Theoretical Study of the Radiative Lifetime for the Spin-forbidden Transition $X^{1}\Sigma^{+}_{*}<- a^{3}\Sigma^{+}_{u}$ in $He2^{4}$

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1988

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Ohio State University

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Using Ab Initio State Averaged MCSCF Plus CI Methods Chemical Research, Development, and Engineering Center Aberdeen Proving Ground, MD 21010-5423 The radiative lifetime for the $a^{3}\Sigma^{+}_{u}$ state in neutral $He2^{\ast}$ was calculated including spin-orbit (SO) interactions between the $a^{3}\Sigma^{+}_{1}$ and $^{1}\Pi_{u}$ manifold of states, and the repulsive ground state $X^{1}\Sigma_{g}$ and the $^{3}\Pi_{g}$ manifold. The SO interactions are treated through first-order perturbation theory wherein the first-order corrections to the wavefunctions are calculated directly by solving a set of linear equations (representing the first-order perturbation expression) involving SO matrix elements between the zeroth-order $X^{1}\Sigma^{+}_{g}$ or $a^{3}\Sigma^{+}_{U}$ wavefunctions, and the list of Configuration State Functions generated by a second-order CI for the states of $^{3}\Pi_{g}$ or $^{1}\Pi u$ symmetries, respectively (1). This partially alleviates the problem of solving explicitly for many eigenstates of the $3\Pi g$ or $^{1}\Pi u$ symmetries. The results show a rapidly changing electric transition dipole moment over the bound region of the $a^{3}\Sigma^{+}_{u}$, i.e. $r(He-He) = 1.5$ to 4.0 bohr. A vibrational analysis gives the lifetime of the v-O level of $a^{3}\Sigma^{+}_{u}$ to be around 18 secs, which is consistent with a recent experimental estimate of 10 secs (v-?) as a lower bound.

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$^{1}$ D. R. Yarkeny, J. Chem. Phys. 86, 1642 (1987); and references therein.
Author Institution: US Army Ballistic Research Laboratory, SLCBR-IB-I; Department of Chemistry, The Johns Hopkins University; Lawrence Livermore National Laboratory, The Johns Hopkins University

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