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

Abstract

As shown in Ref.\cite{Rod09}, the Fermi nuclear matrix element $M_F^{0\nu }$ 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.

7 pages, 2 figures; to appear in the proceedings of the International School of Nuclear Physics: 32nd Course: Particle and Nuclear Astrophysics, Erice, Sicily, Italy, 16-24 Sep 2010

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