# Evaluation of the nuclear factor of the probability of a radiationless
transition by integration over the dominant regions in phase space

## Alexey V. Sergeev and Bilha Segev

*Department of Chemistry, Ben-Gurion University of the Negev*

POB 653, Beer-Sheva 84105, Israel

The most important factor of the probability of a radiationless
transition that could vary by many orders of magnitude is the
square of the Franck - Condon integral, or an overlap integral
between the wavefunction of the donor (which is typically in its
ground vibrational state) and a wavefunction of the acceptor in a
highly excited vibrational state. In the framework of phase space
distribution this factor is estimated by replacing the
wavefunctions by their Wigner functions and by analyzing the phase
space integral. It was found that this integral has one or a few
dominant regions [1 - 3]. Here we present new results showing that the
integral could be easily evaluated by perturbation theory which is
some kind of quasiclassical expansion. Results are illustrated for
one and two dimensional potentials involving harmonic, Morse, and
Poeschl - Teller oscillators.

- B. Segev and E. J. Heller, J. Chem. Phys.
**112**, 4004, 2000.
- A. V. Sergeev and B. Segev, J. Phys. A: Math. Gen.
**35**,
1769, 2002.
- S. Kallush, B. Segev, A. V. Sergeev and J. Heller,
J. Phys. Chem. A
**106**,
6006, 2002.

Poster

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Designed by A. Sergeev.