Comment on "Dynamics of the interactions of rotons with quantized vortices in helium II"

Samuels and Donnelly, [1] in a recent Letter, have successfully applied the unusual kinematics of rotons to an analysis of roton-vortex scattering and mutual friction in He II. We applaud this success, which uses an approach we have advocated in an earlier publication. [2] Our purpose, in the present note, is to point out that the authors have made an unnecessary approximation in analyzing roton trajectories near vortex lines. Application of the conservation of angular momentum yields an exact result, which differs somewhat from theirs. If one uses the conservation laws, the calculation of orbits is reduced to a quadrature, as in the familiar classical mechanics problem of motion in a central force field. [3] The excess energy of an elementary excitation in a superfluid velocity field, given by δε(p) = p · vs(r), takes the form