Vibronic reduction factors for second-order spin-orbit coupling

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Abstract
Second-order vibronic reduction factors for spin-orbit coupling are derived for orbital triplet systems using the recently derived symmetry-related method. This involves the calculation of oscillator overlaps which are projected out of the cubic vibronic states. Details are presented in the weak coupling limit for T(X)e, T(X)t2 and T(X)(e+t2) vibronic systems and in the strong coupling limit for T(X)e and T(X)t2 systems. The analyses are shown to be in agreement with those obtained by other methods. The discussion is then extended to the calculation of the off-diagonal matrix element between the vibronic T1 ground state and the A2 inversion level of a T1 ion for the T(X)t2-system using symmetry-adapted vibronic states. The effects of anisotropy in the problems studied are also briefly discussed.