  We study the energy per particle of symmetric nuclear matter and pure neutron
matter using realistic nucleon--nucleon potentials having non central tensor
and spin--orbit components, up to three times the empirical nuclear matter
saturation density, $\rho_0=0.16$ fm$^{-3}$. The calculations are carried out
within the frameworks of the Brueckner--Bethe--Goldstone (BBG) and Correlated
Basis Functions (CBF) formalisms, in order to ascertain the accuracy of the
methods. The two hole--line approximation, with the continuous choice for the
single particle auxiliary potential, is adopted for the BBG approach, whereas
the variational Fermi Hypernetted Chain/Single Operator Chain theory, corrected
at the second order perturbative expansion level, is used in the CBF one. The
energies are then compared with the available Quantum and Variational Monte
Carlo results in neutron matter and with the BBG, up to the three hole--line
diagrams. For neutron matter and potentials without spin--orbit components all
methods, but perturbative CBF, are in reasonable agreement up to $\rho\sim$ 3
$\rho_0$. After the inclusion of the LS interactions, we still find agreement
around $\rho_0$, whereas it is spoiled at larger densities. The spin--orbit
potential lowers the energy of neutron matter at $\rho_0$ by $\sim$ 3--4 MeV
per nucleon. In symmetric nuclear matter, the BBG and the variational results
are in agreement up to $\sim$ 1.5 $\rho_0$. Beyond this density, and in
contrast with neutron matter, we find good agreement only for the potential
having spin--orbit components.
