Interactions of collective excitations with vortices in superfluid systems

We investigate the interactions of collective excitations with vortices in superfluid systms, including ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ 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)${]}^2$}${\cot }^2$(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.