High-Energy Neutron Scattering from LiquidHe4

Abstract

The scattering of high-energy neutrons from liquid ${\mathrm{He}}^4$ is discussed in terms of the Gram-Charlier series expansion of the incoherent scattering function. It is shown that the series falls naturally into two parts. The first part, which corresponds to keeping only the leading term in each coefficient in the limit of large momentum transfer $\kappa$ can be summed exactly and gives the impulse approximation (IA). The second part, which vanishes in the limit $\kappa \to \infty$, describes the effect of final-state interactions which are neglected in the IA. The first two coefficients in the latter series are evaluated and indicate that final-state interactions are not negligible in the recent experiments of Cowley and Woods, a fact which probably explains why these authors failed to see a sharp peak, due to the condensate, which had been predicted by Hohenberg and Platzman on the basis of the IA. It is also shown that final-state interactions produce a shift in the position of the maximum of the energy distribution of scattered neutrons, and the calculated value is in rough agreement with the value observed by Cowley and Woods.