Abstract

Single-photon transition moments for overtone states of triply degenerate modes of spherical-top molecules applicable to multiple-photon dynamics calculations are derived for zeroth- and first-order theories. In each case the total transition strength for excitation out of a given angular momentum state is in agreement with well-known results for the triply degenerate oscillator. In contrast with recently published results, this work shows that all strongly allowed multiple-photon pathways do occur.

© 1978 Optical Society of America

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  1. J. R. Ackerhalt, H. W. Galbraith, “Collisionless multiple photon excitation of SF6: a comparison of anharmonic oscillators with and without octahedral splitting in the presence of rotational effects,” accepted for publication in J. Chem. Phys. (1978).
  2. H. W. Galbraith, J. R. Ackerhalt, Opt. Lett. 3, 109 (1978).
    [CrossRef] [PubMed]
  3. C. D. Cantrell, K. Fox, Opt. Lett. 2, 151 (1978).
    [CrossRef] [PubMed]
  4. H. Kildal, J. Chem. Phys. 67, 1287 (1977).
    [CrossRef]
  5. C. Marcott, W. G. Golden, J. Overend, “3-quantum transition probabilities in the ν3 manifold of SF6 and the assignment of the observed 3ν3 vibrational spectra of SF6 and UF6,” Spectrochim. Acta, to be published.
  6. K. Fox, “3ν3 vibrational spectra of SF6 and UF6,” J. Chem. Phys. 68, 2812 (1978).
    [CrossRef]
  7. J. Ackerhalt, H. Flicker, H. Galbraith, J. King, W. Person, “Analysis of 3ν3 in SF6,” J. Chem. Phys., to be published.
  8. K. Fox, Opt. Lett. 1, 214 (1977).
    [CrossRef] [PubMed]
  9. M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976).
    [CrossRef]
  10. K. Hecht, J. Mol. Spectrosc. 5, 355 (1960).
    [CrossRef]
  11. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. P., Princeton, N.J., 1960).
  12. J. D. Louck, Diss. Abstr. 19, 840 (1958).
  13. K. Fox, W. Person, J. Chem. Phys. 64, 5218 (1976).
    [CrossRef]
  14. H. Galbraith, J. Ackerhalt, “Comparison of multiple-photon excitation models,” Opt. Lett. 3, 152 (1978).
    [CrossRef] [PubMed]

1978

1977

H. Kildal, J. Chem. Phys. 67, 1287 (1977).
[CrossRef]

K. Fox, Opt. Lett. 1, 214 (1977).
[CrossRef] [PubMed]

1976

K. Fox, W. Person, J. Chem. Phys. 64, 5218 (1976).
[CrossRef]

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976).
[CrossRef]

1960

K. Hecht, J. Mol. Spectrosc. 5, 355 (1960).
[CrossRef]

1958

J. D. Louck, Diss. Abstr. 19, 840 (1958).

Ackerhalt, J.

H. Galbraith, J. Ackerhalt, “Comparison of multiple-photon excitation models,” Opt. Lett. 3, 152 (1978).
[CrossRef] [PubMed]

J. Ackerhalt, H. Flicker, H. Galbraith, J. King, W. Person, “Analysis of 3ν3 in SF6,” J. Chem. Phys., to be published.

Ackerhalt, J. R.

H. W. Galbraith, J. R. Ackerhalt, Opt. Lett. 3, 109 (1978).
[CrossRef] [PubMed]

J. R. Ackerhalt, H. W. Galbraith, “Collisionless multiple photon excitation of SF6: a comparison of anharmonic oscillators with and without octahedral splitting in the presence of rotational effects,” accepted for publication in J. Chem. Phys. (1978).

Cantrell, C. D.

Dows, D. A.

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976).
[CrossRef]

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. P., Princeton, N.J., 1960).

Flicker, H.

J. Ackerhalt, H. Flicker, H. Galbraith, J. King, W. Person, “Analysis of 3ν3 in SF6,” J. Chem. Phys., to be published.

Fox, K.

C. D. Cantrell, K. Fox, Opt. Lett. 2, 151 (1978).
[CrossRef] [PubMed]

K. Fox, “3ν3 vibrational spectra of SF6 and UF6,” J. Chem. Phys. 68, 2812 (1978).
[CrossRef]

K. Fox, Opt. Lett. 1, 214 (1977).
[CrossRef] [PubMed]

K. Fox, W. Person, J. Chem. Phys. 64, 5218 (1976).
[CrossRef]

Galbraith, H.

H. Galbraith, J. Ackerhalt, “Comparison of multiple-photon excitation models,” Opt. Lett. 3, 152 (1978).
[CrossRef] [PubMed]

J. Ackerhalt, H. Flicker, H. Galbraith, J. King, W. Person, “Analysis of 3ν3 in SF6,” J. Chem. Phys., to be published.

Galbraith, H. W.

H. W. Galbraith, J. R. Ackerhalt, Opt. Lett. 3, 109 (1978).
[CrossRef] [PubMed]

J. R. Ackerhalt, H. W. Galbraith, “Collisionless multiple photon excitation of SF6: a comparison of anharmonic oscillators with and without octahedral splitting in the presence of rotational effects,” accepted for publication in J. Chem. Phys. (1978).

Golden, W. G.

C. Marcott, W. G. Golden, J. Overend, “3-quantum transition probabilities in the ν3 manifold of SF6 and the assignment of the observed 3ν3 vibrational spectra of SF6 and UF6,” Spectrochim. Acta, to be published.

Goodman, M. F.

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976).
[CrossRef]

Hecht, K.

K. Hecht, J. Mol. Spectrosc. 5, 355 (1960).
[CrossRef]

Kildal, H.

H. Kildal, J. Chem. Phys. 67, 1287 (1977).
[CrossRef]

King, J.

J. Ackerhalt, H. Flicker, H. Galbraith, J. King, W. Person, “Analysis of 3ν3 in SF6,” J. Chem. Phys., to be published.

Louck, J. D.

J. D. Louck, Diss. Abstr. 19, 840 (1958).

Marcott, C.

C. Marcott, W. G. Golden, J. Overend, “3-quantum transition probabilities in the ν3 manifold of SF6 and the assignment of the observed 3ν3 vibrational spectra of SF6 and UF6,” Spectrochim. Acta, to be published.

Overend, J.

C. Marcott, W. G. Golden, J. Overend, “3-quantum transition probabilities in the ν3 manifold of SF6 and the assignment of the observed 3ν3 vibrational spectra of SF6 and UF6,” Spectrochim. Acta, to be published.

Person, W.

K. Fox, W. Person, J. Chem. Phys. 64, 5218 (1976).
[CrossRef]

J. Ackerhalt, H. Flicker, H. Galbraith, J. King, W. Person, “Analysis of 3ν3 in SF6,” J. Chem. Phys., to be published.

Stone, J.

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976).
[CrossRef]

Diss. Abstr.

J. D. Louck, Diss. Abstr. 19, 840 (1958).

J. Chem. Phys.

K. Fox, W. Person, J. Chem. Phys. 64, 5218 (1976).
[CrossRef]

M. F. Goodman, J. Stone, D. A. Dows, J. Chem. Phys. 65, 5052 (1976).
[CrossRef]

H. Kildal, J. Chem. Phys. 67, 1287 (1977).
[CrossRef]

K. Fox, “3ν3 vibrational spectra of SF6 and UF6,” J. Chem. Phys. 68, 2812 (1978).
[CrossRef]

J. Mol. Spectrosc.

K. Hecht, J. Mol. Spectrosc. 5, 355 (1960).
[CrossRef]

Opt. Lett.

Other

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. P., Princeton, N.J., 1960).

J. R. Ackerhalt, H. W. Galbraith, “Collisionless multiple photon excitation of SF6: a comparison of anharmonic oscillators with and without octahedral splitting in the presence of rotational effects,” accepted for publication in J. Chem. Phys. (1978).

J. Ackerhalt, H. Flicker, H. Galbraith, J. King, W. Person, “Analysis of 3ν3 in SF6,” J. Chem. Phys., to be published.

C. Marcott, W. G. Golden, J. Overend, “3-quantum transition probabilities in the ν3 manifold of SF6 and the assignment of the observed 3ν3 vibrational spectra of SF6 and UF6,” Spectrochim. Acta, to be published.

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Equations (11)

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n l J M ; R K R = K , m C ( J l R ; K m ) n l m * J M K .
μ σ = δ = - 1 , 0 , 1 D σ δ ( 1 ) * ( α β γ ) q δ = T 0 σ ( 1 , 1 ) ,
n J l R K R M + σ μ σ n J l R K R M = [ ( 2 J + 1 ) ( 2 l + 1 ) ] 1 / 2 ( - 1 ) R - J - l J t 1 J × n l t 1 n l W ( J J l l ; 1 R ) δ R R δ K R K R .
J t 1 J = ( 2 J + 1 2 J + 1 ) 1 / 2 C ( J 1 J ; M σ ) .
n + 1 l t 1 n l 2 = { ( n - l + 2 ) 2 · l ( 2 l - 1 ) , l = l - 1 ; ( n + l + 3 ) 2 ( l + 1 ) ( 2 l + 3 ) , l = l + 1.
μ l n + 1 2 = ( 2 J + 1 ) ( 2 l + 1 ) n l t 1 n l 2 × W 2 ( J J l l ; 1 R ) .
l J μ l n + 1 2 = ( n + 3 ) / 2.
l m l J μ l n + 1 2 = ( n + 1 ) ( n + 2 ) ( n + 3 ) / 4 ,
β n + 1 , J , l , K + β , M + σ , m + β D σ β ( 1 ) * q β n J l K M m = β n l t 1 n l C ( l 1 l ; m β ) × [ ( 2 J + 1 ) / ( 2 J + 1 ) ] 1 / 2 × C ( J 1 J ; K β ) C ( J 1 J ; M σ ) .
μ l n + 1 u 2 = β K n l t 1 n l 2 2 J + 1 × C 2 ( l 1 l ; m β ) C 2 ( J 1 J ; K β ) .
m μ l n + 1 u 2 = n l t 1 n l 2 ( 2 l + 1 ) ( 2 J + 1 ) 3 ( 2 J + 1 ) .

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