WIDE-BAND APPROXIMATION IN THE THEORIES OF CHARGE-TRANSFER DURING ION-SURFACE SCATTERING

The validity of the wide-band approximation is discussed and, in particular, the effects of the speed of the ion and the position of ion orbital energy relative to the band are considered. It is shown that care is needed in interpreting the integrals involved using generalized functions and that, for slow ions and a wide band, the wide-band approximation is valid for orbital energies well within the band, partially valid at the band edges, and invalid outside the band. Equations are also derived for mixed bands including the situation where the band can be divided into two parts, a narrow band and a wide band.