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

As shown in Rodin and Faessler (2009) [7], 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 for 82Se are made which show that indeed the tiny cross-section σ n p ( 0 f + → 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 ν β β nuclear matrix element.