Theory of Interaction Between an Atom and a Metal

The problem of the interaction of an atomic system with the surface of a metal at large distances is of significant interest for the theory of gas and vapor adsorption on solids surfaces. Just as in the interaction of two atomic systems, the universal attraction at large distances for neutral and non-polar systems may be obtained only in the second approximation of perturbation theory [1], Hitherto, only one attempt has been made in this direction, but the untenability of the assumptions, methods, and results of this attempt were obvious [2]. 

We feel it reasonable to seek only the order of magnitude and distance-dependence of the forces with which we are concerned. Therefore, in what follows we will systematically omit dimensionless numerical factors of order unity. 

We first consider the one-dimensional problem or, more precisely, the interaction of a single atom with a linear chain of metal atoms. For the 

Choosing for the electrons a Fermi distribution with values of p from 0 to pmax, we obtain for the total energy of interaction the following cumbersome expression  

Due to this rapid decrease of the integral, the only part of significance is that where p and p differ little from one another (and, hence, from Pmax as well)- This allows us to disregard ((p )2/2m) — ((p )2/2m) in the denominator compared to Ek — E0. Then, in the expression for U, the following sum is factored out  

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