The dependence of the photoassisted field emission on the dielectric functions

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Abstract
The photoassisted field emission is described as a tunnelling process through a barrier including the surface potential wall of the free electron metal and the external DC electric field potential. The corresponding transition matrix elements are calculated with application to sodium. The functional dependence of the electron self-energy on the longitudinal dielectric function is derived for finite temperatures. Also discussed is how the boundary conditions for the incoming light beam of arbitrary polarization depend on the transversal and longitudinal dielectric functions. Finally, a transformation formula is presented, which introduces a finite relaxation time parameter in a proper way so that the Thomas-Fermi limit and the Drude approximation take their appropriate values.