Neutron scattering as a probe of particle-Like excitations in superfluid 4He: a model calculation

In the microscopic theory of Bose-condensed liquids, the condensate wave function leads to a coupling of the density fluctuations and the single-particle excitations. A simple parametrized model of this based on coupling weakly damped zero-sound modes with strongly damped free-particle-like excitations similar to Q2/2m explains why the phonon-roton resonance in S(Q,w) for superfluid 4He exists above and below Tλ but only pays the role of an elementary excitation below Tλ. It is pointed out that this model also predicts that S(Q,w) should exhibit a weak, low-frequency peak centered at Q2/2m, with weight roughly proportional to the condensate fraction n/OMICRON/. As a stimulus to further experimental searches for this branch, some model calculations are given for S(Q,w) for Q similar to 1A-1