  It is possible to employ virtual decay paths, including two-particle
transfer, to calculate the nuclear matrix element of neutrinoless double-beta
decay under the closure approximation, in addition to the true double-beta
path. In the quasiparticle random-phase approximation (QRPA) approach, it is
necessary to introduce the product wave functions of the like-particle and
proton-neutron QRPA ground states, for achieving consistency between the
calculations of the true and virtual paths. Using these different paths, the
problem of whether or not these two methods give equivalent nuclear matrix
elements (NME) is investigated. It is found that the two results are
inequivalent, resulting from the different many-body correlations included in
the two QRPA methods, i.e., the use of the product wave functions alone is not
sufficient. The author proposes introduction of the proton-neutron pairing
interaction with an adequate strength in the double-beta-path method, which
carries less many-body correlations without this supplemental interaction, for
obtaining the NME equivalent to that of the two-particle-transfer-path method.
The validity of the proposed modified approach is examined.
