Exact evaluation of the multidimensional Franck–Condon integrals based on the contour integral method

Abstract

Adopting a different method from the Sharp–Rosenstock generating function method and the Doktorov coherent state method, a closed form expression for the Franck–Condon integrals between arbitrary multidimensional harmonic oscillators is derived exactly under the Duschinsky mixing effects on the base of the contour integral form expression of Hermite polynomials. In addition, an analytical expression for the calculation of the four-mode Franck–Condon factors is presented.

Keywords:

• Frank–Condon integral
• Contour integral
• Frank–Condon factors

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.10674002), the Program for Innovative Research Team in Anhui Normal University, and the Doctoral Research Foundation of Anhui Normal University.