The scattering of single-particle excitatins by a vortex in the condensate of an imperfect Bose gas is studied using the Bogoliubov approximation. The S matrix is calculated as in conventional scattering theory, and the phase shifts are determined with the Schwinger variational principle. The differential cross section in the long-wavelength limit is found to be dσdχ=1/2π(mc)²kcot²(1/2χ), where m is the mass of one atom and c is the speed of sound. This cross section agrees precisely with that found previously for scattering of sound by a classical vortex with circulation h/m.
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Alexander L. Fetter (1965) studied this question.
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