Microscopic theory of self-diffusion in a classical one-component plasma

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Abstract
We apply the fully renormalized kinetic-theory formalism of Mazenko to the study of self-diffusion in a dense one-component classical plasma. The memory function associated with the phase-space correlation function for self-diffusion is expressed in terms of an effective two-body problem which allows us to make approximations at a microscopic level in a straightforward manner. We use simple physical arguments to obtain the "effective interaction approximation" for the memory function in which a pair of particles interact via a dynamically screened effective potential. This approximation for the memory function is a nontrivial and natural generalization of the Balescu-Guernsey-Lenard form that includes the exact statics of the system, treats screening at large and small distances consistently, and is valid for all wave numbers and frequencies. The inclusion of the hydrodynamic modes in the memory function leads to an oscillatory long-time tail in the velocity autocorrelation function. We calculate the self-diffusion constant as a function of density using the effective interaction form of the memory function and calculate the memory function associated with the velocity autocorrelation function using an interpolation procedure which incorporates the hydrodynamic modes. Qualitative agreement with recent molecular-dynamics computations of the self-diffusion constant and the memory function is found.