  A simple model to study boson stars is to consider these stellar objects as
quantum systems of $N$ identical self-gravitating particles within a
non-relativistic framework. Some results obtained with point-like particles are
recalled as well as the validity limits of this model. Approximate analytical
calculations are performed using envelope theory for a truncated Coulomb-like
potential simulating a particle size. If the boson mass is sufficiently small,
the description of small mass boson stars is possible within non-relativistic
formalism. The mass and radius of these stellar objects are strongly dependent
on the value of the truncation parameter.
