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Finally, we recall that whereas core-level spectroscopies can determine the charge of surface species, in the case of planar targets ion scattering experiments are used to measure their mass. In ion scattering s p e c t r ~ m e t r y , ~ ~ * ~the ~ *elastic * ’ ~ ~ scattering from surface species of ions in the energy range 103 eV sE51O6 eV is measured. The recoil energy given the incident ion is a direct measure of the mass of the particle with which it ~ o l l i d e d . *In~ secondary ~~~ ion mass s p e ~ t r o m e t r y‘I7~ ~(or , “ion probe microanalysis”), the species sputtered from a surface by an incident ion beam are mass analyzed directly.

For such systems, appearance poten- 28 C . B. DUKE tial spectroscopy and Auger spectroscopy have been shown to be mutually complementary techniques for the detection of i m p ~ r i t i e s . ’The ~ ~ utility of appearance potential spectroscopy for materials other than the 3-d transition metals, however, remains to be demonstrated. , X-ray photoemission). ’6 The short inelastic collision mean free path of the photoelectrons, however, renders X-ray photoemission as well as Auger spectroscopy sensitive to the surface rather than bulk properties of the sample.

The Hamiltonian of these loss modes themselves is, in principle, of the form given in (21b). In practice, however, a more refined spectral density quantum field theory formalism is ~ s e d ~ ’ in , ~which ~ * the ~ ~interactions ~ , ~ ~ of~ these loss mode excitations result in their damping. 46 C. B. An important aspect of the development of LEED theory is that the approximations which work well to describe the ground and low-lying excited states in a bulk solid do not suffice to provide even a qualitative theory of LEED.

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