Nuclear Shell Model Study for Neutrinoless Double Beta Decay of 48Ca

Abstract

The neutrinoless double beta decay is a vital lepton number violating weak nuclear decay that occurs when two neutrons inside some even-even nuclei converted into two protons and two electrons. If this rare process is observed, one can conclude that neutrinos are their own anti-particle (Majorana particle), which is favored by most of the beyond the standard model physics. This process can also give some hints of absolute masses of neutrinos, which are still unknown. The nuclear matrix element is an essential quantity to study neutrinoless double beta decay, as it directly comes in the expression of the decay rate of the process. Di erent mechanisms of neutrinoless double beta decay are proposed. In the present thesis, I have focused on the standard light neutrino-exchange mechanism, and mechanism. The nuclear matrix elements are calculated in interacting shell model, which is a widely used many-body model to calculate nuclear matrix elements. I have performed my calculation for one of the neutrinoless double beta decaying nucleus 48Ca. In my calculations throughout the thesis, I have used both closure and nonclosure approximations. In closure approximation, one approximates the e ects of a large number of excitation energy of the intermediate nucleus (48Sc in the present case), which comes in the denominator of the radial neutrino potential operator of the decay, with constant closure energy. Using both closure and nonclosure approximation, I have used four di erent methods: closure, running closure, running nonclosure, and mixed methods to calculate the nuclear matrix elements. In the interacting shell model, which is used in the thesis, the two-nucleon shell model e ective interaction is an essential component to calculate the relevant states of the isotopes involved in the neutrinoless double beta decay process. These states are further used to calculate the relevant quantities such as one body transition density, and two-nucleon transfer amplitudes to calculate the nal nuclear matrix elements. Thus, two-nucleon e ective interaction plays an important role in nuclear matrix elements calculation in the nuclear shell model. Earlier, the nuclear matrix elements for the light neutrino-exchange mechanism of neutrinoless double beta decay was calculated in the interacting shell model with GXPF1A two-nucleon e ective interaction. In recent years, the contribution of individual components, i.e., central (C), spin-orbit (SO), and tensor force (T), of shellmodel two-nucleon interaction in the single-particle energy gaps has been explored to understand the cause of shell evolution in the neutron-rich nuclei. These studies, thus, motivate us to investigate the e ects of individual components of two-nucleon interaction on the nuclear matrix elements of neutrinoless double beta decay. In chapters 2, and 3, I have examined the role of C, SO, and T component of GXPF1A two-nucleon e ective interaction on nuclear matrix elements of light neutrino-exchange neutrinoless double beta decay of 48Ca. I have used both closure and nonclosure approaches to calculate the nuclear matrix elements. In chapter 4, I have calculated the nuclear matrix elements for mechanism of neutrinoless double beta decay of 48Ca. Earlier nuclear matrix elements for the mechanism were calculated in closure approximation only. Hence, I was motivated to calculate the nuclear matrix elements for the mechanism using both closure and nonclosure approximation. In this case, I have also included the revised formalism of pseudoscalar term in the nucleon current, which was not included earlier. In the thesis, I have also performed a detailed structure calculation of neutrinoless double beta decay nuclear matrix elements. I have examined the dependence of nuclear matrix elements with coupled spin-parity of two initial neutrons and nal protons, spin-parity of the intermediate state, cuto excitation energy, and the number of states of the intermediate nucleus, closure energy, neutrino momentum, internucleon distance. Results show that there is a signi cant role of C, SO, and T components of GXPF1A interaction on the nuclear matrix elements of neutrinoless double beta decay of 48Ca. The e ects of SO and T components are found to be mostly canceled with each other. For the mechanism, it is found that there is a signi cant enhancement of nuclear matrix elements for including the pseudoscalar term of nucleon currents. I found for using near-optimal closure energy hEi=0.5 MeV, the nuclear matrix elements in closure and nonclosure approaches have similar values.