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

摘要

As shown in Ref.cite{Rod09}, the Fermi nuclear matrix element $M^{0u}_F$of neutrinoless double beta ($0uetaeta$) decay can be reconstructed ifone is able to measure the isospin-forbidden single Fermi transition matrixelement from the ground state of the final nucleus to the isobaric analog state(IAS) of the initial nucleus, for instance by means of charge-exchangereactions of the $(n,p)$-type. Here, simple estimates for $^{82}$Se are madewhich show that indeed the tiny cross section $sigma_{np}(0_f^+o IAS)$ isdominated by the admixture of the double IAS in the ground state of the finalnucleus provided that the isospin mixing is weak and can be treatedperturbatively. A measurement of such a cross section would definitely be avery difficult task, but it can advance a lot our knowledge of the$0uetaeta$ nuclear matrix element.