Orbital Susceptibility of an Interaction Electron Gas

The wave-vector and frequency-dependent orbital susceptibility (χᵒʳᵇ) of an interacting electron gas is expressed in terms of suitable vertex functions. This makes the theory parallel to that of the spin susceptibility (χˢᵖ) of this system. The equation for the vertex function is solved in the statically screened exchange approximation by a variational method introduced earlier by one of the authors. The static long-wavelength limit of (χᵒʳᵇ) is shown to be related to the difference between the f- and p-wave decomposition of the effective interaction, whereas χˢᵖ is related to the difference between the corresponding p- and s-wave parts in the same limit. The classic result that χᵒʳᵇ is minus one-third of χˢᵖ for the noninteracting system is modified when the interactions are included. Explicit results are given for a model Yukawa interaction. From these, it follows that, for very short-range interactions, (χˢᵖ) reduces to the Stoner-enhanced form while χᵒʳᵇ is unaffected. The momentum dependence of the interaction is thus more important for the determination of χᵒʳᵇ than for χˢᵖ. In the unscreened Coulomb limit as well as for small screening, our results reduce to those obtained earlier by Kanazawa and Matsudaira. Several errors in the existing expressions for χᵒʳᵇ(→q, q₀) are corrected in this work.