On the calculation of model potential parameters from molecular spectra

摘要

In this paper we propound a procedure for inversion of an energy spectrum in order to obtain the original Hamiltonian function, applicable to nonresonant multidimensional systems. We use the Lie transform method to find the appropriate EBKhyphen;quantizable Hamiltonian, explicitly dependent on the unknown potential parameters. Comparison with the observed spectra allows the determination of explicit expressions for those parameters in terms of the spectral parameters. We first illustrate these concepts with the construction of power series and perturbed Morse oscillator model potentials for diatomics, and its extension to a simple model of triatomics including bending motion. We finally apply the procedure to the construction of a Morse potential model for linear polyatomic molecules.