  To extract information about the neutrino properties from the study of
neutrinoless double-beta (0\nu\beta\beta) decay one needs a precise computation
of the nuclear matrix elements (NMEs) associated with this process. Approaches
based on the Shell Model (ShM) are among the nuclear structure methods used for
their computation. ShM better incorporates the nucleon correlations, but have
to face the problem of the large model spaces and computational resources. The
goal is to develop a new, fast algorithm and the associated computing code for
efficient calculation of the two-body matrix elements (TBMEs) of the
0\nu\beta{\beta} decay transition operator, which are necessary to calculate
the NMEs. This would allow us to extend the ShM calculations for double-beta
decays to larger model spaces, of about 9-10 major harmonic oscillator shells.
The improvement of our code consists in a faster calculation of the radial
matrix elements. Their computation normally requires the numerical evaluation
of two-dimensional integrals: one over the coordinate space and the other over
the momentum space. By rearranging the expressions of the radial matrix
elements, the integration over the coordinate space can be performed
analytically, thus the computation reduces to sum up a small number of
integrals over momentum. Our results for the NMEs are in a good agreement with
similar results from literature, while we find a significant reduction of the
computation time for TBMEs, by a factor of about 30, as compared with our
previous code that uses two-dimensional integrals.
