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.