SHELL MODEL STUDY OF NUCLEAR STRUCTURE AND 2νββ DECAY PROPERTIES IN DIFFERENT MASS REGIONS

Abstract

This thesis explores the intricate aspects of nuclear structure and second-order weak interaction decay processes across a broad region of the nuclear chart. The nuclear structure studies primarily focus on the cadmium and indium isotopic chains between the neutron shell closures at N = 50 and N = 82, while the investigations of weak interaction decays center on two-neutrino double beta (2νββ) decay and twoneutrino double electron capture (2νECEC) in various candidates. From the nuclear structure perspective, key properties such as energy systematics, collectivity, electromagnetic transitions, seniority isomers, shell evolution, and shape deformation are systematically analyzed. In the context of 2νββ decay and 2νECEC processes, nuclear matrix elements (NMEs), the level density of 1+ states in the intermediate nucleus, and half-life predictions are thoroughly examined. Cadmium isotopes serve as an excellent testing ground for nuclear structure theories due to their rich and evolving spectroscopic properties across the isotopic chain. In order to understand these properties, we perform systematic shell-model calculations for both even-even and odd-mass cadmium isotopes, aiming to provide a comprehensive understanding of their structural evolution. For even-A 98−130Cd isotopes, we employ a realistic effective shell-model interaction derived from the G-matrix approach with an inert core 88Sr. The calculated low-lying excitation spectra and electromagnetic properties are systematically compared with the experimental data, and based on recently available measurements, we predict spins and parities for unconfirmed states. Additionally, we analyze the properties of the 8+ isomeric states in 98−104,130Cd. Extending our study to the odd-A 99−129Cd isotopes, we adopt a modified effective interaction by replacing the neutron-neutron (n − n) two-body matrix elements (TBMEs) of the interaction used for the investigation of even-A Cd isotopes with those from the SNBG1 interaction. Our results successfully reproduce the observed systematics of excited states and electromagnetic observables, such as reduced transition probabilities and electromagnetic moments. Notably, we find that the quadrupole moments of the 11/2− 1 states exhibit a linear trend as a function of neutron number, suggesting a persistent prolate shape along the isotopic chain. This interpretation is given by analyzing the energy surface plots and K quantum numbers. Furthermore, we describe several recently observed isomeric states in the neutron-rich 127−131In isotopes and discuss the electromagnetic moments of both the ground state and these isomeric states.