  We study the zero-temperature equation of state (EOS) of solid 4He in the
hexagonal closed packet (hcp) phase over the 0-57 GPa pressure range by means
of the Diffusion Monte Carlo (DMC) method and the semi-empirical Aziz pair
potential HFD-B(HE). In the low pressure regime (P ~ 0-1 GPa) we assess
excellent agreement with experiments and we give an accurate description of the
atomic kinetic energy, Lindemann ratio and Debye temperature over a wide range
of molar volumes (22-6 cm^{3}/mol). However, on moving to higher pressures our
calculated P-V curve presents an increasingly steeper slope which ultimately
provides differences within ~40 % with respect to measurements. In order to
account for many-body interactions arising in the crystal with compression
which are not reproduced by our model, we perform additional electronic
density-functional theory (DFT) calculations for correcting the computed DMC
energies in a perturbative way. We explore both generalized gradient and local
density approximations (GGA and LDA, respectively) for the electronic
exchange-correlation potential. By proceeding in this manner, we show that
discrepancies with respect to high pressure data are reduced to 5-10 % with few
computational extra cost. Further comparison between our calculated EOSs and ab
initio curves deduced for the perfect crystal and corrected for the zero-point
motion of the atoms enforces the reliability of our approach.
