Line shifts and broadenings in polarizable liquids

We present a new dynamical derivation of the approximation used by Thompson, Schweizer, and Chandler and by Ho/ye and Stell for the frequency dependent polarizability of a quantum fluid with harmonically bound dipole moments; the Drude model. The derivation is the same for classical and quantum liquids—as is of course the result which agrees with that of these authors. We then refine the theory by taking account of the limited number of energy levels available, i.e., we replace the harmonic approximation by a two level approximation, for the target atom. This leads to a prefactor ω0I/ω0 in the line shift of an impurity atom in a fluid computed by Chandler, Schweitzer, and Wolynes: ω0 and ω0…