Orbital Susceptibility of an Interaction Electron Gas

The wave-vector and frequency-dependent orbital susceptibility (^orb) of an interacting electron gas is expressed in terms of suitable vertex functions. This makes the theory parallel to that of the spin susceptibility (^sp) 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 (^orb) is shown to be related to the difference between the f- and p-wave decomposition of the effective interaction, whereas ^sp is related to the difference between the corresponding p- and s-wave parts in the same limit. The classic result that ^orb is minus one-third of ^sp 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, (^sp) reduces to the Stoner-enhanced form while ^orb is unaffected. The momentum dependence of the interaction is thus more important for the determination of ^orb than for ^sp. 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 ^orb (q, q₀) are corrected in this work.