3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

Abstract

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid 3He and (for the first time) to liquid 4He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid 3He, it is found that S-wave scattering dominates for wave number k<0.5 A−1. At the Fermi momentum k F, the effective partial cross section σ l (and thus the total cross section σ T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 A−1, the effective total cross section is nearly constant. On the other hand, it is found in liquid 4He that S-wave scattering dominates for k<0.3 A−1, and a peak exists in σ T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the l=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the 3He gas. It is, therefore, a purely many-body effect in liquid 3He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.