We calculate the deep-inelastic response of superfluid ${}^4\mathrm{He}$ and normal ${}^3\mathrm{He}.$ Following the Monte Carlo scheme of Carraro and Koonin, we represent the final-state effects by sampling the one-dimensional scattering wave function of the recoiling atom in a static background. We perform diffusion Monte Carlo simulations, using optimized trial functions and adopting the fixed node approximation for ${}^3\mathrm{He}.$ For ${}^4\mathrm{He}$ the agreement with recent high-precision measurements is excellent, whereas in the case of ${}^3\mathrm{He}$ a small but not negligible discrepancy with available experimental information exists. Possible biases in the calculation are discussed, but the question remains open. This is not the first instance where some inconsistency is found between theoretical calculations and the analysis of neutron-scattering data for ${}^3\mathrm{He}.$ We have also considered two very different fermion wave functions, yielding either a discontinuous or a continuous momentum distribution. They give hardly distinguishable results for the response, ruling out the possibility of detecting the discontinuity by deep-inelastic neutron scattering at the present level of experimental accuracy.

• Received 11 May 1998

DOI:https://doi.org/10.1103/PhysRevB.58.11607