Charge and Spin Response of the Spin--Polarized Electron Gas

The charge and spin response of a spin--polarized electron gas is investigated including terms beyond the random phase approximation. We evaluate the charge response, the longitudinal and transverse spin response, and the mixed spin--charge response self--consistently in terms of the susceptibility functions of a non--interacting system. Exchange--correlation effects between electrons of spin $\sigma$ and $\sigma^{'}$ are included following Kukkonen and Overhauser, by using spin--polarization dependent generalized Hubbard local field factors ${G_\sigma}^{\pm}$ and ${G_{\bar\sigma}}^{\pm}$. The general condition for charge--density and spin--density--wave excitations of the system is discussed.