# Semiclassical estimation of Franck - Condon factors and
transition rates for vertical and nonvertical transitions

*A. V. Sergeev and B. Segev*

## Abstract

We develop a systematic way for estimating multidimensional Franck - Condon factors
and transition rates for vertical and nonvertical transitions.
By analyzing the phase space overlap integral, we find the most
probable positions and momenta of the nuclei immediately after the
electronic transition. We find the transition rate by treating the
dominant region in phase space as a funnel for the transition and by
calculating the flow of probability through this funnel.
We use the Wigner representation and its semiclassical limit and
find that the transition occurs through a point(s) on the final
surface of constant energy where the initial wavefunction is maximal. This
dominant contribution is estimated analytically. Results are
illustrated for Harmonic, Morse and Poeschl - Teller oscillators.

Text of the paper: PDF format, TeX file.

Earlier draft version: PDF format, TeX file.

Paper from the journal in PDF format.

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Designed by A. Sergeev.