Theoretical study of the radiative lifetime for the spin-forbidden transition a 3Σ+u→X 1Σ+g in He2

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Abstract
The radiative lifetime for the spin‐forbidden, dipole‐allowed transition a 3Σ+ u →X 1Σ+ g in neutral He2 was calculated. This transition is assumed to derive its intensity by spin–orbit (SO) induced couplings which are treated using first‐order perturbation theory. The first‐order corrections to the wave functions are calculated directly in the configuration state function (CSF) basis by solving a system of linear equations given by first‐order perturbation theory for the perturbation to the zeroth‐order X 1Σ+ g and a 3Σ+ u wave functions. This approach eliminates the need to solve explicitly for many eigenstates of the unperturbed Hamiltonian which would be required if the spectral representation for the perturbed wave function were used. The results show a rapidly changing electric transition dipole moment as a function of internuclear seperation, R(He–He), over the bound region of the a 3Σ+ u potential energy curve, i.e., R(He–He)=1.5 to 4.0 bohr. The transition dipole reaches a maximum near the small barrier to dissociation around R(He–He)=4.5 bohr. A vibrational analysis gives the lifetime of the v=0 level of a 3Σ+ u to be approximately 18 s, which is consistent with a recent experimental estimate of 10 s (v=?) as a lower bound.

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