Abstract
Elementary excitations of liquid $^{4}\mathrm{He}$ have been studied in the past with either perturbation theory in the basis of Feynman phonon states, or with variational theory using Feynman-Cohen (FC) wave functions. We develop perturbation theory in the basis of FC phonon states. Such a theory appears to have much better convergence. The second-order corrections to the FC spectrum are calculated, and these improve the agreement with experiment very significantly. We also calculate the strength $Z(k)$ of the collective mode. The second-order corrections to the $Z(k)$ of FC phonons also improve the agreement with experiment. Calculations are carried out at pressures of 0, 10, and 24 atm using the variational, Green's-function Monte Carlo and experimental pair distribution functions. Corrections to the Kirkwood superposition approximation for the three- and four-particle distribution functions are calculated with the variational ground-state wave functions containing pair and triplet correlations.
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