Multipolar correlations and deformation effect on nuclear transition matrix elements of double-$\beta $ decay

TL;DR

This paper investigates how multipolar correlations and nuclear deformation influence the nuclear transition matrix elements in double beta decay, using the PHFB framework with effective interactions.

Contribution

It introduces a detailed analysis of hexadecapolar correlations and deformation effects on double beta decay matrix elements within the PHFB model.

Findings

Hexadecapolar correlations can be effectively absorbed as a renormalization of quadrupole interactions.

Nuclear transition matrix elements are maximized when parent and daughter nuclei have similar deformation.

Decreasing deformation difference between parent and daughter nuclei reduces the transition matrix elements.

Abstract

The two neutrino and neutrinoless double beta decay of $^{94,96}$Zr, $^{98,100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes for the $0^{+}\to 0^{+}$ transition is studied within the PHFB framework along with an effective two-body interaction consisting of pairing, quadrupole-quadrupole and hexadecapole-hexadecapole correlations. It is found that the effect of hexadecapolar correlations can be assimilated substantially as a renormalization of the quadrupole-quadrupole interaction. The effect of deformation on nuclear transition matrix elements is investigated by varying the strength of quadrupolar correlations in the parent and daughter nuclei independently. The variation of the nuclear transition matrix elements as a function of the difference in deformation parameters of parent and daughter nuclei reveals that in general, the former tend to be maximum for equal deformation and they decrease as the difference in deformation parameters increases, exhibiting a very similar trend for the $(\beta^{-}\beta ^{-})_{2\nu}$ and $(\beta^{-}\beta ^{-})_{0\nu}$ transition matrix elements.