Third-order perturbation theory and structures of liquid metals: sodium and potassium

Linear screening theory for the interionic interaction in simple liquid metals is extended by including pair and three-ion interactions due to the third-order perturbation term in the electron-ion interaction. Additional pair potentials, phi2sup((3))(r), of both sodium and potassium are large and attractive in the short range. The position of the sharply rising part of the pair potential moves to a smaller distance by several percent with the inclusion of phi2sup((3))(r). The role of phi2sup((3))(r) is essential if the theory of Anderson, Weeks and Chandler is to give a good description of liquid structures. On the other hand, second-order calculations are rather successfull when the Gibbs-Bogoliubov inequality method is employed. The influence of the three-ion interaction phi3sup((3)) on the structures of liquid metals are estimated through the effective pair potential which is defined in the presence of the three body potential. phi3sup((3)) plays a role of similar nature to that of phi2sup((3))(r), whereas it is less important as far as liquid structures are concerned. (author)