Efficient Quantum Reflection
A qualitative estimate for the efficiency of quantum reflection can be made using dimensional analysis. Letting be mass of the atom and the normal component of its wave-vector, then the energy of the normal motion of the particle,
should be compared to the potential, of interaction. The distance, at which can be considered as the distance the which the atom will come across a troublesome discontinuity in the potential. This is the point at which the WKB method truly becomes nonsense. The condition for efficient quantum reflection can be written as . In other words the wavelength is small compared to the distance at which the atom may become reflected from the surface. If this condition holds, the aforementioned effect of the discrete character of the surface may be neglected. This argument produces a simple estimate for the reflectivity, ,
which shows good agreement with experimental data for excited neon and helium atoms, reflected from a flat silicon surface (fig.1), see and references therein. Such a fit is also in good agreement with a single-dimensional analysis of the scattering of atoms from an attractive potential,. Such agreement indicates, that, at least in the case of noble gases and Si surface, the quantun reflection can be described with single-dimensional hermitian potential, as the result of attraction of atoms to the surface.
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