Abstract

The pressure-narrowing theory of Galatry is applied to the calculations of equivalent widths of lines in the quadrupole rotation–vibration spectrum of molecular hydrogen. The theory leads to agreement with the measurements of Rank and associates. A value for the pressure-broadening coefficient of 0.0015 cm−1/atm at 300 K is obtained for the 1–0 S(1) line. The application of the results to the hydrogen abundance on Jupiter is briefly considered.

© 1969 Optical Society of America

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References

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  1. D. H. Rank, U. Fink, and T. A. Wiggins, Astrophys. J. 143, 980 (1966).
  2. R. H. Dicke, Phys. Rev. 89, 472 (1953).
  3. J. P. Wittke and R. H. Dicke, Phys. Rev. 103, 620 (1956).
  4. L. Galatry, Phys. Rev. 122, 1218 (1961).
  5. K. S. Singwi and A. Sjölander, Phys. Rev. 120, 1093 (1960).
  6. G. R. Bird, J. Chem. Phys. 38, 2678 (1963).
  7. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), p. 581.
  8. A. D. May, V. Degen, T. C. Stryland, and H. L. Welsh, Can. J. Phys. 39, 1769 (1961).
  9. V. G. Cooper, A. D. May, E. H. Hara, and H. F. P. Knapp, Can. J. Phys. 46, 2019 (1968),
  10. J. R. Murray and A. Javan, J. Mol. Spectry. 29, 502 (1969).
  11. M. Nelkin and A. Ghatak, Phys. Rev. 135, A4 (1964).
  12. P. Lallemand, P. Simova, and G. Bret, Phys. Rev. Letters 17, 1239 (1966).
  13. P. Harteck and H. W. Schmidt, Z. Physik. Chem. Abt. B21, 447 (1933).
  14. T. Qwen and H. P. Mason, Astrophys. J. 154, 317 (1968).
  15. J. I. Gersten and H. M. Foley, J. Opt. Soc. Am. 58, 933 (1968).

1969 (1)

J. R. Murray and A. Javan, J. Mol. Spectry. 29, 502 (1969).

1968 (3)

T. Qwen and H. P. Mason, Astrophys. J. 154, 317 (1968).

J. I. Gersten and H. M. Foley, J. Opt. Soc. Am. 58, 933 (1968).

V. G. Cooper, A. D. May, E. H. Hara, and H. F. P. Knapp, Can. J. Phys. 46, 2019 (1968),

1966 (2)

D. H. Rank, U. Fink, and T. A. Wiggins, Astrophys. J. 143, 980 (1966).

P. Lallemand, P. Simova, and G. Bret, Phys. Rev. Letters 17, 1239 (1966).

1964 (1)

M. Nelkin and A. Ghatak, Phys. Rev. 135, A4 (1964).

1963 (1)

G. R. Bird, J. Chem. Phys. 38, 2678 (1963).

1961 (2)

A. D. May, V. Degen, T. C. Stryland, and H. L. Welsh, Can. J. Phys. 39, 1769 (1961).

L. Galatry, Phys. Rev. 122, 1218 (1961).

1960 (1)

K. S. Singwi and A. Sjölander, Phys. Rev. 120, 1093 (1960).

1956 (1)

J. P. Wittke and R. H. Dicke, Phys. Rev. 103, 620 (1956).

1953 (1)

R. H. Dicke, Phys. Rev. 89, 472 (1953).

1933 (1)

P. Harteck and H. W. Schmidt, Z. Physik. Chem. Abt. B21, 447 (1933).

Bird, G. R.

G. R. Bird, J. Chem. Phys. 38, 2678 (1963).

Bird, R. B.

J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), p. 581.

Bret, G.

P. Lallemand, P. Simova, and G. Bret, Phys. Rev. Letters 17, 1239 (1966).

Cooper, V. G.

V. G. Cooper, A. D. May, E. H. Hara, and H. F. P. Knapp, Can. J. Phys. 46, 2019 (1968),

Curtiss, C. F.

J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), p. 581.

Degen, V.

A. D. May, V. Degen, T. C. Stryland, and H. L. Welsh, Can. J. Phys. 39, 1769 (1961).

Dicke, R. H.

J. P. Wittke and R. H. Dicke, Phys. Rev. 103, 620 (1956).

R. H. Dicke, Phys. Rev. 89, 472 (1953).

Fink, U.

D. H. Rank, U. Fink, and T. A. Wiggins, Astrophys. J. 143, 980 (1966).

Foley, H. M.

Galatry, L.

L. Galatry, Phys. Rev. 122, 1218 (1961).

Gersten, J. I.

Ghatak, A.

M. Nelkin and A. Ghatak, Phys. Rev. 135, A4 (1964).

Hara, E. H.

V. G. Cooper, A. D. May, E. H. Hara, and H. F. P. Knapp, Can. J. Phys. 46, 2019 (1968),

Harteck, P.

P. Harteck and H. W. Schmidt, Z. Physik. Chem. Abt. B21, 447 (1933).

Hirschfelder, J. O.

J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), p. 581.

Javan, A.

J. R. Murray and A. Javan, J. Mol. Spectry. 29, 502 (1969).

Knapp, H. F. P.

V. G. Cooper, A. D. May, E. H. Hara, and H. F. P. Knapp, Can. J. Phys. 46, 2019 (1968),

Lallemand, P.

P. Lallemand, P. Simova, and G. Bret, Phys. Rev. Letters 17, 1239 (1966).

Mason, H. P.

T. Qwen and H. P. Mason, Astrophys. J. 154, 317 (1968).

May, A. D.

V. G. Cooper, A. D. May, E. H. Hara, and H. F. P. Knapp, Can. J. Phys. 46, 2019 (1968),

A. D. May, V. Degen, T. C. Stryland, and H. L. Welsh, Can. J. Phys. 39, 1769 (1961).

Murray, J. R.

J. R. Murray and A. Javan, J. Mol. Spectry. 29, 502 (1969).

Nelkin, M.

M. Nelkin and A. Ghatak, Phys. Rev. 135, A4 (1964).

Qwen, T.

T. Qwen and H. P. Mason, Astrophys. J. 154, 317 (1968).

Rank, D. H.

D. H. Rank, U. Fink, and T. A. Wiggins, Astrophys. J. 143, 980 (1966).

Schmidt, H. W.

P. Harteck and H. W. Schmidt, Z. Physik. Chem. Abt. B21, 447 (1933).

Simova, P.

P. Lallemand, P. Simova, and G. Bret, Phys. Rev. Letters 17, 1239 (1966).

Singwi, K. S.

K. S. Singwi and A. Sjölander, Phys. Rev. 120, 1093 (1960).

Sjölander, A.

K. S. Singwi and A. Sjölander, Phys. Rev. 120, 1093 (1960).

Stryland, T. C.

A. D. May, V. Degen, T. C. Stryland, and H. L. Welsh, Can. J. Phys. 39, 1769 (1961).

Welsh, H. L.

A. D. May, V. Degen, T. C. Stryland, and H. L. Welsh, Can. J. Phys. 39, 1769 (1961).

Wiggins, T. A.

D. H. Rank, U. Fink, and T. A. Wiggins, Astrophys. J. 143, 980 (1966).

Wittke, J. P.

J. P. Wittke and R. H. Dicke, Phys. Rev. 103, 620 (1956).

Astrophys. J. (2)

D. H. Rank, U. Fink, and T. A. Wiggins, Astrophys. J. 143, 980 (1966).

T. Qwen and H. P. Mason, Astrophys. J. 154, 317 (1968).

Can. J. Phys. (2)

A. D. May, V. Degen, T. C. Stryland, and H. L. Welsh, Can. J. Phys. 39, 1769 (1961).

V. G. Cooper, A. D. May, E. H. Hara, and H. F. P. Knapp, Can. J. Phys. 46, 2019 (1968),

J. Chem. Phys. (1)

G. R. Bird, J. Chem. Phys. 38, 2678 (1963).

J. Mol. Spectry. (1)

J. R. Murray and A. Javan, J. Mol. Spectry. 29, 502 (1969).

J. Opt. Soc. Am. (1)

Phys. Rev. (5)

M. Nelkin and A. Ghatak, Phys. Rev. 135, A4 (1964).

R. H. Dicke, Phys. Rev. 89, 472 (1953).

J. P. Wittke and R. H. Dicke, Phys. Rev. 103, 620 (1956).

L. Galatry, Phys. Rev. 122, 1218 (1961).

K. S. Singwi and A. Sjölander, Phys. Rev. 120, 1093 (1960).

Phys. Rev. Letters (1)

P. Lallemand, P. Simova, and G. Bret, Phys. Rev. Letters 17, 1239 (1966).

Z. Physik. Chem. Abt. (1)

P. Harteck and H. W. Schmidt, Z. Physik. Chem. Abt. B21, 447 (1933).

Other (1)

J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954), p. 581.

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Figures (5)

F. 1
F. 1

Plot of the equivalent width W vs line strength S1 for the 1–0 S(1) line. Solid line calculated with K0 = 1.5×10−3 cm−1/atm·cm, ● calculated with K0 = 1.8×10−3, △ calculated with K0 = 1.2×10−3, ○ Rank’s observations.

F. 2
F. 2

Line width of the 1–0 S(1) line.

F. 3
F. 3

Line shape of the 1–0 S(1) line. Frequency in multiples of the Doppler width γD = 0.0206 cm−1. Curve I: Pressure = 0.2 atm. γ = 0.0173 cm−1. Curve II: pressure = 2.0 atm. γ = 0.0064 cm−1.

F. 4
F. 4

Curves of growth for the 3–0 S(1) line at 150 K. Solid line P = 1 atm; dashed line P = 5 atm.

F. 5
F. 5

Curves of growth for the 4–0 S (1) line at 150 K. Solid line P = 1 atm; dashed line P = 5 atm.

Equations (11)

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Δ ν = 2 π D / c λ 2 ( cm 1 ) .
I ( ω ω ) = 2 Re 0 exp [ i ( ω ω ) t ] F ( t ) d t .
F ( t ) = exp { k T m β 2 ( λ / 2 π ) 2 [ β t 1 + exp ( β t ) ] } ,
I ( ω ) = 2 0 cos ( ω t ) exp [ A ( β t 1 + e β t ) ] e K t d t ,
I ( ω ) = 2 0 cos ω t [ e A ( exp [ ( A β + K ) t ] A exp { [ ( A + 1 ) β + K ] t } + A 2 2 ! exp { [ ( A + 2 ) β + K ] t } ) ] d t .
I ( ω ) = e A π { A β + K [ A β + K ] 2 + ω 2 A [ ( A + 1 ) β + K [ ( A + 1 ) β + K ] 2 + ω 2 + A 2 2 ! [ ( A + 2 ) β + K ] [ ( A + 2 ) β + K ] 2 + ω 2 } .
Δ ω = A β + K = 4 π 2 D λ 2 + K 0 p .
W = [ 1 e S I ( ν ) ] d ν .
I ( ω ) d ω = e A / π [ π A π + ( A 2 π / 2 ! ) ]
= e A [ 1 A + ( A 2 / 2 ! ) ] .
D = D 0 ( T / 273 ) 3 2 p 1 .