Kinematics of Excitation Pair Contributions to Dynamic Structure

This is the authors' abstract. We don't add key points for this paper.

The joint density-of-states integral for production of a pair of elementary excitations in an isotropic fluid is studied as a function of energy and momentum. Isotropy permits one to take advantage of the essentially two-dimensional character of the system. Specializing to liquid He⁴ at $T=0$ ^∘{}K, we show that certain abrupt variations in the density of states are associated with thresholds and saddle points in the energy function. The expected influence of these phenomena on S(→k,ω) is described. Resonant pairs of excitations, as judged by their linesharpening effects, are shown to exist at special values of →k and ω.