  We investigate homogeneous nuclear matter within the Brueckner-Hartree-Fock
(BHF) approach in the limits of isospin-symmetric nuclear matter (SNM) as well
as pure neutron matter at zero temperature. The study is based on realistic
representations of the internucleon interaction as given by Argonne v18, Paris,
Nijmegen I and II potentials, in addition to chiral N$^{3}$LO interactions,
including three-nucleon forces up to N$^{2}$LO. Particular attention is paid to
the presence of di-nucleon bound states structures in $^1\textrm{S}_0$ and
$^3\textrm{SD}_1$ channels, whose explicit account becomes crucial for the
stability of self-consistent solutions at low densities. A characterization of
these solutions and associated bound states is discussed. We confirm that
coexisting BHF single-particle solutions in SNM, at Fermi momenta in the range
$0.13-0.3$~fm$^{-1}$, is a robust feature under the choice of realistic
internucleon potentials.
