He-3 correlation energy in the random phase approximation: The one-ripplon-exchange potential in thin He-3-He-4 superfluid films

A new approach to the calculation of correlation energies in the random pha se approximation (RPA) is introduced. The method is applied to the system o f absorbed He-3 in thin He-4 superfluid films. The He-3 component interacts by means of the exchange of virtual surface interactions (ripplons) in add ition to the usual atom-atom interaction. We report on a calculation of the RPA contribution to the 3He ground-state energy of a previously introduced model for this effective interaction called the one-ripplon-exchange poten tial (OREP). V-OREP is manifestly frequency dependent and complex. In this paper we study the differences in the RPA contribution to the ground-state energy between the fully complex and frequency dependent V-OREP and V-OREP in the real, static limit.