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

The thermal energy He scattering from solid surface (TEAS) is an important tool to investigate the processes on solid surfaces^1,2. Certain classical mechanical models of TEAS show chaotic behaviour. However, the real systems are not always governed by classical mechanics because the interaction is strong enough. In consequence of this fact the classical model may show chaotic effect but the real physical system has no chaotic effect. To resolve this contradiction a time dependent quantum mechanical model has to be applied.

First of all He scattering on clean Rh(311) surface has been discussed within the frame of classical mechanics. The classical model of thermal energy atom scattering on solid surfaces (TEAS) is based on the one particle problem. The mass point of the He atom is scattered on an appropriately chosen interaction potential that describes the solid surface. The motion of the particle presented as a mass point is governed by Newton's second law. The scattering of the atoms on the interaction potential of He-Rh(311) system is investigated as a function of the impact parameter. Detailed computations show 2D and 3D chaotic effects in trajectories, phase diagrams, deflection angle function and dwell time function. A crucial point of the above described model is the numerical method to solve the system of differential equations. For stiff problems - as the present problem is - variable order solver based on numerical differentiation formulas is recommended. The above results underline the existence of two-dimensional and three-dimensional chaotic He scattering on Rh(311) surface. When the Rh(311) surface is characterised by one-dimensional corrugation function chaotic scattering is received. However, this behaviour arises not from the low order dimension of the surface structure. Namely, in the case of the Rh(311) surface with two-dimensional corrugation function also chaotic scattering is received. Actually, the 2D case predicts the region of impact parameters where the effect of chaos appears. The peculiarity of chaotic scattering is typical of both the 2D and 3D He scattering on Rh(311).

After that 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 interaction potential provides the properties of Rh(311) surface. The scattering process is governed by time dependent Schrödinger equation that is solved numerically in the case of two- and three-dimensional coordinate space^3,4,5. The computations ensure the time propagation of the intensity distribution.

This quantum mechanical model recommends not only a simulation of (chaotic) scattering but a real measurement, too. If the dwell time near the surface of scattered He atoms is stochastically fluctuating then the scattering is chaotic. The dwell time of the probe particles can be determined by the flight time measurement of He atoms. When the graph of intensity distribution vs flight time (energy) has a 'chattering' region, the scattering is quantum mechanically chaotic. The well known time of flight (TOF) measurement is suitable to explore the pure quantum chaos. The computations has been executed in the case of He atom scattering on Rh(311) surface. Two methods have been applied. One of them investigated the probability density function of the He atom beam. Experimentally, it corresponds to the standard intensity distribution measurement. By the other method the dwell time of the He atom beam was analysed in the real physical space. Experimentally, this case corresponds to the TOF. None of them has shown quantum chaotic behaviour, although classical mechanical discussion provides chaotic scattering. The explanation may be that quantum mechanics contains in natural mode the different phenomena of scattering (e.g. trapping, adsorption). Only the elastic behaviour of the scattering was investigated because of the time independent interaction potential. The only conclusion may be drawn: the elastic scattering without diffuse scattering (frozen solid surface) does not show quantum chaos. Further investigations of more thorough quantum mechanical models have to be applied.

[1] G. Comsa, Surf. Sci. 299-300 (1994) 77.

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

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

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

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

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