CORRELATIONS AND ACCURACY OF ESTIMATION OF SPECTROSCOPIC CONSTANTS

Author Institution: Department of Physics, The Pennsylvania State UniversityA comparison and evaluation of the various methods for reducing spectroscopic data to spectroscopic constants or term values is made with the aid of an analysis of a number of ``synthetic” $\sum - \sum$ bands generated from fixed sets of constants with random noise superimposed on the line positions. It is shown that the strong correlations that exist between the upper state constants B^{\prime}, D^{\prime} and the lower state constants $B_{o}$, $D_{o}$ can be effectively broken up by using the difference constants $\Delta B$ = B^{\prime} - $B_{o}$ and $\Delta D$ = D^{\prime} - $D_{o}$ along with $v_{o}$, for representing the upper states. The lower state constants $B_{o}$ and $D_{o}$ and their standard errors calculated from the combination differences $\Delta_{2}$F$^{\prime\prime}$ (J) are shown to be as good as chose obtained from direct polynomial fits. If data for a number of bands originating in the same lower state are available, a considerable increase in accuracy of estimating the lower state constants can be attained by analyzing the bands simultaneously, e.g., using combination differences, provided the data are free from systematic errors. The dependence of the accuracy of determining the constants $B_{o}$, $D_{o}$, $\nu_{o}$, $\Delta$B, and $\Delta D$ on the extent of the band analyzed was investigated by varying the minimum and maximum J-values. The plots showing this dependence for both the actual errors and standard errors can be used e.g., to assess the band size necessary to attain a desired accuracy for a given constant