VIBRATIONAL OVERLAP INTEGRAL BETWEEN THE REPULSIVE $b^{3} \Sigma_{u}^{+}$ AND THE METASTABLE $c^{3} \pi_{u}$ STATES OF $H_{2}$
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Date
1976
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Publisher
Ohio State University
Abstract
The decay mechanism for the metastable $c^{3} \Pi_{u}$ state of $H_{2}$ is $considered^{1}$ to be the radiative forbidden transition (due to electric-quadrupole and magnetic-dipole) to the repulsive $b^{3} \Sigma_{u}^{+}$ state, To calculate the decay rate of the $c^{3}\Pi_{u}$ state, we have computed the vibrational overlap integral between $b^{3}\Sigma^{+}_{u}$ and $c^{3} \Pi_{u}$. A WKB semiclassical vibrational wave function, which is generated by using the potential energy curve of kolos and $Wolnicwicz,^{2}$ is used for the repulsive $b^{3} \Sigma_{u}^{+}$ state. The overlap integral, which is weighted by $\Delta E^{3}$ for the magnetic dipole transition and by $\Delta E^{5}$ for the electric quadrupole transition (where $\Delta E = ck$ is the energy difference between these two states) will be summed over the continuum of the final state. $b^{3} \Sigma_{u}^{+}$
Description
$^{1}$C. E. Johnson, Phys. Rev. A5, 1026 (1972). $^{2}$W. Kolos and L. Wolniewicz, J. Chem. Phys. 43, 2429 (1965). This work was supported by a research grant from the U.S. Energy Research and Development Administration.
Author Institution: Department of chemistry, Howard University
Author Institution: Department of chemistry, Howard University