### Abstract

The potential V(z) = C_{9} z^{9} - C_{3} z^{3} is a reasonable parametrization of the atom-surface interaction. We evaluate the discrete spectrum E_{n} of bound states for this potential with arbitrary coefficients C_{9} and C_{3}. The resulting form in the WKB approximation is E_{n} = -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 δ_{n}, 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.

Original language | English (US) |
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Pages (from-to) | 325-335 |

Number of pages | 11 |

Journal | Surface Science |

Volume | 69 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1977 |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Surfaces and Interfaces
- Surfaces, Coatings and Films
- Materials Chemistry

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## Cite this

Cole, M. W., & Tsong, T. T. (1977). Bound state vibrational spectrum of the 3-9 atom-surface interaction.

*Surface Science*,*69*(1), 325-335. https://doi.org/10.1016/0039-6028(77)90177-7