Abstract

The vibration–rotation spectrum of HDO in the 3250–4370-cm−1 region has been studied at 0.01-cm−1 resolution with a Fourier transform spectrometer. Measurements of the positions, strengths, and pressure-broadening parameters of over 1400 lines have been made using a nonlinear least-squares fitting technique. Values of the ground state levels and levels in the (001), (110), and (030) states have been determined from the data. The strengths of 953 lines were analyzed to determine the band strengths, the coefficients of the F factors, and the Fermi interaction parameters. The strengths of the A-type (001), (110), and (030) bands are 86.85 ± 1.10, 7.91 ± 0.13, and 0.111 ± 0.020 cm−2 atm−1 at 296 K, respectively, and the strengths of the B-type (001), (110), and (030) bands are 36.02 ± 0.91, 0.74 ± 0.14, and 0.268 ± 0.023 cm−2 atm−1 at 296 K. The band centers of the (001), (110), and (030) bands are 3707.46673(4) cm−1, 4099.9559(1) cm−1, and 4145.4734(1) cm−1, respectively.

© 1983 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. F. C. De Lucia, R. L. Cook, P. Helminger, W. Gordy, J. Chem. Phys. 55, 5334 (1971).
    [CrossRef]
  8. M. W. Strandberg, J. Chem. Phys. 17, 901 (1949).
    [CrossRef]
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    [CrossRef]
  10. S. Weisbaum, Y. Beers, G. Hermann, J. Chem. Phys. 23, 1601 (1955).
    [CrossRef]
  11. E. B. Treacy, Y. Beers, J. Chem. Phys. 36, 1473 (1961).
    [CrossRef]
  12. H. Bluyssen, J. Verhoeven, A. Dymanus, Phys. Lett. A 25, 214 (1967).
    [CrossRef]
  13. J. Verhoeven, H. Bluyssen, A. Dymanus, Phys. Lett. A 26, 424 (1968).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, C. Amiot, Mol. Phys. 26, 825 (1973).
    [CrossRef]
  17. J.-M. Flaud, C. Camy-Peyret, R. A. Toth, Atlas, H216O, H217O, H218O, Line Positions and Intensities Between 0 and 4350 cm−1 (Pergamon, New York, 1981).
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    [CrossRef]
  19. Y. S. Chang, J. H. Shaw, Appl. Spectrosc. 31, 213 (1977).
    [CrossRef]
  20. C. L. Lin, J. H. Shaw, J. G. Calvert, J. Quant. Spectrosc. Radiat. Transfer 22, 253 (1979).
    [CrossRef]
  21. E. Niple, J. H. Shaw, Appl. Spectrosc. 33, 569 (1979).
    [CrossRef]
  22. L. R. Brown, J. S. Margolis, R. H. Norton, B. Stedry, Appl. Spectrosc., submitted for publication.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1982

R. A. Toth, V. D. Gupta, J. W. Brault, Appl. Opt. 21, 3337 (1982).
[CrossRef] [PubMed]

N. Papineau, C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, J. Mol. Spectrosc. 92, 451 (1982).
[CrossRef]

1981

1979

C. L. Lin, J. H. Shaw, J. G. Calvert, J. Quant. Spectrosc. Radiat. Transfer 22, 253 (1979).
[CrossRef]

E. Niple, J. H. Shaw, Appl. Spectrosc. 33, 569 (1979).
[CrossRef]

1978

Y. Y. Kwan, J. Mol. Spectrosc. 71, 260 (1978).
[CrossRef]

1977

Y. S. Chang, J. H. Shaw, Appl. Spectrosc. 31, 213 (1977).
[CrossRef]

R. A. Toth, C. Camy-Peyret, J.-M. Flaud, J. Quant. Spectrosc. Radiat. Transfer 18, 515 (1977).
[CrossRef]

1976

C. Amiot, G. Guelachvili, J. Mol. Spectrosc. 59, 171 (1976).
[CrossRef]

1975

G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, C. Amiot, J. Mol. Spectrosc. 57, 246 (1975).
[CrossRef]

1973

C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, C. Amiot, Mol. Phys. 26, 825 (1973).
[CrossRef]

R. A. Toth, J. Quant. Spectrosc. Radiat. Transfer 13, 1127 (1973).
[CrossRef]

1971

F. C. De Lucia, R. L. Cook, P. Helminger, W. Gordy, J. Chem. Phys. 55, 5334 (1971).
[CrossRef]

1970

1968

H. J. Babrov, F. Casden, J. Opt. Soc. Am. 58, 179 (1968).
[CrossRef]

J. Verhoeven, H. Bluyssen, A. Dymanus, Phys. Lett. A 26, 424 (1968).
[CrossRef]

1967

H. Bluyssen, J. Verhoeven, A. Dymanus, Phys. Lett. A 25, 214 (1967).
[CrossRef]

1961

E. B. Treacy, Y. Beers, J. Chem. Phys. 36, 1473 (1961).
[CrossRef]

1956

G. Erlandsson, J. Cox, J. Chem. Phys. 25, 778 (1956).
[CrossRef]

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

1955

S. Weisbaum, Y. Beers, G. Hermann, J. Chem. Phys. 23, 1601 (1955).
[CrossRef]

1953

D. W. Posener, M. W. P. Strandberg, J. Chem. Phys. 21, 1401 (1953).
[CrossRef]

1949

M. W. Strandberg, J. Chem. Phys. 17, 901 (1949).
[CrossRef]

Amiot, C.

C. Amiot, G. Guelachvili, J. Mol. Spectrosc. 59, 171 (1976).
[CrossRef]

G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, C. Amiot, J. Mol. Spectrosc. 57, 246 (1975).
[CrossRef]

C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, C. Amiot, Mol. Phys. 26, 825 (1973).
[CrossRef]

Babrov, H. J.

Beers, Y.

E. B. Treacy, Y. Beers, J. Chem. Phys. 36, 1473 (1961).
[CrossRef]

S. Weisbaum, Y. Beers, G. Hermann, J. Chem. Phys. 23, 1601 (1955).
[CrossRef]

Ben Aryeh, Y.

Benedict, W. S.

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

W. S. Benedict, R. F. Calfee, ESSA Professional Paper 2 (U.S. GPO, Washington, D.C., 1967).

Bluyssen, H.

J. Verhoeven, H. Bluyssen, A. Dymanus, Phys. Lett. A 26, 424 (1968).
[CrossRef]

H. Bluyssen, J. Verhoeven, A. Dymanus, Phys. Lett. A 25, 214 (1967).
[CrossRef]

Brault, J. W.

Brown, L. R.

L. R. Brown, J. S. Margolis, R. H. Norton, B. Stedry, Appl. Spectrosc., submitted for publication.

Burch, D. E.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

Calfee, R. F.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

W. S. Benedict, R. F. Calfee, ESSA Professional Paper 2 (U.S. GPO, Washington, D.C., 1967).

Calvert, J. G.

C. L. Lin, J. H. Shaw, J. G. Calvert, J. Quant. Spectrosc. Radiat. Transfer 22, 253 (1979).
[CrossRef]

Camy-Peyret, C.

N. Papineau, C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, J. Mol. Spectrosc. 92, 451 (1982).
[CrossRef]

R. A. Toth, C. Camy-Peyret, J.-M. Flaud, J. Quant. Spectrosc. Radiat. Transfer 18, 515 (1977).
[CrossRef]

C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, C. Amiot, Mol. Phys. 26, 825 (1973).
[CrossRef]

J.-M. Flaud, C. Camy-Peyret, R. A. Toth, Atlas, H216O, H217O, H218O, Line Positions and Intensities Between 0 and 4350 cm−1 (Pergamon, New York, 1981).

Casden, F.

Chang, Y. S.

Clough, S. A.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

Cook, R. L.

F. C. De Lucia, R. L. Cook, P. Helminger, W. Gordy, J. Chem. Phys. 55, 5334 (1971).
[CrossRef]

Cox, J.

G. Erlandsson, J. Cox, J. Chem. Phys. 25, 778 (1956).
[CrossRef]

Dang-Nhu, M.

G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, C. Amiot, J. Mol. Spectrosc. 57, 246 (1975).
[CrossRef]

De Lucia, F. C.

F. C. De Lucia, R. L. Cook, P. Helminger, W. Gordy, J. Chem. Phys. 55, 5334 (1971).
[CrossRef]

Dymanus, A.

J. Verhoeven, H. Bluyssen, A. Dymanus, Phys. Lett. A 26, 424 (1968).
[CrossRef]

H. Bluyssen, J. Verhoeven, A. Dymanus, Phys. Lett. A 25, 214 (1967).
[CrossRef]

Erlandsson, G.

G. Erlandsson, J. Cox, J. Chem. Phys. 25, 778 (1956).
[CrossRef]

Flaud, J.-M.

N. Papineau, C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, J. Mol. Spectrosc. 92, 451 (1982).
[CrossRef]

R. A. Toth, C. Camy-Peyret, J.-M. Flaud, J. Quant. Spectrosc. Radiat. Transfer 18, 515 (1977).
[CrossRef]

C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, C. Amiot, Mol. Phys. 26, 825 (1973).
[CrossRef]

J.-M. Flaud, C. Camy-Peyret, R. A. Toth, Atlas, H216O, H217O, H218O, Line Positions and Intensities Between 0 and 4350 cm−1 (Pergamon, New York, 1981).

Fox, K.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

Gailar, N.

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

Garing, J. S.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

Gordy, W.

F. C. De Lucia, R. L. Cook, P. Helminger, W. Gordy, J. Chem. Phys. 55, 5334 (1971).
[CrossRef]

Guelachvili, G.

N. Papineau, C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, J. Mol. Spectrosc. 92, 451 (1982).
[CrossRef]

C. Amiot, G. Guelachvili, J. Mol. Spectrosc. 59, 171 (1976).
[CrossRef]

G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, C. Amiot, J. Mol. Spectrosc. 57, 246 (1975).
[CrossRef]

C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, C. Amiot, Mol. Phys. 26, 825 (1973).
[CrossRef]

Gupta, V. D.

Helminger, P.

F. C. De Lucia, R. L. Cook, P. Helminger, W. Gordy, J. Chem. Phys. 55, 5334 (1971).
[CrossRef]

Hermann, G.

S. Weisbaum, Y. Beers, G. Hermann, J. Chem. Phys. 23, 1601 (1955).
[CrossRef]

Kwan, Y. Y.

Y. Y. Kwan, J. Mol. Spectrosc. 71, 260 (1978).
[CrossRef]

Lin, C. L.

C. L. Lin, J. H. Shaw, J. G. Calvert, J. Quant. Spectrosc. Radiat. Transfer 22, 253 (1979).
[CrossRef]

Margolis, J. S.

L. R. Brown, J. S. Margolis, R. H. Norton, B. Stedry, Appl. Spectrosc., submitted for publication.

McClatchey, R. A.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

Niple, E.

Norton, R. H.

L. R. Brown, J. S. Margolis, R. H. Norton, B. Stedry, Appl. Spectrosc., submitted for publication.

Papineau, N.

N. Papineau, C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, J. Mol. Spectrosc. 92, 451 (1982).
[CrossRef]

Plyler, E. K.

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

Posener, D. W.

D. W. Posener, M. W. P. Strandberg, J. Chem. Phys. 21, 1401 (1953).
[CrossRef]

Poussigue, G.

G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, C. Amiot, J. Mol. Spectrosc. 57, 246 (1975).
[CrossRef]

Pugh, L. A.

L. A. Pugh, Dissertation, Ohio State U. (1972).

Rothman, L. S.

L. S. Rothman, Appl. Opt. 20, 791 (1981).
[CrossRef] [PubMed]

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

Shaw, J. H.

Stedry, B.

L. R. Brown, J. S. Margolis, R. H. Norton, B. Stedry, Appl. Spectrosc., submitted for publication.

Strandberg, M. W.

M. W. Strandberg, J. Chem. Phys. 17, 901 (1949).
[CrossRef]

Strandberg, M. W. P.

D. W. Posener, M. W. P. Strandberg, J. Chem. Phys. 21, 1401 (1953).
[CrossRef]

Tarrago, G.

G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, C. Amiot, J. Mol. Spectrosc. 57, 246 (1975).
[CrossRef]

Toth, R. A.

R. A. Toth, V. D. Gupta, J. W. Brault, Appl. Opt. 21, 3337 (1982).
[CrossRef] [PubMed]

R. A. Toth, C. Camy-Peyret, J.-M. Flaud, J. Quant. Spectrosc. Radiat. Transfer 18, 515 (1977).
[CrossRef]

R. A. Toth, J. Quant. Spectrosc. Radiat. Transfer 13, 1127 (1973).
[CrossRef]

J.-M. Flaud, C. Camy-Peyret, R. A. Toth, Atlas, H216O, H217O, H218O, Line Positions and Intensities Between 0 and 4350 cm−1 (Pergamon, New York, 1981).

Treacy, E. B.

E. B. Treacy, Y. Beers, J. Chem. Phys. 36, 1473 (1961).
[CrossRef]

Verhoeven, J.

J. Verhoeven, H. Bluyssen, A. Dymanus, Phys. Lett. A 26, 424 (1968).
[CrossRef]

H. Bluyssen, J. Verhoeven, A. Dymanus, Phys. Lett. A 25, 214 (1967).
[CrossRef]

Weisbaum, S.

S. Weisbaum, Y. Beers, G. Hermann, J. Chem. Phys. 23, 1601 (1955).
[CrossRef]

Appl. Opt.

Appl. Spectrosc.

J. Chem. Phys.

W. S. Benedict, N. Gailar, E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
[CrossRef]

G. Erlandsson, J. Cox, J. Chem. Phys. 25, 778 (1956).
[CrossRef]

F. C. De Lucia, R. L. Cook, P. Helminger, W. Gordy, J. Chem. Phys. 55, 5334 (1971).
[CrossRef]

M. W. Strandberg, J. Chem. Phys. 17, 901 (1949).
[CrossRef]

D. W. Posener, M. W. P. Strandberg, J. Chem. Phys. 21, 1401 (1953).
[CrossRef]

S. Weisbaum, Y. Beers, G. Hermann, J. Chem. Phys. 23, 1601 (1955).
[CrossRef]

E. B. Treacy, Y. Beers, J. Chem. Phys. 36, 1473 (1961).
[CrossRef]

J. Mol. Spectrosc.

C. Amiot, G. Guelachvili, J. Mol. Spectrosc. 59, 171 (1976).
[CrossRef]

G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, C. Amiot, J. Mol. Spectrosc. 57, 246 (1975).
[CrossRef]

Y. Y. Kwan, J. Mol. Spectrosc. 71, 260 (1978).
[CrossRef]

N. Papineau, C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, J. Mol. Spectrosc. 92, 451 (1982).
[CrossRef]

J. Opt. Soc. Am.

J. Quant. Spectrosc. Radiat. Transfer

R. A. Toth, J. Quant. Spectrosc. Radiat. Transfer 13, 1127 (1973).
[CrossRef]

R. A. Toth, C. Camy-Peyret, J.-M. Flaud, J. Quant. Spectrosc. Radiat. Transfer 18, 515 (1977).
[CrossRef]

C. L. Lin, J. H. Shaw, J. G. Calvert, J. Quant. Spectrosc. Radiat. Transfer 22, 253 (1979).
[CrossRef]

Mol. Phys.

C. Camy-Peyret, J.-M. Flaud, G. Guelachvili, C. Amiot, Mol. Phys. 26, 825 (1973).
[CrossRef]

Phys. Lett. A

H. Bluyssen, J. Verhoeven, A. Dymanus, Phys. Lett. A 25, 214 (1967).
[CrossRef]

J. Verhoeven, H. Bluyssen, A. Dymanus, Phys. Lett. A 26, 424 (1968).
[CrossRef]

Other

J.-M. Flaud, C. Camy-Peyret, R. A. Toth, Atlas, H216O, H217O, H218O, Line Positions and Intensities Between 0 and 4350 cm−1 (Pergamon, New York, 1981).

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRLTR-0096 (1973).

L. A. Pugh, Dissertation, Ohio State U. (1972).

L. R. Brown, J. S. Margolis, R. H. Norton, B. Stedry, Appl. Spectrosc., submitted for publication.

W. S. Benedict, R. F. Calfee, ESSA Professional Paper 2 (U.S. GPO, Washington, D.C., 1967).

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Figures (1)

Fig. 1
Fig. 1

Unapodized observed and synthetic spectra. The spectral resolution was 0.01 cm−1; the cell length is 25 cm, and the sample temperature is 296 K. The gas sample pressures are as follows: plots A and B, 16.15 Torr; plots C and D, 7.79 Torr; and plots E and F, 4.35 Torr. Lines labeled with a O are H2O, and the remainder are HDO. In each spectral plot (AF), the observed spectrum is overlaid with the respective synthetic spectrum, and the residual plot, shown in the lower portion, gives the percent differences between the observed and synthetic spectra. Line positions and quantum assignments of the lines are listed in Table IV.

Tables (6)

Tables Icon

Table I Energy Levels (cm−1) of the (000), (001), and (030) States of HDO

Tables Icon

Table II Rotational Transitions of HDO (cm−1) from Measurements in the Microwave Regiona; Calculated Values (c) from this Work

Tables Icon

Table III Observed Line Positions of H2O

Tables Icon

Table IV Line Center Positions (cm−1) and Quantum Assignments of Lines Shown in Fig. 1

Tables Icon

Table V Band Strength Sv, Dipole Moment R, and F-Factor Coefficients of the (001), (110), and (030) Bands of HDO

Tables Icon

Table VI Observed and Calculated Line Positions and Strengths In the (001), (110), and (030) Bands of HDO; Strengths in cm−2/atm at 296

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

Δ = [ σ 2 ( upper level ) + σ 2 ( lower level ) ] 1 / 2 ,
S = a 2 · ( ν / ν 0 ) · S υ · l 2 · exp ( E / k T ) · F / Q R ,
A ( V , J , K A , K C ) = a · A ° ( V , J , K A , K C ) + α · b · A ° ( V , J , K A , K C ) , A ( V , J , K A , K C ) = a · A ° ( V , J , K A , K C ) α · b · A ° ( V , J , K A , K C ) , a 2 + b 2 = 1 ,
α = δ / | δ | , δ = E ( V , J , K A , K C ) E ( V , J , K A , K C ) ,
b a = [ | δ | ( δ 2 4 | F V V R R | 2 ) 1 / 2 | δ | + ( δ 2 4 | F V V R R | 2 ) 1 / 2 ] 1 / 2 ,
F V V = f V V ( F o V V + F k V V J z 2 + F J V V J ¯ 2 + F x y V V J x y 2 ) ,
F V V R R = V , J , K A , K C | F V V | V , J , K A , K C = F o + F k · K A 2 ,
l = O , J , K A , K C | ϕ Z α | V , J , K A , K C ,
A ° ( V , J , K A , K C ) = ψ V K C J K γ V · S ( J , K , γ ) ,
F = ( f f f ) 2 , f = ( f υ + f f ) ,
f υ = 1 + a 1 m + a 2 δ E ( κ ) + a 3 δ [ E ( κ ) / κ ] + a 4 m 3 + a 5 m · δ E ( κ ) + a 6 m ( K A 2 K A 2 ) + a 7 m ( K A 2 K A 2 ) 2 + a 8 [ ( K A K A ) 2 1 ] · [ K C K C 1 ] 2 + a 9 m [ ( K A K A ) 2 1 ] · [ K C K C 1 ] 2 ,
δ E ( κ ) = E ( κ ) E ( κ ) , δ [ E ( κ ) / κ ] = [ E ( κ ) / κ ] [ E ( κ ) / κ ] .
f f = a 10 J ( J + 1 ) + a 11 K A 2 + a 12 J ( J + 1 ) K A 2 + a 13 K A 4 .
f f = α · b / a · Z , Z = d ( X , V , V ) · | R ( X , V ) | / | R ( X , V ) | R ( X , V ) = V | μ ( X ) | 0 , Z = d ( X , V , V ) · [ S υ ( X ) · ν 0 ( V ) S υ ( X ) · ν 0 ( V ) ] 1 / 2 ,
S υ ( X ) = 8 π 3 3 h c | R ( X , V ) | 2 · ν 0 ( V ) k T · Q V ,
B = S [ a · ( ν / ν 0 ) ( l 2 / Q R ) exp ( E / k T ) ] 1 .
B = S υ · ( f V + f f ) 2 .
X ( 1,2 ) = [ S ( 1 ) S υ ( 2 ) S ( 2 ) S υ ( 1 ) ] 1 / 2 ,
b / a = [ f ( 1 ) f ( 2 ) · X ( 1,2 ) ] · [ Z ( 1 ) + X ( 1,2 ) · Z ( 2 ) ] 1 ,
f ( i ) = f υ ( i ) + f f ( i ) i = 1 or 2 , E ( 1 , J , K A , K C ) < E ( 2 , J , K A , K C ) , Z ( 1 ) = 1 / Z ( 2 ) .
F o + F k K A 2 = | δ | · a · b ,
C i = B i S υ i · f f i
C i = S υ i + 1 ( f υ i + 1 + f f i + 1 ) .
σ ( o c ) = { n = 1 N [ ( S obs S cal ) / S obs ] 2 / N 1 } 1 / 2 ,
σ ( obs ) = ( n = 1 N obs 2 / N 1 ) 1 / 2 .

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