  The influence of hole-hole propagation in addition to the conventional
particle-particle propagation, on the energy per nucleon and the momentum
distribution is investigated. The results are compared to the
Brueckner-Hartree-Fock (BHF) calculations with a continuous choice and
conventional choice for the single-particle spectrum. The Bethe-Goldstone
equation has been solved using realistic $NN$ interactions. Also, the structure
of nucleon self-energy in nuclear matter is evaluated. All the self-energies
are calculated self-consistently. Starting from the BHF approximation without
the usual angle-average approximation, the effects of hole-hole contributions
and a self-consistent treatment within the framework of the Green function
approach are investigated. Using the self-consistent self-energy, the hole and
particle self-consistent spectral functions including the particle-particle and
hole-hole ladder contributions in nuclear matter are calculated using realistic
$NN$ interactions. We found that, the difference in binding energy between both
results, i.e. BHF and self-consistent Green function, is not large. This
explains why is the BHF ignored the 2h1p contribution.
