Mixed charge-spin response functions of an arbitrarily polarized electron gas

In this paper, we demonstrate the equality of the two mixed charge-spin res ponse functions of a spin-polarized electron gas when orbital effects are n egligible using different approaches. Within a generalized STLS approximati on we show that the two mixed responses are equal. We also present argument s fur the equality of the two dynamic responses by considering a symmetry o f the effective screened interaction between two opposite spin electrons. F urthermore, using the refection symmetry of the system and the fact that th e Hamiltonian is real we prove rigorously that the two responses coincide i dentically. (C) 2000 Elsevier Science Ltd. All rights reserved.