Application of the Third Moment to the Electric and Magnetic Response Function

The third frequency moments of the electric and magnetic response functions of a homogeneous electron gas are shown to reflect the short-time (or high-frequency) motion of an electron relative to its correlation hole. It is found that the relaxation of the local correlation hole effects the magnetic response much more strongly than the electric response, particularly for long wavelengths. Available models for these response functions are found to miss this particular aspect and, therefore, they cannot be valid both for low and high frequencies. An interpolation model, which in a more proper way includes the relaxation of the correlation hole, is used for some illustrative numerical calculations. It leads to damping of the long-wavelength plasmons in good agreement with earlier calculations based on diagram techniques and including multiple particle-hole excitations.