Interactions of collective excitations with vortices in superfluid systems

We investigate the interactions of collective excitations with vortices in superfluid systms, including ⁴He and superconductors. The dynamical equations are obtained by the aid of the many-body wave function and the density-density correlation function. The scattering cross section of collective excitations with a vortex is calculated in the Born approximation (valid at long wavelengths), and is expressed in terms of the Feynman model spectrum {ω}(q) of the collective excitations by the simple and general formula {σ}=({π}/2){q/[{ω}'(q)]²}cot²({θ}/2), where q is the wave number of the excitation, and {θ} is the scattering angle. At short wavelengths, the classical equations of motion are derived.