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

Abstract

The $({\beta }^{+}{\beta }^{+}{)}_{0\nu }$ and $(\epsilon {\beta }^{+}{)}_{0\nu }$ 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 $(\epsilon {\beta }^{+}{)}_{0\nu }$ modes. We also investigate the effect of quadrupolar correlations vis-a-vis deformation on NTMEs required to study the $({\beta }^{+}{\beta }^{+}{)}_{0\nu }$ and $(\epsilon {\beta }^{+}{)}_{0\nu }$ modes.

12 Pages, 3 figure

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• A Next-Generation Liquid Xenon Observatory for Dark Matter and Neutrino Physics
• Nuclear matrix element of neutrinoless double-$\beta$ decay: Relativity and short-range correlations
• Origin of a sensitive dependence of calculated $\beta \beta$-decay amplitudes on the particle-particle residual interaction
• Detection prospects for the second-order weak decays of ${}^{124}$Xe in multi-tonne xenon time projection chambers
• Investigation of pair-correlated $0^{+}$ states in ${}^{134}$Ba via the ${}^{136}$Ba($p,t$) reaction
• On the possibility to measure nuclear matrix elements of neutrinoless double beta decay in charge-exchange reactions