A nonlinear integral equation for the ground-state magnetic structure factor $\tilde{S}\mathrm{}\left(k\right)\mathrm{}$ of an electron liquid has been obtained by using a method originally due to Mihara and Puff. This equation is solved self-consistently to get the values of $\tilde{S}\mathrm{}\left(k\right)\mathrm{}$ which are used to estimate the pair correlation functions of electrons with parallel and antiparallel spins. The results obtained compare favorably with that of earlier sophisticated calculations.

• Received 29 October 1973

DOI:https://doi.org/10.1103/PhysRevB.10.2764