Focusing properties of a bounded cylindrical field

The effect of the solid surface on the X-ray induced low-energy electron emission is analysed, using the formalism of the general scattering theory, by means of an approach, called by us the `diagonalisation methodʹ. Explicit analytical expressions and numerical results, obtained in the one-dimensional approximation, show great sensitivity of the shape of electron emission spectra near the threshold to the surface potential barrier height and to the presence of the amorphous `transitionʹ layer.