### 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) |
---|---|

Pages (from-to) | 325-335 |

Number of pages | 11 |

Journal | Surface Science |

Volume | 69 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1977 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Surface Science*,

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

}

*Surface Science*, vol. 69, no. 1, pp. 325-335. https://doi.org/10.1016/0039-6028(77)90177-7

**Bound state vibrational spectrum of the 3-9 atom-surface interaction.** / Cole, Milton Walter; Tsong, T. T.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Bound state vibrational spectrum of the 3-9 atom-surface interaction

AU - Cole, Milton Walter

AU - Tsong, T. T.

PY - 1977/12/1

Y1 - 1977/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0003174762&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0003174762&partnerID=8YFLogxK

U2 - 10.1016/0039-6028(77)90177-7

DO - 10.1016/0039-6028(77)90177-7

M3 - Article

AN - SCOPUS:0003174762

VL - 69

SP - 325

EP - 335

JO - Surface Science

JF - Surface Science

SN - 0039-6028

IS - 1

ER -