TRACING THE CAUSE OF THE ABSENCE OF SINGULAR BEHAVIOR IN THE RESPONSE OF CONDENSED LIQUID-HE-4

We study a result by Carraro and Koonin, where final-state interactions have numerically been shown to eliminate the singularity in the asymptotic response of condensed liquid He-4. Here we trace the outcome to the following causes: (1) An effective hard core (HC) in the atom-atom interaction upsilon when the collision energy is lower than the maximum of upsilon; (2) an A-body density matrix, which in the condensed phase does not prevent free recoil. Thus a recoiling atom is bound to collide with at least one background atom within the HC range of their mutual interaction. This nonperturbative effect causes the extinction of the singularity. In the normal phase, the density matrix prevents "free" recoil of a particle which undergoes, on average, only a few multiple collisions: HC effects remain small and the normal response can be calculated perturbatively.