Atom-surface scattering theory, helium

Section II is devoted to setting up elementary concepts associated with collective vibrational motion of atoms for reference later in the discussion of experimental results. Section III deals with atom-surface scattering theory so that the reader unfamiliar with this kind of spectroscopy can relate to the quantities which are measured directly. A brief description of the helium scattering instmment then follows in Section IV. 

The theory of atom-surface scattering, applied to the inelastic scattering of helium atoms from crystalline surfaces, is sketched out only briefly enough here to describe the conceptual framework and to identify the quantities and issues which experimentalists deal with in carrying out the measurements [39]. 

The corrugation of the charge density on metal surfaces can be obtained from first-principles calculations or helium scattering experiments. The theory and the experiments match very well. A helium atom can reach to about 2.5-3 A from the top-layer nuclei. At that distance, the repulsive force between the helium atom and the surface is already strong. The corrugation at that distance is about 0.03 A, from both theory and experiments. For STM,... 

In most materials, however, the modification of the forces at the surface is such that the surface localized modes have frequencies which lie below the frequencies of an associated bulk band with the same symmetry they have the appearance of having been peeled down from this bulk band [24]. In the usual case, the lowest energy of all these peeled -down modes derives from the bulk transverse acoustic band and is normally sagittally polarized. This dispersion branch is called the Rayleigh wave (RW) because it was predicted by Lord Rayleigh from continuum wave theory over a century ago [38]. Helium atom scattering experiments on virtually every material so far investigated have detected the RW on clean crystalline surfaces. 

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