Perturbed Series in Line Spectra

There occur many line series in atomic spectra which do not even approximately fit a Ritz formula. They display either a sudden rise in the value of $n^{*}-n$ towards high term values or a gradual fall of almost a unit. The latter type contains an extra term due to some other structure and becomes similar to the first type after the removal of that term. It is shown that all such series obey approximately a series formula of type ${\nu }_n=\frac{R}{n^{*2\mathrm{}}}$, $n^{*}=\mu +\alpha {\nu }_n+(\frac{\beta }{{\nu }_n}-{\nu }_0)$ in which ${\nu }_0$ is the wave number of some level of the same type from a different electron structure. The series in the spectra Ca I, Ba I, Hg I, Cu I, Al II are discussed in detail. The rules governing the occurrence of a perturbation are more restricted than the simple ones that can be deduced from the results in other perturbation problems. The constant $\beta$ is always negative and the trems therefore appear to repel each other. The Ba I levels $5d6p{}_{}{}^{31}{}_{}{}^{}P_{}^0{}_{}{}^{}{D}^0{F}^0$ and the series $6snf{}_{}{}^1{}_{}{}^{}F_{}^0{}_{}{}^{}$ are given for the first time.