Limitations of the Trajectory Approximation in Atom-Surface Scattering

Abstract

We have scattered low energy (100 -400 eV) Na" from a Cu(001) surface, and studied the peak in the energy spectra that corresponds to collisions in which the Na' interacts primarily with a single Cu atom. This peak is broadened by the thermal fluctuations in the momentum of the Cu atom. Its width has been measured as a function of surface temperature, scattering geometry, and incident energy. Our data agree well with a rigorous statistical analysis (within 10%) but poorly with the trajectory approximation (TA), demonstrating that the TA can fail when recoil is substantial.

Theory of direct scattering, trapping, and desorption in atom-surface collisions

“…Under conditions for which the direct scattering of Eq. ͑18͒ appears nearly Gaussian type in the energy transfer, which is the situation in several of the cases shown here, the mean-square energy deviation which is proportional to the full width at half maximum ͑FWHM͒ is 11,12,42 …”

The transition from single phonon to multiphonon energy transfer in atom–surface collisions

“…29,30 A careful examination was made for the presence of anharmonic effects in the current measurements and no evidence of anharmonicity was found up to the highest temperatures of T S ϭ1000 K measured here. This observation has been corroborated for the Cu͑001͒ surface by ion scattering experiments carried out entirely in the classical regime 73 and by theoretical calculations using molecular dynamics simulations. 70 It is interesting to note that, even for initial energies in the classical regime, the effects of anharmonicity appear only as a result of the thermal vibrations of the surface atoms before collision by the projectile.…”

“…Further evidence of this trend is obtained from comparison with ion scattering experiments under extreme classical conditions 73 and with the high energy scattering of rare gases from liquids 74 in which good agreement between experiment and the classical limit theories of Eqs. ͑3͒ and ͑5͒ was obtained for the limit of large ␤ and Q c in which there is no dependence on these parameters at all.…”

“…͑3͒. 73,75 On the other hand, an intermediate case seems to be provided by the experiments of Nathanson et al on the scattering of rare gases ͑Ne, Ar, and Xe͒ from liquid metals ͑In, Ga, and Bi͒. For the specific case of a 0.5 eV beam of Ar scattering from a liquid In or Ga surface over the temperature range from 300 to 500 K the temperature dependence of the inelastic maximum follows an intermediate T S…”

“…͑3͒ and ͑5͒ up to T S Ϸ1000 K with no sign of anharmonic deviation from this behavior. 73 Additional evidence for the lack of anharmonicity comes from recent molecular dynamics simulations of the Cu͑001͒ surface 70 which completely rule out adatom-hole creation below 1000 K and show that anharmonicity becomes noticeable only well above 800 K. These theoretical results corroborate earlier experiments which also indicated that anharmonicity causes a faster than the expected Debye-Waller decrease of the elastic specular peak only at temperatures above 800 K. 72 It should be noted, however, that this observed rapid decrease of the specular peak intensity will have only little influence on the diffuse inelastic background of interest here because the actual value of the specular intensity is negligibly small at that elevated temperature ͑see Figs. 6 and 7͒.…”