Many-body contributions to the equation of state for highly compressed solid helium

Abstract

To investigate the significance of various many_body effects on the equation of state (EOS) of solid helium,the interaction energy of hcp crystal structure is expanded as a sum of two_ to five_body potentials in the present work. Each short_range many_body term between helium atom clusters is computed by means of Hartree_Fock (HF) self_consistent_field (SCF) method. It is indicated that at high densities the many_body expansion formula is an alternative series, in which two_, and four_body terms are positive, whereas three_ and five_body terms are negative. According to such an expansion of crystal interaction energy, the equation of state of solid helium at 0 K is obtained. The specific characteristics of each of the up to five_body contributions in highly compressed helium are discussed. Between 0.26 to 0.23nm, the interaction energy may be well described by two_ and three_body interactions. Over a distance range 0.23—0.20nm, truncated many_body expansion after the four_body term recovers the main part of atomic potential energy. Below 0.20nm the five_body contributions have to be included. The sum of two_ to five_body term accurately reproduces the atomic potential energy from 0.20 to 0.175nm. The inclusion up to five_body potential satisfactorily describes the available experimental data from 7.5 to 2.5 cm3/mol, corresponding to 1—60 GPa.