Hyperfine Splittings and <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>g</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math></span> Values of Metastable <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>

Lue-Yung Chow Chiu

doi:10.1103/PhysRev.145.1

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Hyperfine Splittings and $g_{F}$ Values of Metastable $H_{2}$

Lue-Yung Chow Chiu^*

Catholic University of America, Washington, D. C. and National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland

^*Present address: Theoretical Division, Goddard Space Flight Center, NASA, Greenbelt, Maryland.

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Phys. Rev. 145, 1 – Published 6 May, 1966Erratum Phys. Rev. 159, 190 (1967)

DOI: https://doi.org/10.1103/PhysRev.145.1

Abstract

The energy arising from the hyperfine interaction, the interaction with the magnetic field, and the cross term between them has been studied for ortho- $H_{2}$ in the $c {}^{3}π_{u}$ state. The cross term gives rise to a first-order correction of the $g_{F}$ values which accounts for the discrepancies between the theoretical zeroth-order $g_{F}$ and the experimental values. The interactions are expressed as products of irreducible spherical tensors, and Racah's method is used to derive all the diagonal and off-diagonal matrix elements. The case of the rotational level $N = 1$ is presented in detail. The coupling constants of hyperfine structure have been evaluated by using a single-configuration electronic wave function for the $c {}^{3}π_{u}$ state of $H_{2}$ .

Erratum

Hyperfine Splittings and $g_{F}$ Values of Metastable $H_{2}$

Lue Yung-Chow Chiu

Phys. Rev. 159, 190 (1967)

References (25)

W. Lichten, Phys. Rev. 120, 848 (1960)
W. Lichten, Phys. Rev. 126, 1020 (1962)
W. Lichten and P. Brooks (unpublished)
G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1955)
P. R. Fontana, Phys. Rev. 125, 220 (1962)
L. Y. Chow Chiu, Phys. Rev. 137, 384 (1965)
(a) D. A. Frey and M. Mizushima, Phys. Rev. 128, 2683 (1962) (b) R. A. Forsch and H. M. Foley, ibid. 88, 1337 (1952) (c) H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Academic Press Inc., New York, 1957), p. 107
L. Y. Chow Chiu, J. Chem. Phys. 40, 2276 (1964)
Omitted endnote
Omitted endnote
M. E. Rose, Elementary Theory of Angular Momentum (John Wiley & Sons, Inc. New York 1961)
E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, London, 1953), pp. 69-71
[7] in L. D. Landau and E. M. Lifschitz, Quantum Mechanics (Nonrelativistic Theory) (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1958)
[12] [1]
L. C. Biedeharn, J. M. Blatt, and M. E. Rose, Rev. Mod. Phys. 24, 249 (1952)
[5,8]
Omitted endnote
(a) A. R. Edmonds, Angular Momentum in Quantum Mechanics (Cambridge University Press, New York, 1959), pp. 110, 118
D. M. Brink and G. R. Satchler, Angular Momentum (Oxford University Press, London, 1962)
Omitted endnote
[6]
A. Amemiya, Proc. Phys.-Math. Soc. Japan 21, 394 (1939)
Omitted endnote
Frey and Mizushima's paper ([7])
[6] [6]

[c1] W. Lichten, Phys. Rev. 120, 848 (1960)

[c2] W. Lichten, Phys. Rev. 126, 1020 (1962)

[c3] W. Lichten and P. Brooks (unpublished)

[c4] G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1955)

[c5] P. R. Fontana, Phys. Rev. 125, 220 (1962)

[c6] L. Y. Chow Chiu, Phys. Rev. 137, 384 (1965)

[c7] (a) D. A. Frey and M. Mizushima, Phys. Rev. 128, 2683 (1962) (b) R. A. Forsch and H. M. Foley, ibid. 88, 1337 (1952) (c) H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms (Academic Press Inc., New York, 1957), p. 107

[c8] L. Y. Chow Chiu, J. Chem. Phys. 40, 2276 (1964)

[c9] Omitted endnote

[c10] Omitted endnote

[c11] M. E. Rose, Elementary Theory of Angular Momentum (John Wiley & Sons, Inc. New York 1961)

[c12] E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra (Cambridge University Press, London, 1953), pp. 69-71

[c13] [7] in L. D. Landau and E. M. Lifschitz, Quantum Mechanics (Nonrelativistic Theory) (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1958)

[c14] [12] [1]

[c15] L. C. Biedeharn, J. M. Blatt, and M. E. Rose, Rev. Mod. Phys. 24, 249 (1952)

[c16] [5,8]

[c17] Omitted endnote

[c18] (a) A. R. Edmonds, Angular Momentum in Quantum Mechanics (Cambridge University Press, New York, 1959), pp. 110, 118

[c19] D. M. Brink and G. R. Satchler, Angular Momentum (Oxford University Press, London, 1962)

[c20] Omitted endnote

[c21] [6]

[c22] A. Amemiya, Proc. Phys.-Math. Soc. Japan 21, 394 (1939)

[c23] Omitted endnote

[c24] Frey and Mizushima's paper ([7])

[c25] [6] [6]

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Hyperfine Splittings and $g_{F}$ Values of Metastable $H_{2}$

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Hyperfine Splittings and $g_{F}$ Values of Metastable $H_{2}$

References (25)

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Hyperfine Splittings and gF Values of Metastable H2

Abstract

Erratum

Hyperfine Splittings and gF Values of Metastable H2

References (25)

Hyperfine Splittings and $g_{F}$ Values of Metastable $H_{2}$

Hyperfine Splittings and $g_{F}$ Values of Metastable $H_{2}$