Nuclear deformation and the two neutrino double-\beta decay in ^{124,126}Xe,^{128,130}Te, ^{130,132}Ba and ^{150}Nd isotopes

TL;DR

This paper investigates the two neutrino double-beta decay in various isotopes using the PHFB model, providing theoretical half-lives, transition probabilities, and confirming the inverse relationship between nuclear deformation and transition matrix elements.

Contribution

It applies the PHFB model to calculate double-beta decay properties across multiple isotopes, validating the model with experimental data and exploring deformation effects.

Findings

Calculated half-lives for several isotopes match experimental data.

Confirmed anticorrelation between nuclear deformation and transition matrix elements.

Provided detailed nuclear transition probabilities and moments.

Abstract

The two neutrino double beta decay of $^{124,126}$Xe,$^{128,130}$Te, $ ^{130,132}$Ba and $^{150}$Nd isotopes is studied in the Projected Hartree-Fock-Bogoliubov (PHFB) model. Theoretical 2$\nu $ $\beta^{-}\beta ^{-}$ half-lives of $^{128,130}$Te, and $^{150}$Nd isotopes, and 2$\nu \beta^{+}\beta^{+}$, 2$\nu $ $\beta^{+}EC$ and 2$\nu $ $ECEC$ for $ ^{124,126}$Xe and $^{130,132}$Ba nuclei are presented. Calculated quadrupolar transition probabilities B(E2: $0^+\to 2^+$), static quadrupole moments and $g$ factors in the parent and daughter nuclei reproduce the experimental information, validating the reliability of the model wave functions. The anticorrelation between nuclear deformation and the nuclear transition matrix element $M_{2\nu} $ is confirmed.