STUDY OF THE TWO-QUASIPARTICLE BAND STRUCTURES IN ODD-ODD AND EVEN-EVEN NUCLEI

Abstract

It is now well known that a slight shift from the closed shells of neutrons and protons leads to onset of nuclear deformation. With the recently identified regions for the nuclear deformation, the number of deformed nuclei exceeds the number of spherical nuclei by an. overhelming majority. Existence of a nonspherical shape indicates the presence of a coherent collective motion alongwith the well known single particle motion in nuclei. It also opens up the possibilities of rotational phenomena in nuclei. The three major kind of excitations in deformed nuclei are therefore the intrinsic excitations, the vibrational excitations and the rotational excitations. The energies of these excitations are such that the intrinsic motion can follow adiabatically the vibrational motion which, in turn, follows the rotational motion, It therefore becomes possible to study these excitations independently although some mixing can always occur. A rotational band can be built on each of the intrinsic excitations and the simplest intrinsic excitations of the one-quasiparticle nature are observed in odd-A nuclei. A tremendous progress has recently been made in understanding the new features observed in the band structure of odd-A nuclei. Two-quasiparticle intrinsic excitations are possible in both the doubly-odd and the doubly-even nuclei. The band structure based on these intrinsic excitations are expected to be more complex in nature. The coupling between these bands have recently been studied in great detail by many workers. Interesting features like odd-even staggering in the energy levels of the K =152 P -Q nI bands and almost no staggering in the K+=(E/pn) bands were pointed out by Jain et al [1989] and understood in terms of Coriolis coupling of various order. In the present thesis we have extended this study to the two-quasiparticle band structure in even-even rare-earth nuclei. The two-quasiparticle intrinsic excitations are expected above 1.-.1 1 MeV (the average pairing gap) in the even-even rare-earth nuclei. About SO two-quasiparticle Gallagher doublets and the rotational band based.on them have recently been listed in a compilation by Sood et al [1991]. In chapter II, we present an exposition of the presently available experimental data on the two-quasiparticle bands in the even-even rare-earth nuclei and highlight some of the important and unusual features observed by us. To understand their behaviour we present a formulation for the coupling of the 2qp rotational bands within the framework of a two-quasiparticle plus rotor model. This formulation is very similar to the one presented for the odd-odd nuclei; however some additional features come in due to the different nature of the wavefunction. In chapter [II, we report the results of the TQFRM calculations for 168Er, Application of the TQPRM to 168Er assumes considerably importance since this nucleus Is presently one of the best studied deformed even-even nuclides with almost 41 assigned rotational bands. Almost 27 of these 41 bands have been assigned a two-quasiparticle configuration. This represents a wealth of data in a single nucleus and presents an unique opportunity to apply our model. We have succeeded in reproducing the odd-even staggering observed in rotational bands of 168Er. We present the detailed results of our calculations and discuss the effect of Coriolis coupling in the various bands. We hope that the present analysis will contribute to resolve some of the problems in the interpretation of the data of 168Er. In chapter IV, we have discussed the anomalous signature dependence observed in two-quasiparticle bands of deformed even-even nuclei. The signature effects in the 2qp rotational bands of even-even nuclei are expected to be far more complicated. The decoupling effects again give the favored spin as If1+j2)mo2; however, the odd-even shift in the K=0 bands of the even-even nuclei differ in sign from that in the odd-odd nuclei giving the favored spin as If=(j1+j2-1) mod2. The two effects now oppose each other. There is no experimental data on Newby-shifts in the even-even nuclei; our calculations Indicate that it may be as large as few hundred keV. It is therefore very difficult to predict the signature effects in the even-even nuclei.In this chapter we consider two specific examples namely170Yb and 180Os. The two Gallagher partners, the n K =3 1/2[5217n} and i7/2[633)nel/21521)n} bands in 170Yb exhibit opposite phase of odd-even staggering while normally one would expect the same phase. Large irregularities are also observed in the ler=7 (7/2[633)ne 7/2(614]n) band in 1800s, Both these bands are explained reasonably well by the TQPRM calculations. The mechanism which is responsible for this anomalous behaviour is also discussed in detail. These calculations therefore indicate that the Coriolis coupling can spring quite a few surprises and may explain what may look like an irregular behaviour. In chapters V and VI, we discuss the two specific problems which relate to the two-quasiparticle rotational bands in doubly-odd nuclei. More specifically in chapter V we consider the special character of the K=0 bands in the rare-earth nuclei where we briefly summarise the TQPRM formulation proposed by Jain et al [1989] with special emphasis on the nature of the K=0 bands in odd-odd nuclei. We have presented the experimental data on the K=0 bands in the rare-earth region and examined the reliability on the data. We have also redetermined the values of the Newby-shifts due to the n-p residual interaction by removing the effects of Coriolis and particle-particle coupling. These new empirical values help to resolve the inconsistency in the sign of the Newby-shifts in 160Th and 174Lu. Also the Newby-shifts are modified in two other cases namely in 168Tm and 172Lu. The new set of values for the Newby-shifts obtained by us should be used in fitting the parameters of n-p residual interaction. The set of parameters so obtained may be more useful in predicting the Newby-shifts for configurations not observed so far. In chapter VI, we focus our attention on another important problem of odd-odd deformed nuclei, namely the phenomenon of signature inversion observed in the high-K rotational bands. The favored signature in the high-j Hi11/2)p(113/2)n configuration bands is given by a1,=1/2(-1)jp1/2+1/2(-1)-J n-1/2 ; however, a signature inversion has been observed at the lower spins which gets corrected around spins I= 11 to 14. Explanations based on the cranked shell model , the particle-rotor model with zero and non-zero 7-deformation and angular momentum projection approach have been pursued by various authors . Our recent calculations based on the particle-rotor model suggest that the Coriolis coupling has all the necessary ingredients to cause a signature inversion. We included a set of selected bands emanating from the (h11/2)p(i13/2)n set of orbitals in the calculations. Our calculations reproduced the subtle inversion effect seen in 160Ho - but failed in 152 156 Eu and Tb; it is indeed surprising. However if we incorporate the 1/2(5411 state into our calculations which belongs to the h9/2 proton orbital, we do get an inversion. The mechanism of signature inversion IS discussed in detail. In chapter VII, we present an extension of the variable moment of inertia model (VMI-model) to the rotational bands of the odd-odd nuclei in the rare-earth region, which do not possess significant Coriolis mixing. It has been noticed that the K + =(I-2p +S-2 n) bands in odd-odd nuclei show feast staggering and therefore minimum Coriolis mixing. These bands are therefore readily amenable to VMI-analysis. However, we must exclude those K+ bands where high-j neutron-proton orbitals are involved. On the other hand, some K-=IQp-QnI bands exhibit a very small degree of odd-even staggering in their energy levels; we will therefore discuss the applications of the VMI-model to the K as well as to some of the K bands and also discuss the systematics of the parameters obtained, The region of the validity of the model has been calculated and Mailmann like curves obtained for the first time in the odd-odd nuclei. The available data of the rotational bands satisfy the predictions of these curves very well. Further an interesting analysis of the moment of inertia parameter and its variation with angular momentum is made in comparison to the behaviour of the neighbouring odd-A rotational bands involving either the neutron or the proton configuration which is also present in the odd-odd rotational bands. Such a comparison brings out the strong configuration dependence of the pairing correlations and the associated blocking phenomena. it is clear that a significant amount of pairing correlations remains in most of the odd-odd rotational bands. We summarise the main findings of our work in chapter VIII, where we also list some of the future directions for the present work.