Relation of the Lauer–Fong formula to the SCC model: Application to Sm+2 5d?5D crossovers

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Abstract
In single‐h/ω models in any number of coordinates, the transition nuclear factor is known to be the Huang–Rhys–Pekar Wp function for the operator 1 and certain combinations of Wp functions for the operators z and ∂/∂z. Since Wp satisfies a linear recursion formula, the z and ∂/∂z combinations can be written in different but equivalent ways. The Wp functions in these nuclear factors can be approximated under Poisson b1 and Stirling conditions (both defined in text). The Lauer–Fong formula is the ∂/∂z‐operator rate for the one‐coordinate model (equal‐force‐constants SCC model) with the Wp combination written in a particular 5‐Wp form and with the five Wp functions Stirling approximated. The Fong–Wassum formula is the analogous formula under Poisson b1 conditions. The application of the Lauer–Fong formula to the quenching of Sm+2 5D states in KCl, SrF2, BaBr2, and BaCl2 is re‐examined. A necessary correction is made which increases the transition electronic factors for Sm+2 5d?5D nonradiative crossovers by four orders of magnitude.