A STATISTICAL-MECHANICAL STUDY ON THE MELTING LINES OF HE-3 AND HE-4

A theoretical melting line is sensitive to a small difference in solid and fluid free energies. Such a difference may arise from different a pproximations made in fluid and solid theories and also from inaccurac ies in handling anharmonic lattice vibrations. Statistical mechanical calculations have been made for liquid and solid He-4 and He-3 and the ir melting lines, using a new perturbation theory (PT) which does not suffer from the above limitations. These calculations, which use the A ziz potential for helium, are augmented by additional calculations usi ng quasiharmonic lattice dynamics and Mansoori-Canfield-Ross theory (w ith an exponential-6 potential). Comparisons of these results and avai lable Monte Carlo and real experimental data show that the PT can accu rately predict solid, fluid, and the melting data of a model of helium (based on the Aziz potential) and that the melting line of real 4He i s insensitive to many-body effects up to 200 K, but their influence gr ows gradually with pressure (approximate to 6% in melting pressure at 300 K). An effective pair potential is suggested which can handle many -body contributions over an extended density range. The calculations o n the isotopic pressure shift, Delta P-m = P-m(He-3) - P-m(He-4), alon g the melting lines of helium isotopes show that Delta P-m > 0 at T < 100 K in agreement with experiment at T approximate to 30 K and Delta P-m < 0 at T > 100 K in agreement with path integral Monte Carlo data. The PT with the first-order quantum correction was found to explain t he experimental melting data surprisingly well; i.e., beyond an estima ted range of applicability of the Wigner-Kirkwood expansion. It can im ply a rapid convergence of the Wigner-Kirkwood expansion along the mel ting line of He-4.