Abstract

Selection rules for many-electron transitions are derived by taking into account the first order perturbed eigenfunctions. The perturbations considered are the electrostatic interactions between the pairs of electrons, and the spin-orbit interaction of each electron. It was found that the possibly occurring terms in the first order eigen-function were narrowly limited, and that this limitation provided the selection rules as follows: No more than three electrons can jump at a time. (a) when three electrons jump all change their $n$ by an arbitrary amount, one changes its $l$ by \ifmmode\pm\else\textpm\fi{}1, the others by $\ensuremath{\delta}$ and $\ensuremath{\epsilon}$, $\ensuremath{\delta}+\ensuremath{\epsilon}$ being even. (b) when two electrons jump both can change their $n$ arbitrarily, one changes its $l$ by $\ensuremath{\delta}\ifmmode\pm\else\textpm\fi{}1$, the other one by $\ensuremath{\epsilon}$. Breaking off the series expansion for $\frac{1}{{r}_{FG}}$ in the electrostatic interaction after the second term gives for $\ensuremath{\delta}$ and $\ensuremath{\epsilon}$ only the values 0, \ifmmode\pm\else\textpm\fi{}1. The Heisenberg two-electron selection rule is therefore to be considered as a special case of (b). The Laporte rule is verified making use only of the properties of spherical harmonics. Qualitative rules have been derived to tell when many-electron transitions may be expected to be strong. The first order terms also cause anomalies in the intensities of one-electron transitions.

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