The potential V(z) = C9 z9 - C3 z3 is a reasonable parametrization of the atom-surface interaction. We evaluate the discrete spectrum En of bound states for this potential with arbitrary coefficients C9 and C3. The resulting form in the WKB approximation is En = -D [1 - (n + l 2) L]6, where L depends on the mass and D is the well depth. We find that the exact solution of the Schrödinger equation can be written in the same form, with n shifted slightly by an amount δn, which we calculate. The results are applied to the case of He near a NaF surface, in which the calculated eigenvalue spectrum agrees well with experimental values.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Surfaces and Interfaces
- Surfaces, Coatings and Films
- Materials Chemistry