The mobility of a heavy impurity in a degenerate Fermi system

A theory is developed for the dynamics of a heavy quantum particle interacting via a local potential with the particles of a degenerate Fermi system. The dynamic density response function of the impurity is represented in terms of two relaxation kernels such that the two lowest sum rules and the correct hydrodynamic limit are guaranteed. The momentum and frequency dependent relaxation kernals again are expressed in terms of the dynamic structure factor S(k, omega ) of the impurity in leading order in the impurity-Fermi-system correlation, yielding a set of self-consistent nonlinear integral equations for S(k, omega ). The self-consistency problem is discussed and solved numerically with simple model assumptions for the interaction potential and the dynamic structure factor of the Fermi system. The mobility of the impurity is found to vary as ln (T₀T) for a range of temperatures T and interaction strengths, before diverging like 1/T² for T to 0. The relevance of the theory to the mobility of ions in ³He is discussed. It is shown that the present theory accounts for the observed temperature dependence of the positive ion mobility and is consistent with that of the negative ions. The theory also implies that the effective mass has a strongly temperature dependent contribution, which should be observable in the frequency dependence of the mobility.