PROTON EMISSION FROM TWO QUASIPARTICLE STATES IN DEFORMED ODD-ODD NUCLEI

Abstract

A fundamental theory for understanding the structure and decay of nuclei remains as elusive as the exact form of the nuclear force. The theoretical nuclear physics is envisaged through several models constructed mostly in a phenomenological way. With the nucleus being a complex many body system, the nuclear models are not so versatile due to the strong dependence on the parameters, which is generic for any many body theory. Most of the nuclear models agree well with each other while explaining nuclei for which experimental information is known, whereas these models poorly perform when extended to study the nuclei yet to be observed in a laboratory. Hence, it is important to study the nuclei far from stability, which can enable us to test and validate the nuclear models and their underlying theories. This thesis work is an attempt in this direction with the study of the properties of extremely proton-rich nuclei. Understanding the structure of nuclei near proton drip line has been possible by investigating the process of proton emission which is well complemented by other spectroscopic studies. As a consequence of higher Coulomb barrier in the region of ground state proton emitters (Z > 50), the unbound proton spends enough time to be measurable experimentally. Most of the models for proton emission explain very well the measured half-lives for spherical as well as deformed nuclei. Simple models are based on semiclassical WKB methods while the deformed proton emitters can be studied more rigorously by identifying that the decay proceeds from the single-particle resonances. Microscopic study of the deformed proton emitters allows us to test the details of the nuclear wavefunction to which the half-lives are quite sensitive. The most consistent theoretical approach in this regard is the nonadiabatic quasiparticle approach which is very successful in bringing out several interesting features of dev formed proton emitters including the triaxially deformed ones. All these works are on odd-even proton emitters, and the odd-odd nuclei were studied only in the adiabatic limit. Deformed odd-odd nuclei, in general, are more interesting as they provide access to study the interaction between the valence (odd) proton and the valence neutron while the rest of the even numbers of protons and neutrons can be thought of forming an inert core. The knowledge of interaction between valence nucleons contributes valuably in the theoretical understanding of angular momentum couplings. The ground state and other low lying states of the deformed odd-odd nuclei are strongly influenced by such an interaction between the odd particles. However, energy spectra built on these states are still dominated by the rotational motion of the deformed system. Consequently, the excited states of many odd-odd nuclei are quite well known but the spin and parity of their ground states are still ambiguously assigned for many of the cases, even for the nuclei near the β -stable region. In the case of odd-odd nuclei around proton drip line, the Fermi energies of proton and neutron are separated by far. However, the number of protons is closer to that of neutrons (especially in the lower mass region) and hence the valence proton and the valence neutron have same set of single-particle states (Nilsson orbitals) to occupy. This may enhance the role of the residual neutron-proton (np) interaction which can influence the properties of the ground state from which the proton is emitted. Proton emission studies being regarded as an accurate probe for nuclear structure, has a potential to unravel several interesting features of odd-odd nuclei including the residual np interaction. The primary goal of this work is to identify the ground states of odd-odd nuclei in the proton drip line with the aid of decay properties of these nuclei, namely the proton emission half-lives. In case wherever data exists, the rotational spectra are also utilized to extract additional information. Work of this nature has been carried out previously but with the neglect of several correlations including the Coriolis interaction between the quasiparticles and the rotor. Here we present for the first time, a microscopic approach to study proton emission from odd-odd deformed nuclei which includes the pairing, Coriolis and residual np interactions. While most of the studies on odd-odd nuclei concern only the energies, a description of decay can test the details of the wavefunctions which could be strongly influenced by the residual np interaction. Chapter 1: In this chapter of introduction, we start by highlighting the need for studying nuclei at drip lines and discuss the evolution and mapping of the nuclear vi chart. After a brief introduction to proton emission, different nuclear structure models are outlined with the aim of introducing the basics and conventions needed to follow forthcoming discussions. Both theoretical and experimental studies of proton emitters are reviewed. The interesting features and scope of studying odd-odd nuclei are also outlined, before listing down the thesis goals. Chapter 2: In chapter 2, we discuss the details of the nuclear mean field which is chosen to be of Woods-Saxon type with axial symmetry. Starting with the shape parameterization through the multipole expansion, most of the information regarding the parameterization and computational details for calculation of the Woods-Saxon, spinorbit and Coulomb potentials are discussed in this chapter. The pairing correlations treated within the BCS approach are also discussed in this chapter. Chapter 3: The chapter deals with the intricacies of rotational particle coupling in odd-odd nuclei. We present in detail the various matrix elements obtained in the conventional constant moment of inertia approximation. So far, the rotation particle coupling has been carried out only in this approach for odd-odd nuclei. We put forth a new formalism developed in this work, named as the coupling matrix approach. The core idea of this formalism is based on the coupled channels approach for odd-even nuclei suggested in the work of Bohr and Mottelson and of Esbensen and Davids. The methods for incorporating the residual np interaction and Newby shift in our calculations are presented. The adiabatic and nonadiabatic approaches dealt within the strong coupling limit also have been discussed with essential details. The phenomenon of rotational alignment has been discussed and for the first time a rotational alignment plot has been proposed for the odd-odd nuclei. The results for the nuclei 170,171Au highlight the importance of the coupling matrix approach when the energy levels of the core deviate from that of a rigid rotor. Chapter 4: The formalism to calculate proton emission half-lives is discussed in this chapter. The fundamentals of dealing proton emission as a decay from resonant states, leading to a microscopic description is elucidated in this chapter. The decay width is expressed in terms of the overlap between the initial (parent nucleus) and final (daughter and proton) states, where the parent is considered to be a two quasiparticle plus rotor system. The way in which states in daughter (one quasiparticle plus rotor) nuclei are obtained and the organization of our computer code is also discussed in this chapter. Chapter 5: In this chapter, the main results obtained in this work are discussed. The rotational spectrum of 180Ta is discussed first, justifying our approach for the vii interpretation of rotational bands. Following this, we discuss proton emission from the nuclei 130Eu, 112,113Cs and 170,171Au. Without assuming an exact Nilsson state from where the decay could happen, we could explain the experimentally observed halflives in all these nuclei. For the considered nuclei, the ground state spin and parity have been confirmed or reassigned with the aid of the measured proton emission halflives. We discuss the interplay between the Coriolis and the residual np interaction as well. We demonstrate that the description of proton emission can test the details of the wavefunctions which may be strongly influenced by the residual np interaction. Chapter 6: A succinct summary of this thesis is presented in chapter 6 along with the outlook of this work, highlighting the most important conclusions and the future aspects.