  By using a full many-body approach, we calculate the excitation energy, the
effective mass and the density profile of soliton states in a three dimensional
Bose gas of hard spheres at zero temperature. The many-body wave function used
to describe the soliton contains a one-body term, derived from the solution of
the Gross-Pitaevskii equation, and a two-body Jastrow term which accounts for
the repulsive correlations between atoms. We optimize the parameters in the
many-body wave function via a Variational Monte Carlo procedure, calculating
the grand-canonical energy and the canonical momentum of the system in a moving
reference frame where the soliton is stationary. As the density of the gas is
increased, significant deviations from the mean-field predictions are found for
the excitation energy and the density profile of both dark and grey solitons.
In particular, the soliton effective mass $m^\ast$ and the mass $m\Delta N$ of
missing particles in the region of the density depression are smaller than the
result from the Gross-Pitaevskii equation, their ratio being however well
reproduced by this theory up to large values of the gas parameter. We also
calculate the profile of the condensate density around the soliton notch
finding good agreement with the prediction of the local density approximation.

Quantum Gases