A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations

TL;DR

This paper introduces a Pfaffian formula for efficiently calculating matrix elements of three-body operators in complex nuclear configurations, enhancing beyond-mean-field methods for nuclear structure and decay studies.

Contribution

It provides a novel Pfaffian-based approach for matrix element calculations involving three-body operators in multiple quasi-particle states, extending current computational techniques.

Findings

Derivation of a Pfaffian formula for three-body matrix elements

Application potential in generator coordinate method with chiral interactions

Relevance to nuclear matrix elements in neutrinoless double beta decay

Abstract

We present a Pfaffian formula to calculate matrix elements of three-body operators in symmetry-restoration beyond-mean-field methods, including the case of multiple quasi-particle configurations. Detailed derivation based on [Mizusaki et al., Phys. Lett. B 715, 219 (2012)] and [Hu et al., Phys. Lett. B 734, 162 (2014)] is provided, and potential applications in generator coordinate method with chiral interactions, as well as in study of nuclear matrix elements in neutrinoless double beta decay are discussed.