Monte Carlo study of vacancies in the bcc and hcp phasesof4He

We use the shadow wave function formalism to determine the energy of formation of single and double vacancies in ${}^4\mathrm{He}$ crystals at $T=0\mathrm{}\mathrm{K}.$ Data are presented for both the bcc and hcp phases. The activation energy for a single vacancy in bcc ${}^4\mathrm{He}$ was found to be about 50% of that in hcp ${}^4\mathrm{He},$ which is approximately 15.6 K. By determining the occupation of the Voronoi regions around the crystal sites, we determine the location of vacancies in the crystal and studied the relaxation of the neighboring atoms. We also present data on the correlations between vacancies, and between vacancies and ${}^3\mathrm{He}$ impurities. Following the position of the vacancy through successive configurations we observed the motion of the vacancy as seen in our Monte Carlo simulations. On the shorter Monte Carlo time scales, greater vacancy motion was observed in the bcc phase than in the hcp phase.