Atomic H over crystal surface: effective potential dependence on sample properties

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Abstract We considered the behavior of the lowest electronic level of atomic H in a semi-infinite space bounded by a flat surface. 
We impose a third kind boundary condition on the electronic wave functions, where the boundary condition parameter models the adsorbent properties of the surface.
For the crystal surface, the double periodic function as the boundary parameter seems reasonable; therefore, this case is considered.
It is shown that there are two modes of atom adsorption on the sample surface depending on the parameters of the boundary condition. 
In the first case the effective atomic potential, considered as a function of the distance between H and the boundary plane, exhibits a well pronounced minimum at some finite distance and a relatively small effective range of interaction distances between the atoms and samples.
The second case occurs under the condition of a large positive affinity of the atomic electron to the sample boundary and low initial H-concentration inside the sample. 
In such a situation, the minimum of the effective potential is close to the sample surface, and a significant amount of energy can be emitted throughout the adsorption process.