  The thermodynamics of a homogeneous dilute Bose gas with an arbitrary strong
repulsion between particles is investigated on the basis of the exact relation
connecting the pair correlation function with the in-medium pair wave functions
and occupation numbers. It is shown that the effective-interaction scheme which
is reduced to the Bogoliubov model with the effective pairwise potential, is
not acceptable for investigating the short-range particle correlations in a
dilute strongly interacting Bose gas. In contrast to this scheme, our model is
thermodynamically consistent and free of the ultraviolet divergences due to
accurate treatment of the short-range boson correlations. The equation for the
in-medium scattering amplitude is derived that makes it possible to find the
in-medium renormalization for the pair wave functions at short boson
separations. Low-density expansions for the main thermodynamic quantities are
reinvestigated on the basis of this equation. Besides, the expansions are found
for the interaction and kinetic energies per particle. It is demonstrated that
for the many-boson system of the hard spheres the interaction energy is equal
to zero for any boson density. The exact relationship between the chemical
potential and in-medium pair wave functions is also established.
