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

Abstract

As shown in Ref. [Vadim Rodin, Amand Faessler, Phys. Rev. C 80 (2009) 041302(R) ], the Fermi nuclear matrix element M F 0 ν of neutrinoless double beta ( 0 ν β β ) 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 made for 82 Se show that indeed the tiny cross-section σ n p ( 0 f + → I A S ) 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 could advance a lot our knowledge of the 0 ν β β nuclear matrix element.