On the possibility to measure nuclear matrix element for neutrinoless double beta decay of Ca48

TL;DR

This paper explores the potential to measure the nuclear matrix element for neutrinoless double beta decay of Ca-48 by relating it to charge-exchange reactions, specifically estimating the cross-section of a relevant reaction.

Contribution

It proposes a method to experimentally access the Fermi part of the nuclear matrix element for Ca-48 decay via charge-exchange reactions, providing a new approach to study neutrinoless double beta decay.

Findings

Estimated the cross-section of the $^{48}$Ti(n,p)$^{48}$Sc(IAS) reaction.

Discussed the feasibility of measuring the Fermi matrix element in Ca-48.

Linked the matrix element to charge-exchange reaction observables.

Abstract

As shown in Ref. \cite{Rod09}, the Fermi part $M_{F}^{0\nu}$ of the total $0\nu\beta\beta$-decay nuclear matrix element $M^{0\nu}$ can be related to the single Fermi transition matrix element between the isobaric analog state (IAS) of the ground state of the initial nucleus and the ground state of the final nucleus. The latter matrix element could be measured in charge-exchange reactions. Here we discuss a possibility of such a measurement for $^{48}$Ca and estimate the cross-section of the reaction $^{48}$Ti(n,p)$^{48}$Sc(IAS).