Investigation of the stability of the inverse spectroscopic problem of diatomic molecules

The stability and convergence of the inverse spectroscopic problem is investigated for diatomic molecules in the¹ electron state for a potential representation by series in the Dunham variable z_d=(r-r_e)/r_e, the Ogilvie-Tipping z_ot=(r-r_e)/(r + r_e), the Simmond-Parr-Finlan z_S= (r-r_e)/r and the Tucker z_t=sign (p)1 -(r_e/r)^P]. None among the representations under investigation was that which would give a significant systematic improvement in stability as compared with others. The convergence is related to the selection of the initial approximation in the method of least squares, and is practically independent of the functional form of the potential. For the Dunham representation the solutions of the inverse problem yield quantities close to the true values of the expansion coefficients.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–101, May, 1984.