  The energy and structure of dilute hard- and soft-sphere Bose gases are
systematically studied in the framework of several many-body approaches, as the
variational correlated theory, the Bogoliubov model and the uniform limit
approximation, valid in the weak interaction regime. When possible, the results
are compared with the exact diffusion Monte Carlo ones. A Jastrow type
correlation provides a good description of the systems, both hard- and
soft-spheres, if the hypernetted chain energy functional is freely minimized
and the resulting Euler equation is solved. The study of the soft-spheres
potentials confirms the appearance of a dependence of the energy on the shape
of the potential at gas paremeter values of $x \sim 0.001$. For quantities
other than the energy, such as the radial distribution functions and the
momentum distributions, the dependence appears at any value of $x$. The
occurrence of a maximum in the radial distribution function, in the momentum
distribution and in the excitation spectrum is a natural effect of the
correlations when $x$ increases. The asymptotic behaviors of the functions
characterizing the structure of the systems are also investigated. The uniform
limit approach results very easy to implement and provides a good description
of the soft-sphere gas. Its reliability improves when the interaction weakens.

Soft Condensed Matter