AB INITIO NO CORE SHELL MODEL STUDY OF LOWER MASS NUCLEI

Abstract

The development of the ab initio many-body methods is the mainstream of nuclear theory to study the nuclear properties from rst principles. The ab initio no-core shell model (NCSM) has been very successful in providing the explanation of nuclei in the lighter mass region of the nuclear chart. Advancement in computational facility makes it possible to work in a large basis space so as to obtain convergent results. Progress in the construction of realistic internucleon interactions from chiral e ective eld theory and meson-exchange theory leads to the description of the nuclear data with high precision. The aim of the present thesis is to study the nuclear structural properties of lower mass nuclei, speci cally boron and carbon nucleus, which pose challenges to the ab initio methods because of exotic features across the isotopic chains. The ab initio NCSM calculations demonstrated that the three-body force is required to correctly reproduce the ground-state spin 3+ of 10B. Since the exact form of the nuclear potential is still unknown, the main goal is to examine which interaction is the most suitable for a chosen nuclei or an isotopic chain. We have applied di erent realistic nucleon-nucleon (NN) interactions, i.e., the inside non{local outside Yukawa (INOY), the charge{dependent Bonn 2000 (CDB2K) potential, the next-to-next-tonext- to-leading order (N3LO) potential, and the optimized next-to-next-to-leading order (N2LOopt) potential in the NCSM method to address this issue. New precise experimental measurements of nuclear observables such as proton radii allow us to test the predictive strength of this ab initio nuclear method. This motivates us to perform systematic NCSM calculations for boron and carbon isotopes with di erent realistic interactions. We have reached basis sizes up to Nmax = 10 for 10B and 10C, Nmax = 8 for 11;12;13B and 11;12;13;14C, and Nmax = 6 for 14B with m-scheme dimensions up to 1.7 billion. We have determined the low-lying energy spectra of natural parity for 10􀀀14B and both positive and negative parity states for the 10􀀀14C isotopes and investigated the level structures. We also compare the NCSM calculations with the phenomenological YSOX interaction using the shell model. Overall, our NCSM results are consistent with the available experimental data. The INOY interaction without the inclusion of the three-body force correctly reproduces the 3+ as the ground state for 10B, which indicates that the INOY force produces e ects similar to those produced by including three-nucleon forces. This is an encouraging result for the goal of nding a way of calculating the structure of atomic nuclei microscopically using only the NN interaction as input. We have also calculated electromagnetic observables such as quadrupole moment, reduced electric quadrupole transition strength, magnetic moment, and reduced dipole magnetic transition strength. We found that the INOY interaction gives the best description of the ground state energies, while the N3LO interaction best reproduces the point{proton radii. We have extended the application of the ab initio NCSM approach, which gives the reliable description of nuclei up to A = 16, to study neutron rich 18C, 19C and 20C isotopes. We also show the behavior of ground state energy and point-proton radii with the NCSM parameters. We report a strong sensitivity of the B(E2) values from the rst excited 2+ to the ground state of 18C and 20C to the nuclear interaction. More experimental studies for energy spectra, B(E2), electric quadrupole, and magnetic dipole moments for neutron-rich carbon isotopes are required for a complete nuclear structure description. Our theoretical prediction of these nuclei will be helpful in the future for comparison with the experimental data. With increasing mass number, the dimension of the Hamiltonian matrix increases in the NCSM method, which becomes computationally challenging. To get around this problem, a new technique is proposed to build e ective valence shell interactions using the NCSM wave functions and the Okubo-Lee-Suzuki transformation method. Newly developed microscopic e ective sd-shell interactions are chiral N3LO, J-matrix inverse scattering potential (JISP16), Daejeon16 (DJ16), and monopole-modi ed DJ16 (DJ16A). We have employed these interactions to study silicon, phosphorous, sulphur, chlorine, and argon isotopes. We have calculated level schemes and spectroscopic properties for these sd-shell nuclei. We have also performed shell model calculations with the empirical USDB interaction for comparison. It is found that the results obtained from the DJ16A interaction are closest to the experimental data as compared to other microscopic interactions. A proton subshell closure at Z = 14 in Si and the presence of N = 20 shell closure in the S chain are obtained. Spin-tensor decomposition of two-body interaction is presented to understand the contributions from central, vector, and tensor components to these interactions. Spectroscopic strengths of 23Al(d,n)24Si are examined for the newly performed experiment at NSCL. The shell model predictions are also made using these interactions for observables where experimental data are unknown. The root-mean-square deviations are also calculated to provide an idea of how accurate the interactions are. In order to provide theoretical insight for recently available experimental data measured from the GRIFFIN spectrometer at TRIUMF-ISAC from 􀀀 decay of 46K and 47K [Phys. Rev. C 100, 054327 (2019); Phys. Rev. C 102, 054314 (2020)], we have carried out a comprehensive nuclear shell model study with the SDPF-MU interaction to calculate low-lying energy spectra and electromagnetic properties of 46;47K and 46;47Ca. We have computed the log ft values for 􀀀 decay of 46K and 47K for the rst time. The e ective value of gA is also extracted using the chi-squared tting method. Based on the energy and log ft values, we have assigned spin-parity of several levels, which were previously tentative, in both the calcium isotopes.