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

Milton W. Cole; T. T. Tsong

doi:10.1016/0039-6028(77)90177-7

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

Milton W. Cole, T. T. Tsong

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

The potential V(z) = C₉ z⁹ - C₃ z³ 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 C₉ and C₃. 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	https://doi.org/10.1016/0039-6028(77)90177-7
State	Published - Dec 1 1977

All Science Journal Classification (ASJC) codes

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

Access to Document

10.1016/0039-6028(77)90177-7

Cite this

@article{12cb0f5fa6ff4e1cb9e8b8d2470e5a48,

title = "Bound state vibrational spectrum of the 3-9 atom-surface interaction",

abstract = "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 Schr{\"o}dinger 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.",

author = "Cole, {Milton W.} and Tsong, {T. T.}",

note = "Funding Information: by National Science Foundation grant number DMR 76 11418.",

year = "1977",

month = dec,

day = "1",

doi = "10.1016/0039-6028(77)90177-7",

language = "English (US)",

volume = "69",

pages = "325--335",

journal = "Surface Science",

issn = "0039-6028",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

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

AU - Cole, Milton W.

AU - Tsong, T. T.

N1 - Funding Information: by National Science Foundation grant number DMR 76 11418.

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

SN - 0039-6028

VL - 69

SP - 325

EP - 335

JO - Surface Science

JF - Surface Science

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this