Estimation of exponentially small Franck-Condon factors in the framework of phase space distributions

Seminar in BGU at Oct. 23, 2002

Abstract

We study a radiationless transition in a polyatomic molecule when the electronic energy of an excited electronic state is transferred to vibrational degrees of freedom of the nuclei, and when some nuclear coordinates change abruptly. The rate of the transition is proportional to the square of the Franck - Condon integral, or an overlap integral between the nuclear components of the wavefunctions. In the Wigner representation, the bulk of the phase space overlap integral goes from a region near the point (q*, p*) on the surface of constant energy where the Wigner function is maximal. This dominant contribution is estimated analytically. Results are illustrated for harmonic, Morse, and Poeschl - Teller oscillators.

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