  It is pointed out that simulation computation of energy performed so far
cannot be used to decide if the ground state of solid 4He has the number of
lattice sites equal to the number of atoms (commensurate state) or if it is
different (incommensurate state). The best variational wave function, a shadow
wave function, gives an incommensurate state but the equilibrium concentration
of vacancies remains to be determined. In order to investigate the presence of
a supersolid phase we have computed the one--body density matrix in solid 4He
for the incommensurate state by means of the exact Shadow Path Integral Ground
State projector method. We find a vacancy induced Bose Einstein condensation of
about 0.23 atoms per vacancy at a pressure of 54 bar. This means that bulk
solid 4He is supersolid at low enough temperature if the exact ground state is
incommensurate.
