On the possibility to measure nuclear matrix elements of neutrinoless double beta decay in charge-exchange reactions

TL;DR

This paper explores the theoretical possibility of measuring nuclear matrix elements relevant to neutrinoless double beta decay through charge-exchange reactions, potentially improving understanding of this rare process.

Contribution

It proposes a method to reconstruct the Fermi nuclear matrix element of neutrinoless double beta decay using charge-exchange reactions and provides estimates for specific isotopes.

Findings

Tiny cross section dominated by double IAS admixture

Weak isospin mixing allows perturbative treatment

Measurement could significantly enhance knowledge of nuclear matrix elements

Abstract

As shown in Ref.\cite{Rod09}, the Fermi nuclear matrix element $M^{0\nu}_F$ of neutrinoless double beta ($0\nu\beta\beta$) decay can be reconstructed if one is able to measure the isospin-forbidden single Fermi transition matrix element from the ground state of the final nucleus to the isobaric analog state (IAS) of the initial nucleus, for instance by means of charge-exchange reactions of the $(n,p)$-type. Here, simple estimates for $^{82}$Se are made which show that indeed the tiny cross section $\sigma_{np}(0_f^+\to IAS)$ is dominated by the admixture of the double IAS in the ground state of the final nucleus provided that the isospin mixing is weak and can be treated perturbatively. A measurement of such a cross section would definitely be a very difficult task, but it can advance a lot our knowledge of the $0\nu\beta\beta$ nuclear matrix element.