Intensity Summation Rules and Perturbation Effects in Complex Spectra

After reviewing the present status of the problem of line intensities in complex spectra, and commenting on the relationship of the sum rule, the extended sum rule, and the general sum rule, a new $J$-group sum rule is derived. A $J$-group is defined as the totality of lines arising from transitions between all terms from one electron configuration having a given value $J_1$ of the inner quantum number and all terms from a second having a given value $J_2$; it maintains its identity for all couplings. It is proved that the total intensity of the lines in a $J$-group is independent of coupling, provided a third configuration does not produce terms which perturb those considered; where such perturbation occurs an extension of the new sum rule to an enlarged $J$-group is required. One can accordingly calculate the intensities of the individual lines for $\mathrm{LS}$ coupling, and the total intensities found for each $J$-group or enlarged $J$-group should apply to $\mathrm{jj}$ and all intermediate couplings. Verification of the rule is found in special cases which have been calculated theoretically, and, after ${\nu }^4$ and excitation corrections have been applied, in Dorgelo's measurements in neon. Where only certain terms of a $J$-group perturb one another lines arising from the remaining terms need not be considered in taking the sums; experimental verification of this is given by measurements in the spectrum of Ti I. Bartlett's statement that the extensions of the sum rule must be modified when configurations containing equivalent electrons are involved is discussed, and a procedure for applying them and the $J$-group sum rule in such cases is suggested. Finally, intensity data for a number of cases in Ti I are given to illustrate the method used in assigning the causes of intensity anomalies in lines to their originating terms, and qualitative results on relationships between term separations and intensity perturbations are given.