Variational study of vacancies in solid4Hewith shadow wave functions

We employ the shadow wave function (SWF) formalism to obtain estimates of the energy of formation of a vacancy in hcp, fcc, and bcc ${}^4\mathrm{He}$ crystal at $T=0\mathrm{}\mathrm{K}.$ We find that this energy is a strong function of density, in agreement with experiment. The use of a more efficient sampling with a smart Monte Carlo technique, allowed us to observe the motion of the vacancy through the crystal. We also present data on the occupation of the Wigner-Seitz cells. The occupation of the cells changes along the run, showing the mobility of the particles and of the vacancy. As a byproduct of this study we present results for the energy of perfect hcp and bcc crystals described by a SWF.