Long-wavelength-phonon spectrum in liquidHe4

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.