Solid helium. I. Ground-state energy and compressibility

Abstract

The ground-state energy and the compressibility of solid helium is calculated by means of a modified Brueckner theory. The Bethe-Goldstone equation is solved to give the reaction matrix or the effective interaction in coordinate space, and the ground-state energy for the two helium isotopes3He and4He is calculated. Also, the compressibility is estimated from the dependence of the ground-state energy on density or molar volume. Both bcc and hcp structures are considered. The calculations are done for two different two-body potentials, an Yntema-Schneider potential given by Brueckner and Gammel, and a Frost-Musulin potential given by Bruch and McGee. Theoretical results for the ground-state energy per particle are 0.2 to 2.6 K for solid3He at a molar volume of 24 cm3/mole, and −2.4 to −5.9 K for solid4He at a molar volume of 20 cm3/mole. The corresponding experimental results are −1.0 and −5.6 K, respectively. Theoretical results for the compressibility are 0.0031–0.0042 atm−1 for solid3He at a molar volume of 22 cm3/mole, and 0.0014–0.0022 atm−1 for solid4He at a molar volume of 18 cm3/mole. The corresponding experimental results are 0.0032 and 0.0014 atm−1, respectively. The agreement with experimental results is reasonably good since higher order cluster terms are not included in this first approximation.