Investigation of the stability of the inverse spectroscopic problem of diatomic molecules
Abstract
The stability and convergence of the inverse spectroscopic problem is investigated for diatomic molecules in the^{1}∑ electron state for a potential representation by series in the Dunham variable z_{d}=(rr_{e})/r_{e}, the OgilvieTipping z_{ot}=(rr_{e})/(r + r_{e}), the SimmondParrFinlan z_{S}= (rr_{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.
 Publication:

Soviet Physics Journal
 Pub Date:
 May 1984
 DOI:
 10.1007/BF00898618
 Bibcode:
 1984SvPhJ..27..436V