Inelastic scattering of He-atoms

Wrr Witte, G., Fuhrmann, D., Well, C. Low-Energy Molecular Vibrations investigated by Inelastic Scattering of He Atoms Chem. Phys. Lett. 265 (1997) 347. 

Brusdeylins, G., Doak, R.B., and Toennies, J.P. (1980) Observation of surface phonons in inelastic-scattering of He atoms from Iif(001) crystal-surfaces. Phys. Rev. Lett., 44, 1417. 

Besides the inelastic component, always a certain number of He atoms are elastically scattered in directions lying between the coherent diffraction peaks. We will refer to this scattering as diffuse elastic scattering. This diffuse intensity is attributed to scattering from defects and impurities. Accordingly, it provides information on the degree and nature of surface disorder. It can be used for example to study the growth of thin films or to deduce information on the size, nature and orientation of surface defects Very recently from the analysis of the diffuse elastic peak width, information on the diffusive motion of surface atoms has been obtained. ... 

It is tempting to identify the superfluid and normal fluid components of He II with the atoms of the condensate and excited states, respectively, of an ideal Bose-Einstein gas, but this, too, turns out to be a gross oversimplification. Nonetheless, it is clear that Bose-Einstein statistics do play an essential role in determining the properties of the liquid. If one calculates the Bose-Einstein condensation temperature of an ideal gas with the same density and atomic mass as liquid " He, one finds 7 3.1 K, and the difference between this value and 7 may plausibly be ascribed to the influence of the interatomic forces. The presence of a condensate of " He atoms in the zero momentum state has recently been confirmed by inelastic neutron scattering measurements. As shown in Fig. 14, the condensate fraction rises from zero at Tx towards an asymptotic limit of about 14% at low temperatures. This departure from the approximately 100% condensate characteristic of an ideal gas for r 7c is an expected consequence of the non-negligible interatomic forces. Of couse, as already noted in Fig. 13, the superfluid component does form 100% of the liquid at 7 = 0 and it cannot, therefore, be directly identified with the condensate fraction. 

An important simplification in the analysis of He scattering is the large mass mismatch between He and most other atoms that are the constituents of solid surfaces. Therefore, energy transfer between the He atom and the surface is very much limited and elastic He diffraction or inelastic He scattering can be modelled rather easily and quantum mechanically. The situation is very different when heavier atoms or molecules are scattered from a surface. In this case energy exchange between projectile and surface will be facile, and in most cases only classical mechanics can be used to model the interaction. Most of the... 

More information on excitation processes can be gained from measurements of the differential cross section of the elastically or inelastically scattered particles. The phenomena expected in the differential cross sections will be the same as found in the corresponding ion-atom scattering experiments. They have been demonstrated most beautifully in the standard case He+ + Ne which has been studied thoroughly both experimentally and theoretically.97-99100101 102 A fully developed theory exists for the interpretation of differential cross sections in cases where excited states play an important role.10 96 9798... 

The atom-multiphonon component of the inelastic scattering can be obtained from the theory of Manson [44] by subtracting off the zero- and first-order terms from the power series expansion of the exponential displacement correlation function. With the assumption that the major contribution to the multiphonon scattering is due to low-energy, long-wavelength phonons, he is able to arrive at an expression with a very simple form for the transition rate. 

Vibration frequencies and phonon dispersion See Figs. 20 - 23. Table 13. Perpendicular vibration frequencies /zcoi and characteristics of the phonon dispersion curves for the noble gas monolayers. The sound velocities c/ and c, were obtained from the initial slope of the dispersion curves for the longitudinal (L) and shear-horizontal (SH) modes, respectively. Where complete or partial dispersion curves are available, oidy the value at the boundary of the surface Brillouin zone is indicated. Abbreviations used F, M, K high syrtunetry points of the 2D adlayer Brillouin zone (BZ) [001], [110] and [112] crystallographic directions of the substrate surface. All data were obtained using inelastic He-atom scattering. (Ad. = adsorbate) ... 

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