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It is possible to employ virtual decay paths, including two-particletransfer, to calculate the nuclear matrix element of neutrinoless double-betadecay under the closure approximation, in addition to the true double-betapath. In the quasiparticle random-phase approximation (QRPA) approach, it isnecessary to introduce the product wave functions of the like-particle andproton-neutron QRPA ground states, for achieving consistency between thecalculations of the true and virtual paths. Using these different paths, theproblem of whether or not these two methods give equivalent nuclear matrixelements (NME) is investigated. It is found that the two results areinequivalent, resulting from the different many-body correlations included inthe two QRPA methods, i.e., the use of the product wave functions alone is notsufficient. The author proposes introduction of the proton-neutron pairinginteraction with an adequate strength in the double-beta-path method, whichcarries less many-body correlations without this supplemental interaction, forobtaining the NME equivalent to that of the two-particle-transfer-path method.The validity of the proposed modified approach is examined.

Two decay paths for calculation of nuclear matrix element of neutrinoless double-beta decay using quasiparticle random-phase approximation