail in the literature already

mentioned.

Another interesting facet in this mass region is that, because of a low Coulomb

barrier, proton emission may compete with 1 decay of excited states of mid-mass

neutron deficient nuclei. In fact, the first observation of a prompt ( T <3 ns) decay


of a well deformed excited band in 58 Cu via emission of mono-energetic protons into

a spherical excited state in 57 Ni, has been recently reported [17]. Since the nucleus 58 Cu has only one more proton and neutron than its doubly-magic neighbor 56 Ni, it

is an excellent example of a spherical nucleus. The spherical states in 58 Cu have their

angular momenta generated by aligning the spins of the individual nucleons along a

common axis. These states lie in the lowest or first minimum in the potential energy

surface. However, well deformed states in 58Cu also exist, albeit at higher energies

and spins, in the so-called second minimum of the energy potential. One such

band,. corresponding to collective rotation of the nucleus as a whole, was recently

identified in 58Cu [17]. A unique and surprising feature of this band is its decay

mode. Commonly nuclei that are trapped in the second minimum eventually make

a transition to the first minimum by emitting 1 rays, although they may, in principle,

also decay by emission of f3 rays or even by fission when the nucleus is very heavy.

However, in addition to the common mode of gamma decay, 58 Cu was observed

to decay to its neighboring nucleus 57Ni by emitting a proton. This was confirmed

experimentally by detection of a 2.4 MeV proton line that is emitted from the lowest

member of the collective band in 58Cu. The final state in 57Ni that is fed by this

proton decay may have some special properties since the decay does not populate

other states that could have also been fed. Similarly, two well deformed rotational

bands have been identified in doubly magic 56 Ni [44], where it is evident that one of

the bands, which is identical to a sequence in the odd-odd neighbor 58Cu, partially

decays via proton emission into the ground state of 55Co. This unprecedented decay

mode represents a very interesting quantum mechanical process - the emission of

such a proton is forbidden in classical mechanics. Theoretical studies of this process

will help elucidate how the proton 'tunnels' through a potential energy barrier in a

deformed nucleus.

2.3 Aim of Present Study

Now it is clear from previous section that the nuclei lying in the mass region 60

- 70 exhibit a wide variety of structural effects at low as well as at high spins.

Therefore, it needs further experimental investigations for the sake of complete and


better understanding of the behavior of nuclei at high spins. Among the above

mentioned features, superdeformation and smooth band termination - have been

studied very recently and theoretical understanding of these features in this mass

region still needs a systematic survey- which is a separate issue. Here we would look

for the feature of some shell model nuclei. The high spin spectroscopic data from

the nearest neighbors of doubly magic nucleus 56 Ni serve and act as an important

constraints on the parameter sets of the nuclear shell model, and consequently, define

the effective nuclear interactions. The nuclei near 56 Ni are of particular interest as

they are amenable of different microscopic theoretical treatments while studying

the competition between single particle and collective excitations. Large scale shell

model calculations in the full fpg configuration space will be used to describe the

high spin structures of two nuclei 62,63 Cu. This will be the excellent testing ground

for the large-scale shell model calculations.

Another motivating factor is to look for the features associated with collective

rotational bands in this mass region. Therefore, we would also like to study the

features, for example, shape transition, band crossing and alignment. The spectro

scopic data of lower mass nuclei in this region indicate that in these nuclei, mostly

spherical in nature, spins are generated by particle excitations only, which is, in prin

ciple, because of the proximity of the N = Z = 28 single particle magic gap (see

Fig. 2.1). However, the nuclei near the middle of this shell exhibit highly collective

bands with large quadrupole moments. The nuclei in the transitional region of these

two limits are expected to have complicated structure with both single-particle and

collective states. This would imply that once the proton and/or neutron occupy

the deformation driving g9; 2 orbital, the collectivity in nuclei emerges. Therefore,

in the present work, our aim will also include the investigation of the high spin

states of some transitional nuclei in this region. This would define the competition

between single particle and collective degrees of freedom, and would indicate the

onset ·of high spin collectivity in this mass region. For this purpose we would study

the high spin states of the nuclei 65 Zn, 70 Ge, and 70 As. The part of the chart of

the nuclides around the doubly magic 56 Ni is shown in Fig. 2.4. The nuclei to be

studied are marked by asterisks, whereas the rest of the chart contains those nuclei


* ?As ?As 33

* oYGe 7Ge 32 '-"' -o

66Ga

6tta

6ha 6Ga 31 ~

::l .:

* o3Zn 64Zn

6·zn .: 0

30 ..., 0 '-

* * 0...

62Cu 63Cu ii4Cu 29

33 34 35 36 37 38

Neutron number

Figure 2.4: The part of the chart of the nuclides to be studied. The asterisk mark stands for nuclei to be studied in our experiments. Only those neighbors of nuclei are shown which might be used for systematic comparison with our results. Also these nuclei are of major importance for determination and verification of the parameters of the nuclear shell model in this mass region.

which are very well studied by different experiments. So in this work we will also

try to compare our results with those of nearby nuclei from others' experiments for

a systematic comparison.

The odd-odd nucleus ~§Cu has been the subject of number of studies in the

past and the results can be found in the latest compilation by King [45]. It has

been conveniently studied by f3 decay of 62 Zn (t1; 2 = 9.186 h) which populate states

up to an excitation energy of 1.52 MeV. The spin-parities of the levels up to Ex

"" 1.0 MeV have been firmly established by these works. It has also been studied

using (n, 2n!), (p, n1), eHe, p) reactions and transfer reactions such as (d, t) and

( d, a). As far as the high spin part of the level scheme is concerned, the relevant

information has been obtained from the work based on the 60 Ni(o:, pn1) reaction, 52 Cr(l4 N, 2p2n!) [46] and 5°Cr(160, 3pn) [22] heavy ion induced reaction studies.

But these later studies using heavy ion did not populate any more new levels that

had n.ot been found using a projectile. The latest reaction study [22] has provided

energy levels up to an excitation energy of 7.6 MeV and the highest spin observed


is 911 for both the parity states. The low-lying level structure of 63 Cu has also been

investigated mostly through various light-ion induced reactions [47, 48, 49], but the

information of high-spin states is limited [50]. In the latest experiment to study

the high-spin states in 63 Cu [50] by two Ge(Li) detectors, Mustafffa et al. did not

populate any new level that had not been found using a projectile. The level of

highest excitation energy observed through these studies was limited to 6.2 MeV

without any spin parity assignment.

The level scheme of the odd-A zinc isotope, 65 Zn, has been studied experimen

tally mostly through light-ion induced reactions [51, 52, 53] and in the framework

of different theoretical models. These studies have indicated that the 1g9; 2 neutron

orbital, which lies in the vicinity of the Fermi level, plays a significant role in the

formation of some of the excited states of this isotope. The recent study [51] on this

nucleus through a-induced reaction using only 3 HPGe detectors, has confirmed the

level scheme only up to 5.773 MeV without any spin-parity assignment. Therefore,

the experimental information in the literature on the high-spin states is incomplete.

The spins and parities of several states in this nucleus are inconclusive. However, by

a very recent development to study the superdeformed and highly deformed bands

in this nucleus [43], it has established the existence of three excited highly deformed

bands decaying to the ground state, with the linking transitions being unobserved.

With the experimental limitation to explore the highly deformed structure in this

nucleus, our aim would be rather confined to the study of normal-deformed yrast

configuration of this nucleus, which have been not yet looked into.

The even-even nucleus 70Ge has been studied via the (p, p'), (n, n'1), (p, t), and e He, d) [54, 55, 56] reaction up to 5.1 MeV excitation energy. More recent

experiments [54] by a and 16 0 projectiles have produced levels up to 5.5 MeV with

a tentative assignment of 10- spin-parity state. The enhanced collectivity of the

negative-parity levels was explained very consistently as it was observed to increase

with Z when going from Ge to more deformed Kr isotopes.

In the neighboring odd-odd nucleus 70 As, the low-lying states are similar to 72 As and were experimentally well investigated by the works of Brink et al. [58] and

Filevich et al. [59] using proton, a and light ions as projectiles. These states could


also be described by the shell model without invoking the deformations. The high

spin states of this nucleus, however, are not very well studied. The first attempt

of studying the high spin states of this nucleus, using heavy projectile was done by

Badika et al. [57] using 160 as projectile. But they could only populate up to the

11 + and tentatively up to 13+ state at 4076 keV. All these states were described

using the parabolic rule derived from the cluster vibration model. In this model,

they assigned a ( 1r g9; 2 , v g9; 2)t configuration to the 1752 ke V g+ level. They also

suggested that the states above this would represent a collective band. The lifetime

measurements of the 11 + and 13+ levels, by Garcia Bermudez et al. [60] indicated

an enhancement in the B(E2) values of the 981 keV and 1343 keV transitions. This

suggests the possibility of onset of deformation in the odd-odd 70 As nucleus having

rotational bands similar to those found in neighbouring 72 As nucleus. However, the

band structure of 70 As have not been studied prior to this work.

2.4 Plan of the Work

The heavy-ion induced fusion evaporation reaction would be used to populate the

high spin states of the nuclei. The whole experimental work has been planned to

be carried out at Nuclear Science Centre, New Delhi, India. For the spectroscopic

study of these nuclei, the fusion reactions to be used are:

1. 52 Cr(l60, xaypzn) 62•63 Cu, 65 Zn at 65 MeV of beam energy.

2. 52 Cr(l9F, xaypzn) 62 •63 Cu, 65 Zn at 70 MeV of beam energy.

3. 46 Ti(28Si, xpyn)1° As, 70 Ge at 110 MeV of beam energy.

In the first two experiments natural chromium target is 1 mg/cm2 thick with a Au

backing of 7 mgjcm2, while the second experiment would be performed with two

self-supporting stacked targets of enriched 46Ti of thickness rv 300 and 210 f-Lgm /em 2 .

The beam would be delivered from 15-UD Pelletron accelerator at NSC. For

the first two experiments, the set-up of the Gamma Detector Array (GDA) with 12

HPGe detectors in conjunction with a Charged Particle Detector Array (CPDA),

which is newly devised for this type of experiments only, would be used to collect


r rays along with lightly charged particles (namely, protons and a's for channel

selection). For the third experiment, the set-up of HIRA + GDA configuration

would be used to collect the r-rays in eight HPGe detectors along with the recoils

to be detected in the Recoil Mass Spectrometer (RMS), HIRA at NSC. Another

experiment to study the nuclei 70 As and 70Ge, using the same reaction, would be

used with the GDA alone with twelve HPGe detectors. The experimental details

and set-up used, are described in Chapter 4.

2.5 Conclusion

A brief survey of the basic features of the nuclei in the mass region 60 - 70 is given

in the beginning of this chapter. It has been pointed out that many interesting

features, both at low and high spins, are expected in these nuclei. In the subsequent

part, the aim of the present work is discussed. The high spin features of these

nuclei, particularly, the different modes of generation of angular momentum through

delicate interplay between single particle and collective excitations, the occurence

of yrast rotational bands, and their change in shape due to particle alignments, are

planned to be studied experimentally through spectroscopic measurements.

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47

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