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

Rigorous expressions for the potential functions of a molecule in terms of the probability amplitudes of an electron transition are obtained. The resu lts refine the formulas published in [13]. An algorithm for using these exp ressions for solving the inverse spectroscopic problem on the determination of the potential of a bound state of a diatomic molecule from the experime ntal spectrum of a bound-free electron transition from a selectively popula ted vibrational-rotational level is proposed. The potentialities of the met hod are demonstrated by the example of the analysis of the experimental con tinuum of the 2 (3)Sigma (+)(g) (v = 15, N = 27) --> a(3)Sigma (+)(u) trans ition in Na-2. The possibilities for the extension of the expressions obtai ned to the case of polyatomic molecules and to the case of transitions wher e the combining states are not adiabatic are noted. Considerations on the q uestion 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. (C) 2000 MAIK "Nauka/Interp eriodica".