Dynamics of quantum liquids at high momentum

The dynamic form factor S(Q,{ω}) in liquid ³He and ⁴He is evaluated in the wave-vector transfer range 3{≤}Q{≤}15 A^-1. The input is the pair interatomic potential, developed by Aziz et al. The S(Q,{ω}) is calculated within the random-phase approximation (RPA) which becomes valid when {}Q is much larger than the average momentum in the liquid. A T-matrix approximation represents the interaction appearing in the RPA. The aim is to explore how well S(Q,{ω}) can be described for 3{≤}Q{≤}15 A^-1 from first principles. In ³He, we find S(Q,{ω}) is a broad, nearly Gaussian function, centered just below the recoil frequency having a width and shape that agrees well with experiment. It does, however, have tails at high frequency which make important contributions to its moments. In ⁴He, S(Q,{ω}) is a more sharply peaked function which also agrees quite well with experiment. We are able to reproduce the oscillations in the peak position and in the width of S(Q,{ω}) with Q in liquid ⁴He observed by Martel et al. In the present model, these oscillations originate from oscillations in the magnitude of the T-matrix interaction with Q. The corresponding oscillations are predicted to be very small and probably unobservable in liquid ³He.