Variational Monte Carlo study of heavy-atom impurities in liquidHe4

The static behavior of a single massive atomic impurity in bulk liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is studied variationally, based on a Jastrow ground-state wave function for the host-impurity complex. Techniques are devised for efficient Monte Carlo integration of expectation values relating to the impurity, making possible accurate evaluation of the relevant chemical-potential difference, partial radial-distribution functions, and partial structure functions. Taking the specific examples of a single Xe or Cs impurity, we obtain extensive variational Monte Carlo results for these quantities, using approximately optimal Jastrow two-body pseudopotentials determined by paired-phonon analysis within a hypernetted-chain scheme. By virtue of the extremely different impurity-host potentials involved (essentially attractive versus essentially repulsive, respectively), the Xe and Cs examples are seen to represent opposite extremes in the nature of the structural disturbance of the host medium produced by the impurity. Concomitantly, the Monte Carlo simulations are much more strongly dependent on the particle number in the Cs impurity problem than for Xe. Parallel results for the chemical potential differences, radial-distribution functions, and structure functions have been obtained via the leading hypernetted-chain approximation, permitting some conclusions to be drawn regarding the accuracy of this approximation.