  The local environment and the energetic properties of one $^3$He atom solved
in bulk superfluid $^4$He are studied by means of the diffusion Monte Carlo
method. The chemical potential of the $^3$He impurity is calculated with a
generalized reweighting method which allows for a reliable estimation of this
quantity. Results for the chemical potential, radial distribution and structure
functions, volume-excess parameter, and effective mass are given for several
pressures and compared with available experimental data. An overall agreement
with experiment is obtained except for the kinetic energy of the $^3$He atom
which, in accordance with previous theoretical estimations, appears to be
considerably larger than determinations from deep-inelastic neutron scattering.
