Abstract

The refractivity of natural hydrogen gas has been measured at eighteen wavelengths from 0.4047 to 1.6945 μm by means of a corner-reflector interferometer. The resulting refractivity at 0.5462252 μm, and at standard conditions, is 139.304 × 10−6. Sixteen points of our data are well fitted by the dispersion formula 106(n − 1) = 21.113 + 12723.2/(111 − σ2), where σ is wave number in reciprocal micrometers. The combination of our data with recent measurements in the ultraviolet by Smith, Huber, and Parkinson is fitted by the formula 106(n − 1) = [14895.6/(180.7 − σ2)] + [4903.7/(92 − σ2)]. Comparisons are made with the literature in respect to refractivity, dispersion, dielectric constant, molecular polarizability, Rayleigh scattering cross section, and Verdet constant.

© 1977 Optical Society of America

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References

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  1. P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422–1434 (1976).
    [CrossRef]
  2. C. Cuthbertson and M. Cuthbertson, “On the Refraction and Dispersion of Air, Oxygen, Nitrogen, and Hydrogen, and their Relations,” Proc. R. Soc. A 83, 151–171 (1909).
    [CrossRef]
  3. J. Koch, “Über die Dispersion gasförmiger Körper im ultra-violetten Spektrum,” Ark. Mat. Astron. Phys. 8, 20 (1913).
  4. M. Kirn, “Die Dispersion des Wasserstoffs im Ultraviolett,” Ann. Phys. (Paris) 64, 566–576 (1921).
  5. E. R. Peck and B. N. Khanna, “Dispersion of Air in the Near-Infrared,” J. Opt. Soc. Am. 52, 416–419 (1962).
    [CrossRef]
  6. E. R. Peck and B. N. Khanna, “Dispersion of Nitrogen,” J. Opt. Soc. Am. 56, 1059–1063 (1966).
    [CrossRef]
  7. E. R. Peck and K. Reeder, “Dispersion of Air,” J. Opt. Soc. Am 62, 958–962 (1972).
    [CrossRef]
  8. R. D. Goodwin, D. E. Miller, H. M. Roder, and L. A. Weber, “Second and Third Virial Coefficients for Hydrogen,” J. Res. Natl. Bur. Stand. U.S. A 68, 121–126 (1964).
    [CrossRef]
  9. C. Cuthbertson and M. Cuthbertson, “Refractivity of Para-hydrogen,” Proc. R. Soc. A 139, 517–520 (1933).
    [CrossRef]
  10. L. Essen, “The Refractive Indices of Water Vapour, Air, Oxygen, Nitrogen, Hydrogen, Deuterium and Helium,” Proc. Phys. Soc. Lond. B 66, 189–193 (1953).
    [CrossRef]
  11. J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).
  12. W. Kolos and L. Wolniewicz, “Polarizability of the Hydrogen Molecule,” J. Chem. Phys. 46, 1426–1432 (1966).
    [CrossRef]
  13. A. L. Ford and J. C. Browne, “Direct-Resolvent-Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418–426 (1973).
    [CrossRef]
  14. R. R. Rudder and D. R. Bach, “Rayleigh Scattering of Ruby-Laser Light by Neutral Gases,” J. Opt. Soc. Am. 58, 1260–1266 (1968).
    [CrossRef]
  15. R. Serber, “The Theory of the Faraday Effect in Molecules,” Phys. Rev. 41, 489–506 (1932).
    [CrossRef]
  16. L. R. Ingersoll and D. H. Liebenberg, “Faraday Effect in Gases and Vapors. II,” J. Opt. Soc. Am. 46, 538–542 (1956).
    [CrossRef]

1976 (1)

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422–1434 (1976).
[CrossRef]

1973 (1)

A. L. Ford and J. C. Browne, “Direct-Resolvent-Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418–426 (1973).
[CrossRef]

1972 (1)

E. R. Peck and K. Reeder, “Dispersion of Air,” J. Opt. Soc. Am 62, 958–962 (1972).
[CrossRef]

1968 (1)

1966 (2)

W. Kolos and L. Wolniewicz, “Polarizability of the Hydrogen Molecule,” J. Chem. Phys. 46, 1426–1432 (1966).
[CrossRef]

E. R. Peck and B. N. Khanna, “Dispersion of Nitrogen,” J. Opt. Soc. Am. 56, 1059–1063 (1966).
[CrossRef]

1964 (1)

R. D. Goodwin, D. E. Miller, H. M. Roder, and L. A. Weber, “Second and Third Virial Coefficients for Hydrogen,” J. Res. Natl. Bur. Stand. U.S. A 68, 121–126 (1964).
[CrossRef]

1962 (1)

1956 (1)

1953 (1)

L. Essen, “The Refractive Indices of Water Vapour, Air, Oxygen, Nitrogen, Hydrogen, Deuterium and Helium,” Proc. Phys. Soc. Lond. B 66, 189–193 (1953).
[CrossRef]

1933 (1)

C. Cuthbertson and M. Cuthbertson, “Refractivity of Para-hydrogen,” Proc. R. Soc. A 139, 517–520 (1933).
[CrossRef]

1932 (1)

R. Serber, “The Theory of the Faraday Effect in Molecules,” Phys. Rev. 41, 489–506 (1932).
[CrossRef]

1921 (1)

M. Kirn, “Die Dispersion des Wasserstoffs im Ultraviolett,” Ann. Phys. (Paris) 64, 566–576 (1921).

1913 (1)

J. Koch, “Über die Dispersion gasförmiger Körper im ultra-violetten Spektrum,” Ark. Mat. Astron. Phys. 8, 20 (1913).

1909 (1)

C. Cuthbertson and M. Cuthbertson, “On the Refraction and Dispersion of Air, Oxygen, Nitrogen, and Hydrogen, and their Relations,” Proc. R. Soc. A 83, 151–171 (1909).
[CrossRef]

Bach, D. R.

Beckett, C. W.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Benedict, W. S.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Browne, J. C.

A. L. Ford and J. C. Browne, “Direct-Resolvent-Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418–426 (1973).
[CrossRef]

Cuthbertson, C.

C. Cuthbertson and M. Cuthbertson, “Refractivity of Para-hydrogen,” Proc. R. Soc. A 139, 517–520 (1933).
[CrossRef]

C. Cuthbertson and M. Cuthbertson, “On the Refraction and Dispersion of Air, Oxygen, Nitrogen, and Hydrogen, and their Relations,” Proc. R. Soc. A 83, 151–171 (1909).
[CrossRef]

Cuthbertson, M.

C. Cuthbertson and M. Cuthbertson, “Refractivity of Para-hydrogen,” Proc. R. Soc. A 139, 517–520 (1933).
[CrossRef]

C. Cuthbertson and M. Cuthbertson, “On the Refraction and Dispersion of Air, Oxygen, Nitrogen, and Hydrogen, and their Relations,” Proc. R. Soc. A 83, 151–171 (1909).
[CrossRef]

Essen, L.

L. Essen, “The Refractive Indices of Water Vapour, Air, Oxygen, Nitrogen, Hydrogen, Deuterium and Helium,” Proc. Phys. Soc. Lond. B 66, 189–193 (1953).
[CrossRef]

Fano, L.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Ford, A. L.

A. L. Ford and J. C. Browne, “Direct-Resolvent-Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418–426 (1973).
[CrossRef]

Goodwin, R. D.

R. D. Goodwin, D. E. Miller, H. M. Roder, and L. A. Weber, “Second and Third Virial Coefficients for Hydrogen,” J. Res. Natl. Bur. Stand. U.S. A 68, 121–126 (1964).
[CrossRef]

Hilsenrath, J.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Hoge, H. J.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Huber, M. C. E.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422–1434 (1976).
[CrossRef]

Ingersoll, L. R.

Khanna, B. N.

Kirn, M.

M. Kirn, “Die Dispersion des Wasserstoffs im Ultraviolett,” Ann. Phys. (Paris) 64, 566–576 (1921).

Koch, J.

J. Koch, “Über die Dispersion gasförmiger Körper im ultra-violetten Spektrum,” Ark. Mat. Astron. Phys. 8, 20 (1913).

Kolos, W.

W. Kolos and L. Wolniewicz, “Polarizability of the Hydrogen Molecule,” J. Chem. Phys. 46, 1426–1432 (1966).
[CrossRef]

Liebenberg, D. H.

Masi, J. F.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Miller, D. E.

R. D. Goodwin, D. E. Miller, H. M. Roder, and L. A. Weber, “Second and Third Virial Coefficients for Hydrogen,” J. Res. Natl. Bur. Stand. U.S. A 68, 121–126 (1964).
[CrossRef]

Nuttall, R. L.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Parkinson, W. H.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422–1434 (1976).
[CrossRef]

Peck, E. R.

Reeder, K.

E. R. Peck and K. Reeder, “Dispersion of Air,” J. Opt. Soc. Am 62, 958–962 (1972).
[CrossRef]

Roder, H. M.

R. D. Goodwin, D. E. Miller, H. M. Roder, and L. A. Weber, “Second and Third Virial Coefficients for Hydrogen,” J. Res. Natl. Bur. Stand. U.S. A 68, 121–126 (1964).
[CrossRef]

Rudder, R. R.

Serber, R.

R. Serber, “The Theory of the Faraday Effect in Molecules,” Phys. Rev. 41, 489–506 (1932).
[CrossRef]

Smith, P. L.

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422–1434 (1976).
[CrossRef]

Touloukian, Y. S.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Weber, L. A.

R. D. Goodwin, D. E. Miller, H. M. Roder, and L. A. Weber, “Second and Third Virial Coefficients for Hydrogen,” J. Res. Natl. Bur. Stand. U.S. A 68, 121–126 (1964).
[CrossRef]

Wolniewicz, L.

W. Kolos and L. Wolniewicz, “Polarizability of the Hydrogen Molecule,” J. Chem. Phys. 46, 1426–1432 (1966).
[CrossRef]

Woolley, H. W.

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

Ann. Phys. (Paris) (1)

M. Kirn, “Die Dispersion des Wasserstoffs im Ultraviolett,” Ann. Phys. (Paris) 64, 566–576 (1921).

Ark. Mat. Astron. Phys. (1)

J. Koch, “Über die Dispersion gasförmiger Körper im ultra-violetten Spektrum,” Ark. Mat. Astron. Phys. 8, 20 (1913).

J. Chem. Phys. (1)

W. Kolos and L. Wolniewicz, “Polarizability of the Hydrogen Molecule,” J. Chem. Phys. 46, 1426–1432 (1966).
[CrossRef]

J. Opt. Soc. Am (1)

E. R. Peck and K. Reeder, “Dispersion of Air,” J. Opt. Soc. Am 62, 958–962 (1972).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Res. Natl. Bur. Stand. U.S. A (1)

R. D. Goodwin, D. E. Miller, H. M. Roder, and L. A. Weber, “Second and Third Virial Coefficients for Hydrogen,” J. Res. Natl. Bur. Stand. U.S. A 68, 121–126 (1964).
[CrossRef]

Phys. Rev. (1)

R. Serber, “The Theory of the Faraday Effect in Molecules,” Phys. Rev. 41, 489–506 (1932).
[CrossRef]

Phys. Rev. A (2)

A. L. Ford and J. C. Browne, “Direct-Resolvent-Operator Computations on the Hydrogen-Molecule Dynamic Polarizability, Rayleigh, and Raman Scattering,” Phys. Rev. A 7, 418–426 (1973).
[CrossRef]

P. L. Smith, M. C. E. Huber, and W. H. Parkinson, “Refractivities of H2, He, O2, CO, and Kr for 168 ≤ λ ≤ 288 nm,” Phys. Rev. A 13, 1422–1434 (1976).
[CrossRef]

Proc. Phys. Soc. Lond. B (1)

L. Essen, “The Refractive Indices of Water Vapour, Air, Oxygen, Nitrogen, Hydrogen, Deuterium and Helium,” Proc. Phys. Soc. Lond. B 66, 189–193 (1953).
[CrossRef]

Proc. R. Soc. A (2)

C. Cuthbertson and M. Cuthbertson, “Refractivity of Para-hydrogen,” Proc. R. Soc. A 139, 517–520 (1933).
[CrossRef]

C. Cuthbertson and M. Cuthbertson, “On the Refraction and Dispersion of Air, Oxygen, Nitrogen, and Hydrogen, and their Relations,” Proc. R. Soc. A 83, 151–171 (1909).
[CrossRef]

Other (1)

J. Hilsenrath, C. W. Beckett, W. S. Benedict, L. Fano, H. J. Hoge, J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and H. W. Woolley, Properties of Gases, Natl. Bur. Stand. Circ. No. 564 (U.S. GPO, Washington, D.C., 1955).

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Tables (4)

Tables Icon

TABLE I Measured refractivity of hydrogen vs vacuum wavelength, compared with Eq. (4). Refractivities are rounded to three decimals, but four are retained in the differences. The two points in parentheses were not used in curve fitting. The number of digits in which the refractivity is given is appropriate to relative values and internal consistency. Absolute accuracy is not claimed to this precision.

Tables Icon

TABLE II Refractivity of hydrogen at 0. 546 225 2 μ m, under standard conditions. Values from the literature are according to Cuthbertson and Cuthbertson (1933). The present value is added for comparison.

Tables Icon

TABLE III Percentage differences of the data of Koch and of Kirn from Eq. (4), representing this work, and from Eq. (6), representing the data of Smith, Huber, and Parkinson.

Tables Icon

TABLE IV Molecular polarizability of hydrogen: theoretical values from the literature, compared with values calculated from refractivity measurements. Units are a 0 3.

Equations (16)

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ρ 0 / ρ m = ( Z m / Z 0 ) p 0 T m / p m T 0 .
Z 1 = ( 0. 255 / T 23. 9 / T 2 ) p .
( n 1 ) 0.5462 = ( 139. 304 ± 0. 017 ) × 10 6 .
10 6 ( n 1 ) = 21. 113 + 12 723. 2 / ( 111 σ 2 ) ,
10 6 ( n 1 ) = 17 692. 45 / ( 130. 3516 σ 2 )
10 6 ( n 1 ) = 23. 79 + 12 307. 2 / ( 109. 832 σ 2 ) .
10 6 ( n 1 ) = 14 895. 6 180. 7 σ 2 + 4903. 7 92 σ 2 .
V 0 = Z 0 R T 0 / p 0 .
V 0 = 22 427. 4 cm 3 / mol .
N 0 = 2. 685 15 × 10 19 molecules / cm 3 .
α = ( 3 / 4 π N 0 ) ( n 2 1 ) / ( n 2 + 2 ) .
α 5. 927 09 × 10 21 ( n 1 ) cm 3 .
α / α 0 3 = 4. 000 03 × 10 4 ( n 1 ) .
σ 0 = [ 4 π 2 ( n 1 ) 2 / N 0 2 λ 1 4 ] 3 / ( 3 4 ρ υ ) .
V n = e 2 m 0 c 2 σ d n d σ ,
γ V / V n