Beyond mean field effects in the high momentum energy spectrum of a Bose gas: revisiting Beliaev's theory

The well-known Bogoliubov expression for the spectrum of a weakly interacting dilute Bose gas becomes inadequate when the density or interactions strength are increased. The corrections to the spectrum due to stronger interactions were first considered by Beliaev (S. T. Beliaev, Sov. Phys.-JETP, 7:289, (1958)). We revisit Beliaev's theory and consider its application to a dilute gas with van der Waals interactions, where the scattering length may be tuned via a Fano-Feshbach resonance. We numerically evaluate Beliaev's expression for the excitation spectrum in the intermediate momentum regime, and we also examine the consequences of the momentum dependence of the two-body scattering amplitude.These results are relevant to the interpretation of a recent Bragg spectroscopy experiment of a strongly interacting Bose gas.