Deformation effects and neutrinoless positron $\beta \beta $ decay of $^{96}$Ru, $^{102}$Pd, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba and $^{156}$Dy isotopes within Majorona neutrino mass mechanism

TL;DR

This study calculates nuclear transition matrix elements for neutrinoless positron double-beta decay in several isotopes using the Projected Hartree-Fock-Bogoliubov method, providing insights into neutrino masses and nuclear deformation effects.

Contribution

It introduces a consistent calculation of NTMEs for multiple isotopes within the Majorana neutrino mass mechanism using a validated nuclear structure model, and examines deformation effects on decay rates.

Findings

Limits on effective neutrino masses are derived from half-life data.

Deformation significantly influences the nuclear transition matrix elements.

Theoretical predictions agree with available spectroscopic data.

Abstract

The $(\beta ^{+}\beta ^{+})_{0\nu}$ and $(\varepsilon \beta ^{+})_{0\nu}$ modes of $^{96}$Ru, $^{102}$Pd, $^{106}$Cd, $^{124}$Xe, $^{130}$Ba and $^{156}$Dy isotopes are studied in the Projected Hartree-Fock-Bogoliubov framework for the $0^{+}\to 0^{+}$ transition. The reliability of the intrinsic wave functions required to study these decay modes has been established in our earlier works by obtaining an overall agreement between the theoretically calculated spectroscopic properties, namely yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments $Q(2^{+})$ and gyromagnetic factors $g(2^{+})$ and the available experimental data in the parent and daugther even-even nuclei. In the present work, the required nuclear transition matrix elements are calculated in the Majorana neutrino mass mechanism using the same set of intrinsic wave functions as used to study the two neutrino positron double-$\beta $ decay modes. Limits on effective light neutrino mass $< m_{\nu} >$ and effective heavy neutrino mass $< M_{N} >$ are extracted from the observed limits on half-lives $T_{1/2}^{0\nu}(0^{+}\to 0^{+})$ of $(\beta ^{+}\beta ^{+})_{0\nu}$ and $(\varepsilon \beta ^{+})_{0\nu}$ modes. We also investigate the effect of quadrupolar correlations vis-a-vis deformation on NTMEs required to study the $(\beta ^{+}\beta ^{+})_{0\nu}$ and $(\varepsilon \beta ^{+})_{0\nu}$ modes.