  We approach the calculation of the nuclear matrix element of the neutrinoless
double-beta decay process, considering the light-neutrino-exchange channel, by
way of the realistic shell model. To this end, we start from a realistic
nucleon-nucleon potential and then derive the effective shell-model Hamiltonian
and neutrinoless double-beta decay operator within the many-body perturbation
theory. We focus on investigating the perturbative properties of the effective
shell-model operator of such a decay process, aiming to establish the degree of
reliability of our predictions. The contributions of the so-called short-range
correlations and of the correction of Pauli-principle violations to the
effective shell-model operator, the latter introduced in many-valence nucleon
systems, are also taken into account. The subjects of our study are a few
candidates to the neutrinoless double-beta decay detection, in a mass interval
ranging from A=48 up to A=136, whose spin- and spin-isospin-dependent decay
properties we have studied in previous works. Our results will be finally
compared with shell-model calculations for the same set of nuclei.
