Partial restoration of isospin symmetry for neutrinoless double beta decay in the deformed nuclear system of $^{150}$Nd

TL;DR

This paper calculates neutrinoless double beta decay matrix elements for $^{150}$Nd using a deformed pn-QRPA approach, demonstrating partial isospin symmetry restoration reduces Fermi matrix elements significantly.

Contribution

It introduces a method to restore isospin symmetry in deformed nuclear systems, affecting the Fermi matrix elements in neutrinoless double beta decay calculations.

Findings

Fermi matrix elements are reduced by about 30% after isospin symmetry restoration.

Gamow-Teller matrix elements remain unchanged with symmetry restoration.

Model space enlargement changes matrix elements by less than 10%.

Abstract

In this work, we calculate the matrix elements of $0\nu\beta\beta$-decay of $^{150}$Nd with the deformed pn-QRPA method. We adopted the approach introduced by Rodin, Faessler [Phys. Rev. C84, 014322 (2011)] and Simkovic {\it et. al.} [Phys. Rev. C87,045501(2013)] to restore the isospin symmetry by enforcing $M^{2\nu}_F=0$. We found that with this restoration, the Fermi matrix elements are reduced by about 30\% while the more important Gamow-Teller matrix elements remains the same. The results of an enlarged model space is also presented, which changes the matrix elements by less than 10\%.