Self-consistent second-order approximation for the liquid-helium-II excitation spectrum

The equations of the self-consistent second-order approximation for the dynamical structure factor $S(q,\omega )$ of liquid helium II at zero temperature formulated by Jackson are solved by iteration. The elementary excitation spectrum obtained for wave numbers around and above the roton minimum exhibiting Pitaevskij bending is in better agreement with experiment than the original first iteration result due to Jackson and Feenberg but the description of the maxon is unsatisfactory.