Description of the $2\nu\nu\beta\beta$ decay within a fully renormalized pnQRPA approach with a restored gauge symmetry

TL;DR

This paper develops a fully renormalized pnQRPA method with gauge symmetry restoration to accurately describe two-neutrino double beta decay, applying it to $^{100}$Mo decay with results matching experimental data.

Contribution

It introduces a gauge-restored, fully renormalized pnQRPA approach for double beta decay, improving the treatment of nuclear interactions and wave functions.

Findings

Calculated decay rates agree with experimental data.

The formalism obeys the Ikeda sum rule.

Gauge projection reduces the effectiveness of the $pp$ interaction.

Abstract

A many body Hamiltonian involving the mean field for a projected spherical single particle basis, the pairing interactions for alike nucleons and the dipole-dipole proton-neutron interactions in the particle-hole ($ph$) and particle-particle ($pp$) channels is treated by the projected gauge fully renormalized proton-neutron quasiparticle random phase approximation (PGFRpnQRPA) approach. The resulting wave functions and energies for the mother and the daughter nuclei are used to calculate the $2\nu\beta\beta$ decay rate and the process half life. For illustration, the formalism is applied for the decay $^{100}$Mo$ \to$ $^{100}$Ru. The results are in good agreement with the corresponding experimental data. The Ikeda sum rule ($ISR$) is obeyed. The gauge projection makes the $pp$ interaction inefficient.