Cubic Symmetry Effects in SolidHe3

A detailed analysis is made of the single-particle model for solid ${\mathrm{He}}^3$ at 0°K under an external pressure of 30 atm. The correct Hamiltonian being assumed, it is shown at the outset that the calculation gives a rigorous upper bound for the ground-state enthalpy of the system. The many-body wavefunction is taken to be a product of single-particle wave functions which are cubically symmetric about their respective lattice sites. In order to obtain the best product wave function of this type, the usual minimization principles are applied, and a set of self-consistent equations are obtained which differ as expected from the spherically symmetric Hartree equations. These cubically symmetric equations are then solved numerically, and the ground-state energy obtained is 10% lower than that obtained in the spherically symmetric approximation. This result is still significantly higher than the probable experimental value.