The Debye-Waller factor in helium scattering by a crystalline surface

On the dense face of a metallic crystal or the (001) face of lithium fluoride, the distance between nearest neighbours is of the same order of magnitude as the helium diameter. The hypothesis of simultaneous interaction between incident helium atoms of thermal kinetic energy and surface atoms belonging to a surface unit cell is therefore introduced. Then the exponent of the Debye-Waller factor contains mean square and mean correlated displacement between atoms of the cell. This gives for the (00) peak an apparent surface Debye temperature Θ_sa higher than the corresponding value usually deduced for instance from LEED measurements. For the (001) face of copper the calculated value is: 323 < Θ_sa < 354 K according to the value ascribed to bulk Debye temperature. On this face, recent experimental results show that helium atoms are coherently scattered in the specular (00) peak. From its intensity analysis is deduced an attractive well depth of 0.009 ± 0.002 eV and Θ_s = 370 ± 10 K, very close to the calculated result. The simultaneous interaction implies that the one phonon exchange can only take place with phonons of long wavelength. This theoretical expectation seems to be in qualitative agreement with experimental data.