Calculation of the mutual friction parameters in liquid helium II and the nature of the vortex core

Abstract

The total force between a vortex line and the rotons in rotating superfluid helium (mass 4) is calculated by summing -nabla(p.v₅) over the entire roton fluid (rather than via the determination of roton-vortex collision diameters as in previous calculations). The corresponding values of the mutual friction parameters B and B' are determined using the Hall-Vinen theory (1956) and compared with experiment. Without a core one finds no longitudinal force, while the transverse force is of the wrong sign; these are results which are shown to be in close agreement with previous calculations when mistakes in the latter are corrected. With a roton absorbing core, very good agreement with experiment is achieved, except very close to T_lambda . The data show that the core radius is approximately 0.45 nm at 1.3K, increasing slowly with temperature until T approximately=1.7K and faster thereafter as T_lambda is approached.