The ³He-Roton Interaction

Abstract

For lack of more detailed knowledge concerning the interactions between elementary excitations in liquid helium, Khalatnikov’s theory¹ of transport phenomena has described such interactions in terms of δ-function potentials. Recent measurements by Herzlinger and King² of the diffusion constant of very dilute ³He-⁴He solutions at temperatures slightly above 1°K call into question the validity of such simple models. It is indicated that the temperature variation of the kinetic coefficients may depend sensitively upon the form of the ³He—roton scattering cross section. We present here, as a first leg of the journey toward obtaining the diffusion coefficient D(T), a microscopic calculation of the effective ³He-roton cross section.

Work supported in part by the National Science Foundation through Grant No. GP-29130 and through the Materials Research Center of Northwestern University.

H. T. Tan and M. Tan are with the Physics Department and the Faculty of Engineering, respectively.

Alfred P. Sloan Research Fellow.