Keywords: Atom-solid interactions, scattering, diffraction; Computer simulations; Quantum effects

Thermal energy atomic scattering (TEAS) is a useful tool to investigate the structure, the phonon spectra and the disorders of the solid surfaces¹. The probe particles do not penetrate into the surfaces, the TEAS is non-destructive. TEAS has been treated by an appropriate quantum mechanical model. The atomic beam is described by Gaussian wave-packet as an ensemble of independent particles. The atom - solid surface interaction is characterised by an interaction potential. The applied interaction potential describes the properties of ideally periodic or disordered surfaces, respectively. The scattering process is governed by time dependent Schrödinger equation that is solved numerically in the case of two- and three-dimensional coordinate space^2,3. The computations ensure the time propagation of the intensity distribution quantitatively and as an animation, respectively⁴.

First of all the resolution of TEAS has been investigated as a function of energy spread of atomic beam². Taking ideally periodic surface the resolution of diffraction peaks increases when the energy spread is decreased. This fact proves that the efficiency of the supersonic atomic source is higher than that of an effusive atomic source. Furthermore the transfer width of experimental equipment increases - when the atomic beam monochromaticity is also decreased - according to the concept of the transfer width. The relation between the transfer width and the size of the period of the surface topography significantly determines the resolution of the diffraction pattern. The results support the idea that the transfer width have to be significantly greater than the surface period. Otherwise, the resolution of the experiment is not fine enough to determine the exact surface structure.

After that we focused on the scattering from ideally periodic and disordered surfaces³. The probability density function has been rendered in real space and in momentum space. The slices of the probability density function parallel to the surface provide the surface topography not only in the case of an ideally periodic surface structure but also in the case of disorder. The computations has been executed in the case of a model surface and Rh(311) surface, respectively. The regularly and irregularly stepped surfaces have been investigated too. Relevant question is what happens near the surface in the quantum region. To answer this problem parallel slices of the probability density function of the probe particles to the solid surface have been rendered as time propagated around the classical turning point.

At last model computations represent the effect of thermal vibration in the case TEAS. The model contains a time dependent interaction energy that describes the fluctuating surface. The interaction energy is composed of a time independent and a time dependent perturbation part. The time independent part of the interaction energy corresponds to the frozen solid surface. The time dependent interaction energy describes the phenomena of the thermal vibration without energy transfer. There is no energy coupling between the probe particle and the surface in this model. The computations have been executed in the case of time independent and time dependent interaction energy, respectively. The thermal vibration causes a diffuse background of the intensity distribution. This effect changes the intensity pattern. The diffraction peaks overlap each other and their intensities decrease because of the diffuse background.

The examples demonstrate that the present time dependent Schrödinger equation (TDSE) model is appropriate to analyse the dynamics of atom scattering from solid surfaces. Simulations of different atom-solid surface systems provide typical structures of the intensity distributions that describe the given atom-solid surface systems. Comparing the experimental results with the simulation results, the surface structure can be determined to first order. This advantage of the TDSE model may provide a useful theoretical tool in the thorough investigation of atom-surface scattering.

[1] D. Farías and K.H. Rieder, Rep. Prog. Phys. Vol. 61 (1998) p. 1575-1664.

[2] G. Varga, Applied Surface Science, (1999) vol.144-145 p. 64-68.

[3] G. Varga, Surface Science, (1999) vol. 441 p. 472-478.

[4] G. Varga, Home Page, Scattering animations (2000): http://goliat.eik.bme.hu/~vargag/