An inelastic focusing mechanism has been identified in the angular distributions of helium atoms scattered from single-crystal NaCl~001! surfaces as being due to energy exchange with a Rayleigh phonon mode. This effect, called inelastic focusing, occurs under special conditions in which the small spread of energies in the incident beam is sharply focused into a very narrow range of final angles. For a fixed initial scattering angle this is mathematically described as a singularity associated with the density of states in the incident momentum as a function of final scattering angle. This effect is an intrinsic feature of any scattering event of particles from surfaces and could be used to greatly enhance the intensity of weak single-phonon features in inelastic timeof-flight spectra. @S0163-1829~98!50416-X# The scattering of atoms and molecules from single-crystal surfaces has provided a wealth of information both on the physical properties of surfaces 1 and also on the interactions of the particles with the surface. Initially, most experiments concentrated on diffraction studies of the surface structure, but during the last two decades, the development of highintensity nearly monoenergetic helium-atom beams has provided sufficiently high intensities so that dynamical features of the surface such as phonon dispersion curves could also be explored. 2 In the ensuing period many of the unexpected features observed in these measurements 2‐6 were explained in terms of selective adsorption resonances, both elastic and those involving phonons, as well as kinematic focusing. 7 More recently, focused inelastic resonance ~FIR !~ Refs. 8 and 9! and diffuse elastic 10 resonance ~DER! effects have also been identified as causing distinct features in heliumatom scattering experiments. Since the interaction potential between He atoms and the NaCl~001! surface is reasonably well known, 9‐11 many of these new resonance mechanisms and focusing phenomena have first been studied on this surface. In parallel with experiments, the theory of atom-surface scattering has also undergone significant development. However, the energy resolution of the incident He-atom beam has usually been considered to have no substantial effect on the distribution of the scattering intensity. Thus, for example, in the calculations of the differential reflection coefficients for elastic and inelastic scattering the incident beam of the He atoms is usually considered to be sharp in both energy and angles, i.e., the finite energetic width of the incident beam is neglected and it is usually represented by a well-defined plane wave. In practice, this would appear to be justified since in most He-atom scattering experiments the energy resolution is usually as small as DEi /Ei’2%. If the finite angular width of the incident beam is included in the calculations several singularities appear that strongly modify the final scattering intensity. One of these new singularities, the inelastic focusing ~IF! singularity discussed here, was observed previously in the rotationally inelastic diffraction of molecular beams of H2 and its isotopes from single crystals of MgO~001 !~ Ref. 12! as well as in the inelastic scattering of D2 from NaF~001!. 13 In this communication, experimental evidence for the atomic IF effect in the scattering of He from NaCl~001! is presented. Moreover, in atomic scattering from other surfaces such as, for example, He/LiF~001!, 6 certain features were previously observed that can now be attributed to IF. In this work, the IF singularity is reexamined and found to have more far-reaching physical implications than previously envisaged. We note that the IF is a quite distinct effect from the previously investigated FIR ~Ref. 9! and DER ~Ref. 10! resonances. Both FIR and DER involve a resonant transition through a bound state of the interaction potential, whereas the IF is a kinematic enhancement of any selected inelastic feature and does not require the presence of a bound state. To experimentally demonstrate the IF singularity, highresolution helium-atom scattering experiments were carried on the well-studied NaCl~001! surface. In the scattering apparatus, which has been described in detail previously, 14 a nearly monoenergetic helium-atom beam (DEi /Ei<2%) is scattered through a fixed angle of 90° between source and detector in a plane perpendicular to the crystal surface. The parallel wave-vector transfer DK is changed by rotating the crystal and is given by 15
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