Lattice dynamics of quantum crystals

A theory of lattice dynamics for quantum crystals is developed. This is done by summing an infinite class of diagrams of the usual anharmonic expansion and by avoiding the harmonic approximation as starting point. The zero order of the expansion given in this paper corresponds to the harmonic approximation with an effective potential. Higher orders correspond to higher anharmonic corrections with the same potential. Since the new potential varies more slowly the expansion seems to converge more rapidly than the usual anharmonic expansion. Numerical calculations on bcc He³ show that the ground state energy is lowered by about 3–4 cal/mol by taking into account long range correlations due to phonons. The elastic constants and the Debye temperature are calculated in zero and second order. The lowering of the bulk modulus due to the second order is about 10%. Experiments agree quite well with the second order results.