Abstract
The energy spectrum of elementary excitations in liquid $^{4}\mathrm{He}$ is studied in the long-wavelength limit by means of the Brillouin-Wigner (BW) perturbation theory for two-phonon processes. Calculation of an additional second-order BW energy correction to the Bijl-Feynman excitation spectrum is carried out by considering contributions from the leading correction to the convolution approximation for the three-particle distribution function. The resulting correction is found to be positive and about 7.9% of the second-order perturbation energy obtained previously with the convolution approximation.
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