A dielectric response approach to the dynamic image potential of a charged particle approaching a planar metal surface is formulated. A self-consistent scheme for calculating the instantaneous speed of the particle, and its image potential is also derived. It is shown that the scheme does not rely on the actual approximations made while describing the response of the metal with surface. Various approximations are discussed and the corresponding numerical results compared. The effect of self-consistency and inclusion of dispersion in metal is noticeable.

We present here an approximate scheme to obtain the complex frequency-dependent local field correction,G (q, ω). Using the equation of motion approach we develop here a methodology from which the results obtained by earlier workers, for density-density response function of an electron gas, can be arrived at in a simple systematic manner. We study in detail an approximation made along the similar lines as Singwi and coworkers, which leads to a compact expression for a complex frequency-dependent local field correction. We give results for damping coefficient of long wavelength plasmons which depends on ImG(q, ω). The real and imaginary parts ofG(q, ω) as functions ofω for various values ofq are also calculated. The dynamic structure factorS(q, ω) is evaluated forq=1.6q_F and compared with earlier theoretical and experimental results.