DOES ANTISYMMETRY MATTER IN BCC HE-3 CRYSTALS

By comparing the results of both variational and ea:act Diffusion Mont e Carlo (DMC) results for states of different symmetries we conclude t hat antisymmetry plays a fundamental role in stabilizing the b.c.c. He -3 crystal. We performed calculations for a system of 54 particles of mass 3 at density rho = 0.02557 Angstrom, just above the experimental freezing point. Symmetric (Jastrow and Shadow wave functions) and unsy mmetrized wave functions (of the Nosanow-Jastrow type), fail to descri be the system. In particular, a shadow wave function predicts a fluid as lowest energy state at the density considered, and this is confirme d by the computation of the exact symmetric ground state with DMC, whi ch predicts an energy well below the experimental energy of the crysta l. On the other hand, DMC calculations projecting the ground state in the space of the Nosanow-Jastrow functions, give an energy which is mu ch above the experimental energy. The use of antisymmetric functions, and in particular of the recently introduced Fermionic Shadow Wave Fun ction (FSWF), leads to the prediction that the b.c.c. crystal is the s table ground state. Antisymmetry plays therefore a fundamental role in this system. FSWF calculations also demonstrate the peculiar characte ristics of this crystal (very low order parameter, a non Gaussian dens ity profile around the lattice. sites, and very wide vibrations of the atoms around the lattice sites, small dependence of the energy with r espect to the magnetic order), which cannot be seen in the Nosanow fra mework.