Exchange and correlation potentials for finite temperature quantum calculations at intermediate degeneracies

Abstract

The exchange and correlation potentials which are needed in the study of electron systems (atoms, plasmas) at finite temperatures and finite degeneracies have been calculated and presented in a parametrised form convenient for use in Thomas-Fermi, Hartree-Fock, density-functional type effective single-particle models. The exchange corrected single-particle energies and chemical potential are calculated self-consistently and in the linear approximation. The natural generalisation of the Debye-Huckel screening length is used to extract a static model valid at intermediate degeneracies. The higher-order corrections (i.e., beyond Hartree-Fock) are evaluated from the ring sum and the second-order screened contributions to the thermodynamic grand potential. The ring sum is calculated via an approximation to the polarisation function which is known to be satisfactory at 0K and exact in the Debye-Huckel limit. The numerical results show that the correlation potential at finite temperatures consists of a static contribution and a dynamic part which goes to zero at high temperatures.