Comparative study of vacancies in the bcc and hcp phases of 4He using shadow wave functions

We use the shadow wave function formalism (SWF) to determine the energy of formation of single and double vacancies in He-4 crystals at T=0 K. Data is presented for both the bce and hcp phases. The activation energy for single vacancies in bcc He-4 was found to be 6.7+/-3.9 K, about 43% of that in the hcp He-4, 15.6+/-3.9 K. By determining the occupation of the Voronoi regions of the crystal sites, we determined 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 He-3 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.