Solid Helium. I. Ground-State Energy and Compressibility

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 isotopes He-3 and He-4 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 solid He-3 at a molar volume of 24 cm(3)/mole, and -2.4 to -5.9 K for solid He-4 at a molar volume of 20cm(3)/mole. The corresponding experimental results are -1.0 and -5.6K, respectively. Theoretical results for the compressibility are 0.0031.0.0042 atm(-1) for solid He-3 at a molar volume of 22 cm(3)/mole, and 0.0014-0.0022 atm(-1) for solid He-4 at a molar volume of 18 cm(3)/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.