Exact Expressions for the Potential Functions of a Molecule in Terms of the Probability Amplitudes of Electron Transitions and Their Utilization in the Inverse Spectroscopic Problem

摘要

Rigorous expressions for the potential functions of a molecule in terms of the probability amplitudes of an electron transition are obtained. The results refine the formulas published in [13]. An algorithm for using these expressions for solving the inverse spectroscopic problem on the determination of the potential of a bound state of a diatomic molecule from the experimental spectrum of a bound-free electron transition from a selectively populated vibrational-rotational level is proposed. The potentialities of the method are demonstrated by the example of the analysis of the experimental continuum of the 2~3Σ_g~+ (ν = 15, N = 27) → A~3Σ_u~+ transition in Na_2. The possibilities for the extension of the expressions obtained to the case of polyatomic molecules and to the case of transitions where the combining states are not adiabatic are noted. Considerations on the question concerning uniqueness of the solution of the problem of determining the potential function from the experimental spectrum are advanced on the basis of the analysis of the expressions found.