MICROSCOPIC CALCULATION OF THE DYNAMIC STRUCTURE-FUNCTION IN THE DEEP-INELASTIC REGIME

We study the dynamic structure function S(k,omega) of Bose liquids in the asymptotic limit k,omega --> infinity at constant y = (m/k)(omega-k2/2m), using the orthogonal correlated basis of Feynman phonon states. This approach has been traditionally and successfully used to study the S(k,omega) at small k,omega, and it appears possible to develop it further to obtain a unified theory of S(k,omega) at all k and omega. In the present work, we prove within this approach that the S(k,omega) scales exactly in the k,omega --> infinity limit, as is well known. We also show that, within a very good approximation, the scaling function J(y) is determined solely by the static structure function S(q) of the liquid. In contrast, the traditional approach to the S(k,omega) at large k,omega is based on the impulse approximation (IA), and the J(IA)(y) is solely determined by the momentum distribution n(q) of the particles in the liquid. In weakly interacting systems, where the IA is exact, we show that the J(y) calculated from the Feynman phonon basis is identical to the J(IA)(y). The theory is applied to liquid He-4 and the J(y) is calculated using the experimental S(q). This J(y) is quite similar to the J(IA)(y) obtained from the theoretical n(q) of liquid He-4. A number of technical developments in orthogonal-correlated-basis theories are reported.