  We calculate the nuclear matrix elements of the neutrinoless double beta
($0\nu\beta\beta$) decays of $^{76}$Ge and $^{82}$Se for the light-neutrino
exchange mechanism. The nuclear wave functions are obtained by using realistic
two-body forces within the proton-neutron quasiparticle random-phase
approximation (pnQRPA). We include the effects that come from the finite size
of a nucleon, from the higher-order terms of nucleonic weak currents, and from
the nucleon-nucleon short-range correlations. Most importantly, we improve on
the presently available calculations by replacing the rudimentary Jastrow
short-range correlations by the more advanced unitary correlation operator
method (UCOM). The UCOM corrected matrix elements turn out to be notably larger
in magnitude than the Jastrow corrected ones. This has drastic consequences for
the detectability of $0\nu\beta\beta$ decay in the present and future double
beta experiments.
