Interactions of collective excitations with vortices in superfluid systems.

We investigate the interactions of collective excitations with vortices in superfluid systems, including 4He and superconductors. The dynamical equations are obtained by the aid of the many-body wavefunction 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 collective excitation spectrum ω(q) by the simple and general formula σ = π2 q [ω′(q)]2 cot 2 θ 2 , where q is the wave number of the excitation, and θ is the scattering angle. At short wave lengths, the classical equations of motion are derived.