  Saturation properties are directly linked to the short-range scale of the
two-body interaction of the particles. The case of helium is particular, from
one hand the two-body potential has a strong repulsion at short distances. On
the other hand, the extremely weak binding of the helium dimer locates this
system very close to the unitary limit allowing for a description based on an
effective theory. At leading order of this theory a two- and a three-body term
appear, each one characterized by a low energy constant. In a potential model
this description corresponds to a soft potential model with a two-body term
purely attractive plus a three-body term purely repulsive constructed to
describe the dimer and trimer binding energies. Here we analyse the capability
of this model to describe the saturation properties making a direct link
between the low energy scale and the short-range correlations. We will show
that the energy per particle, $E_N/N$, can be obtained with reasonable accuracy
at leading order extending the validity of this approximation, characterizing
universal behavior in few-boson systems close to the unitary limit, to the
many-body system.
