CRITIQUE OF THE METHODS OF ANALYZING SPECTRAL LINE POSITIONS

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1972

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Ohio State University

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Molecular constants can be determined from spectral data by (a) fitting the observed line positions with a set of calculated line positions given by the differences between the eigenvalues of numerically diagonalized Hamiltonians for the upper and lower states, and by (b) fitting the observed lines with a set of calculated term values and then subsequently fitting these term values with the eigenvalues of the Hamiltonians. It is shown that, in method (b), the resulting molecular constants and their associated uncertainties can be significantly in error if the relative uncertainties and correlations of the term values are not used in the subsequent fitting of these term values with the eigenvalues of a Hamiltonian. Moreover, it is shown that method (b) is equivalent to method (a) only if these uncertainties and correlations are indeed maintained in method (b). In addition, it is pointed out how a simultaneous fit to all of the recorded bands of a band system may mask the effects of systematic errors between the bands, leading to erroneously optimistic uncertainties for the resulting molecular constants. Method (a) is applied to the $O_{2} b^{1} \Sigma_{g}^{+} -X^{3} \Sigma_{g}^{-}$ Red Atmospheric bands. The discrepancies concerning the optical and microwave values for $B_{O}$ and $D_{O}$ of the $X^{3}\Sigma_{g}^{-}$ state are removed by a non-linear least-squares fit to all of the lines recorded by Babcock and Herzberg (Astrophys. J. 108, 167, 1948).

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Author Institution: Aeronomy Laboratory, National Oceanic and Atmospheric Administration Environmental Research Laboratories Boulder; Department of Chemistry, Columbia University

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