Density fluctuations in liquid ⁴He. Path integrals and maximum entropy

We estimate the dynamic structure factor S(q, ω) for liquid ⁴He in both its normal and superfluid phases. A path integral Monte Carlo simulation is performed to compute the imaginary-time polarization propagator F(q, τ), from which S(q, ω) is extracted by maximum entropy. Results for normal ⁴He are in good quantitative agreement with recent neutron scattering experimental data; broad agreement is found for superfluid ⁴He as well, though sharp features are lost, particularly at low q. We attribute the excessive smoothness of the results to the entropie "prior probability" function used in the maximum entropy reconstruction. The experimentally observed ground state excitation spectrum E(q) is accurately reproduced in the 0 ≤ q ≤ 2.5 Å^-1 range.