Solid hydrogen: Ground-state energy,pressure, and compressibility

The ground-state energy, the pressure, and the compressibility of solid molecular hydrogen is calculated by means of a modified Brueckner theory. The Bethe-Goldstone equation is solved to give the reaction matrix or an effective interaction in coordinate space; the ground-state energies for normal hydrogen and deuterium are calculated. Also, the pressure and the compressibility is estimated from the dependence of the ground-state energy on density or molar volume. Both hcp and fcc structures are considered. Theoretical results for the ground-state energy per particle are –82 K for solid hydrogen at a molar volume of 22 cm³/mole and –135 K for solid deuterium at a molar volume of 19 cm³/mole. The corresponding experimental results are –92 and –138 K, respectively. We obtain zero pressure for solid hydrogen at a molar volume of 22.45 cm³/mole and for solid deuterium at a molar volume of 19.2 cm³/mole. The corresponding experimental results are 22.65 and 19.56 cm³/mole, respectively. Theoretical results for the compressibility at zero pressure are 5.3×10^–4 atm^–1 for solid hydrogen and 2.6×10^–4 atm^–1 for solid deuterium. The corresponding experimental results are 4.9×10^–4 and 3.0×10^–4 atm^–1, respectively. The agreement with experimental results is reasonably good since higher order cluster terms are not included in this first approximation.