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.

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


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