SHEARS MECHANISM IN HIGH-K MAGNETIC DIPOLE ROTATIONAL BANDS

Abstract

ABSTRACT Nuclear high spin states have remained at the center of attraction of both experimental and theoretical studies for the past three decades. Many new experimental developments in populating and detecting high spin states in nuclei have led to the discovery of several new phenomena in nuclear structure physics. Among the most interesting and the earliest findings, while studying the level spectra of certain nuclei was the observation of regular rotational bands. The level energies of these bands were found to exhibit a nearly I(I+1) dependence. This kind of bands were seen in nuclei that have non-spherical distribution of nuclear density. Being a quantum system, such a deformed nucleus can, as a whole, rotate about an axis other than a symmetry axis. Since many nucleons outside the closed shell contribute to such a motion, it falls under the category of "collective" motion. The two most prominent regions of nuclear deformation are found to be the rare-earth region (150<A<190) and the actinide region (A>225). The nuclei in these two regions are characterized by their large quadrupole moments (axes ratio N 1.4:1) and exhibit a clearly recognizable rotational pattern of level spectra. When the nuclear deformation becomes very large such that the axes ratio in the ellipsoidal shaped nucleus becomes close to 2:1, such a nucleus is said to be superdeformed (SD). The most regular and long rotational patterns of 'y rays have been observed in SD bands. The observation of regular rotational bands in normal deformed (ND) and SD nuclei made us believe that only deformed nuclei can rotate. This was a general belief until early 1990's. The year 1992 brought several puzzles for the nuclear physicists when working independently H. Ethel and group and R. M. Clark and co-workers found regular pattern of gamma rays in the spectra of near spherical Pb nuclei. A detailed study of these bands yielded that the intraband transitions were magnetic dipole (AI=1, Ml) in nature and this was in contrast with the rotational bands in ND and SD nuclei where the intraband transitions were of electric quadrupole (AI=2, E2) type. These bands were, therefore, named as Magnetic Dipole Rotational (MR) bands. Since then, a, large number of such bands have been found in near spherical nuclei in four mass regions of the periodic table. All these bands carry some similarities with ND and SD bands like, (i) The bandhead of all these bands lie at a high excitation energy (a few MeV) and has a high spin (I-4-15h), both indicative of a multi-quasiparticle character of the configuration. (ii) Most of these bands are regular and exhibit a nearly 41+1) bahaviour. The similarities however end here and the bands display some new and puzzling features such as: (i) The intraband transitions are AI=1, and predominantly magnetic dipole in nature with B(M1) values of the order of 1 1.12A,. (ii) Crossover A1.2 electric quadrupole transitions are either absent or very weak, indicative of small deformation and enhancing the ratio B(M1)1B(E2) to ,10-100(mqv /eb)2. (iii) The dynamical moment of inertia W2) is of the order of 10-25 h2MeV-2 which is much smaller than the value in ND and SD bands. The ratio (2)/B(E2) is larger than 150 Ti2MeV-1(eb)-2 here, in comparison to a value of 15 h MeV-1(eb)-2 in well-deformed nuclei and 5 h2MeV-1(eb)-2 in superdeformed nuclei. In addition, some of these bands also exhibit the following features: (i) Many MR bands display signature splitting. (ii) A large number of MR bands display backbending. The work presented in this thesis aims at studying the physics behind the formation of MR bands in nearly spherical nuclei. The thesis has been divided into seven chapters. In the present thesis, an overview of the phenomenon of magnetic rotation and the MR bands and also their comparison with the collective rotational bands in ND and SD nuclei has been presented. Since the anisotropic charge density distribution in nuclei results in a breaking up of the spherical symmetry which leads to the observation of rotational motion, it is clear that some kind of anisotropy is also playing an important role in the formation of magnetic rotational bands. The "shears mechanism" proposed by Stefan Frauendorf does provide for the breaking up of spherical symmetry even in nearly spherical nuclei. The anisotropy now exists in currents and hence the magnetic dipole, which rotates about a ii tilted axis. The bands are therefore also termed as "shears bands" . The phenomenon of shears mechanism will be presented in detail. In chapter II of the thesis, we examine the experimentally observed level structures which are supportive of the MR phenomenon. We classify them according to their intrinsic structures, deformation and the reduced transition probabilities etc, we find that more than 120 MR bands observed in about 60 nuclei spread over four mass regions namely A=80, 110. 130 and 190 can be considered as MR bands. Maximum number of MR bands have been observed in Pb isotopes. Other high-spin features of these bands such as signature splitting, signature inversion and backbending etc. have also been discussed. The cranking model has been a standard tool in nuclear physics to calculate a large number of nuclear properties such as the energies, nuclear deformation, occurrence of AI=2 bands and transition probabilities etc. in ND and SD nuclei. It however fails to interpret the properties of MR bands observed in nearly spherical nuclei. A tilted axis version of the cranking model was therefore proposed which incorporates the shears mechanism quite successfully and gives a good estimate of the excitation energies, spins and transition prob-abilities of the MR bands. Chapter III presents the various versions of this model in detail. We also present a brief account of the Strutinsky renormalization technique and also the hybrid version of TAC that combines the best of the Woods-Saxon potential and the Nilsson potential to calculate the single particle energies. We are generally familiar with geometrical symmetries and their consequences and, dynamical symmetries and their conse-quences. However, MR provides us with a situation where a combination of dynamical and geometrical symmetries arises. The role of new symmetries and the symmetry breaking that arises as a result of the presence of triaxial shape and rotation about an axis other than the principle axis has been discussed. A breaking up of the chiral symmetry also gives rise to `chiral' pair of rotational bands. Consequences and examples of these symmetries have also been presented. While the existence of magnetic rotation phenomenon is well established in A=190 and. A=110 mass regions from experiments as well as theory, the evidence is lacking in the A=80 iii and A=130 mass regions. This is particularly true for the A=80 mass region where both the experimental and theoretical evidence is small. We have therefore focused our attention on these mass regions. We perform calculations for bands in mass-80 region using the hybrid version of TAC and present the results in chapter IV. More specifically, results for 79,81-85Rb, 77'78179181Br and 79Kr nuclei have been presented. We find that the odd-A Rb isotopes present an interesting scenario where they exhibit a rapid onset and declination of MR. This is indeed very interesting as such a rapid development of MR has not been seen in any other mass region. From a systematic study of these bands, we find that the MR is present in these nuclei. However, collectivity is also playing a role and these nuclei may be at the edge of MR and normal rotation. It also points to the manner in which MR bands may evolve towards high-K rotational bands. In chapter V, the results of the hybrid TAC model calculations for mass-130 region have been presented. Nuclei in this mass region are -y soft and exhibit shape coexistence. The deformation in these nuclei is substantially larger than those in mass-190 and mass-110 regions. These nuclei are therefore considered as intermediate betWeen the magnetic rotation and high-K bands of well deformed nuclei. We have performed calculations for the 124Xe, 1"Ba, 131La,.135,136Ce nuclei. Here we try to interpret the nature of these bands within the framework of the TAC model. Several interesting results are presented. Although the MR bands are not expected to display any signature splitting, we present evidence of signature splitting in many bands classified as MR bands; signature inversion is also present in some.cases. Particle Rotor models have been extensively used to explain the rotational spectra and features such as odd-even staggering and signature inversion in odd-A and odd-odd nuclei. We use two quasiparticle plus rotor model (TQPRM) and present our findings in chapter VI. The TQPRM simulates the conditions of shears mechanism quite well and the observation of signature splitting in many MR bands is in line with the PRM. The TAC calculations for the 134Nd reveals some interesting results suggesting a novel mechanism for the band crossing in band 3. The nucleus possibly has a chiral pair of bands also. iv To conclude, the MR phenomenon in different mass regions has been studied. Whereas. the phenomenon is already well established in mass-110 and 190 regions, we have tried to interpret the nature of 6,1=--1 bands in mass-80 and mass-130 regions using the hybrid version of the TAC. The phenomenon of signature splitting which is quite large in some cases, has been studied and the explanation has been given in terms of TQPRM. The conclusions and future scope of the thesis are contained in chapter VII.