Energy density functional study of nuclear matrix elements for neutrinoless $\beta\beta$ decay

TL;DR

This study uses advanced energy density functional methods to calculate nuclear matrix elements for neutrinoless double beta decay across multiple isotopes, highlighting the effects of nuclear deformation and pairing.

Contribution

It provides a comprehensive and consistent calculation of NMEs for various isotopes using state-of-the-art EDF methods, including beyond mean-field effects.

Findings

NME values are generally around 4.7 for most isotopes.

Deformation and pairing significantly influence NME calculations.

Smaller NMEs are found for $^{48}$Ca and $^{150}$Nd.

Abstract

We present an extensive study of nuclear matrix elements (NME) for the neutrinoless double beta decay of the nuclei $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Sn, $^{128}$Te, $^{130}$Te, $^{136}$Xe, and $^{150}$Nd based on state-of-the-art energy density functional methods using the Gogny D1S functional. Beyond mean-field effects are included within the generating coordinate method with particle number and angular momentum projection for both initial and final ground states. We obtain a rather constant value for the NME's around 4.7 with the exception of $^{48}$Ca and $^{150}$Nd, where smaller values are found. We analyze the role of deformation and pairing in the evaluation of the NME and present detailed results for the decay of $^{150}$Nd.