  The methods used till now to calculate the neutrinoless double beta decay
matrix elements are: the Quasiparticle Random Phase Approximation (QRPA), the
Shell Model (SM), the angular momentum projected Hartee-Fock-Bogoliubov
approach (HFB) and the Interacting Boson Model (IBM). The different approaches
are compared specifically concerning the the angular momenta and parities of
the neutron pairs, which are changed into two protons by the $0\nu\beta\beta$
decay. The QRPA and SM involve about the same angular momentum and parity
neutron pairs, while the HFB is restricted to $0^{+}, 2^{+}, 4^{+}, ...$, and
IBM to $0^{+}$ and $2^{+}$ nucleon pairs. The differences in the seniority
contributions for the QRPA and the SM are discussed.
