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Fine Structure Constants of Metastable H 2 in the c Π u 3 State

Fine Structure Constants of Metastable H 2 in the c Π u 3 State The expectation values of spin-orbit ( A 1 ) spin-other-orbit ( A 2 ) and spin-spin ( B 0 and B 2 ) interactions have been evaluated over the electronic wave function for the c Π u 3 state of H 2 . A 1 = 5.737 kMc/sec, A 2 = - 9.8 kMc/sec, B 0 = - 1.33 kMc/sec, and B 2 = - 3.84 kMc/sec. These values agree well with those obtained from Lichten's experimental fine-structure splittings. The electronic wave function used is a linear combination of Heitler-London-type and ionic-type wave functions. By expressing the gradient operators as components of a spherical tensor, the spin-other-orbit interaction can be expressed as a linear combination of irregular solid spherical harmonics of the first order, while the space part of the spin-spin interaction consists of irregular solid spherical harmonics of the second order. The method of expansion and evaluation of these irregular solid spherical harmonics for a two-electron system is discussed in detail. The small second-order perturbations due to the nearby rotational states are also calculated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review American Physical Society (APS)

Fine Structure Constants of Metastable H 2 in the c Π u 3 State

Chiu, Lue-Yung Chow
Physical Review , Volume 137 (2A) – Jan 18, 1965
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Publisher
American Physical Society (APS)
Copyright
Copyright © 1965 The American Physical Society
ISSN
1536-6065
DOI
10.1103/PhysRev.137.A384
Publisher site
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Abstract

The expectation values of spin-orbit ( A 1 ) spin-other-orbit ( A 2 ) and spin-spin ( B 0 and B 2 ) interactions have been evaluated over the electronic wave function for the c Π u 3 state of H 2 . A 1 = 5.737 kMc/sec, A 2 = - 9.8 kMc/sec, B 0 = - 1.33 kMc/sec, and B 2 = - 3.84 kMc/sec. These values agree well with those obtained from Lichten's experimental fine-structure splittings. The electronic wave function used is a linear combination of Heitler-London-type and ionic-type wave functions. By expressing the gradient operators as components of a spherical tensor, the spin-other-orbit interaction can be expressed as a linear combination of irregular solid spherical harmonics of the first order, while the space part of the spin-spin interaction consists of irregular solid spherical harmonics of the second order. The method of expansion and evaluation of these irregular solid spherical harmonics for a two-electron system is discussed in detail. The small second-order perturbations due to the nearby rotational states are also calculated.

Journal

Physical Review – American Physical Society (APS)

Published: Jan 18, 1965

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