  Pair wave functions (PWF) which are eigenfunctions of the reduced density
2-matrix are considered for a homogeneous Bose liquid. With the Bogoliubov
principle of the correlation weakening it is proved that the distribution of
the "dissociated" pair states over momenta is exactly the product of the
single-particle distribution functions. Thus, the "dissociated" pair states are
naturally classified as condensate-condensate, condensate-supracondensate and
supracondensate-supracondensate ones provided the Bose-Einstein condensate
exists. The condensate-condensate as well as condensate-supracondensate PWF are
expressed in terms of the averages of products of the creation and destruction
Bose operators. This leads to the simple interpretation of the anomalous
averages as the "scattering parts" of the condensate-condensate and
condensate-supracondensate PWF. It is shown that in contrast to the Fermi
liquid, the appearance of the anomalous averages for the Bose liquid does not
necessarily mean that there exist bound states of pairs of particles. The PWF
in the Hartree-Fock-Bogoliubov (HFB) approach are found. Given the density of
the condensate is not zero, there are no bound pair states in the HFB scheme.
The expansion of the pair correlation function in the set of PWF is very useful
in order to take into account both short-range and long-range spatial
correlations. Applications (possible and already realized) of the formalism
developed are discussed.
