Derivation and Characteristics of a Generalized Form of Susceptibility Used in the Analysis of Raman Line Shape for an Overdamped Mode

Abstract

On the basis of Onsager’s phenomenological equation of motion, the generalized form of susceptibility is derived. This includes the damped harmonic oscillator (DHO), Van Vleck-Weisskopf and Fröhlich susceptibility (VWF) and Debye relaxational model as different limiting cases, and is equivalent to that obtained from the Bloch equation for the Ising model in a transverse field which are used in the pseudo-spin model for KDP-type crystals. Characteristics and mutual relations of susceptibilities are discussed with an emphasis on the difference between DHO and VWF. For a heavily damped mode, DHO becomes difficult to physically interpret since the eigenfrequency and the damping factor may lose their original meaning. In such cases, the only important parameter is the distance from the origin to the pole of χ(ω) in the complex ω-plane.