ACCURATE AND APPROXIMATE RESULTS FOR THE TIME-CORRELATION FUNCTION AND MEMORY FUNCTION-ASSOCIATED WITH TRACER DIFFUSION IN A PURE CRYSTAL

The time correlation function associated with the tracer diffusion coe fficient for the vacancy mechanism in a pure simple cubic substance ha s been calculated accurately from an integral equation in time derived from the kinetic equation for tracer migration. Results for different tracer to host jump frequency ratios are compared with approximate so lutions valid at short and long times. The memory function of the time correlation function has been calculated. Simple approximations to th e memory function and the time correlation function generated from the Mori continued fraction representation of the memory function are tes ted. The Fourier transform of die time correlation function, which is proportional to the frequency dependent part of the frequency dependen t diffusion coefficient, is also described.