New approach to lattice dynamics applied to solid He3 at 0°K

The expansion of a crystal potential in terms of a set of three-dimensional polynomials orthogonalized with respect to the weight function f2(r1, r2, rN)exp[(ri-Ri)·Gij·(rj-Rj)] is shown to be a logical generalization of the previously introduced self-consistent harmonic approximation which is particularly appropriate for highly anharmonic systems. Explicit expressions for the calculation of the ground-state energy and phonon spectrum of a crystal at 0°K are given and certain numerical results for solid He3 at 0°K are presented. © 1967 The American Physical Society.