Influence of the hexadecapole deformation on the two neutrino double-$\be ta $ decay

TL;DR

This paper investigates how hexadecapole deformation influences the two-neutrino double beta decay nuclear matrix elements across several isotopes using the PHFB model, emphasizing the role of nuclear shape and structure.

Contribution

It introduces the inclusion of hexadecapole-hexadecapole interactions in the PHFB model to study their effect on double beta decay matrix elements and validates the wave functions with spectroscopic data.

Findings

Hexadecapole deformation significantly affects $M_{2 u}$ values.

Nuclear deformation shows an inverse relation with $M_{2 u}$.

The model reproduces spectroscopic properties accurately.

Abstract

The two neutrino double beta $(\beta ^{-}\beta ^{-})_{2\nu}$ decay of $ ^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd nuclei for the $0^{+}\to 0^{+}$ transition is studied in the PHFB model in conjunction with the pairing plus quadrupole-quadrupole plus hexadecapole-hexadecapole effective two-body interaction and the effect of the latter is investigated on the calculation of nuclear transition matrix elements $M_{2\nu}$. The reliability of the intrinsic wave functions of parent and daughter nuclei involved in the $(\beta ^{-}\beta ^{-})_{2\nu}$ decay of above mentioned nuclei is established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties, namely the yrast spectra, reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, static quadrupole moments $Q(2^{+})$ and $g$-factors $g(2^{+})$ and the available experimental data. The effect of deformation on $M_{2\nu}$ is also investigated to inveterate its inverse relation with nuclear deformation.