Many-Electron Selection Rules

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 ±1, the others by $\delta$ and $\epsilon$, $\delta +\epsilon$ being even. (b) when two electrons jump both can change their $n$ arbitrarily, one changes its $l$ by $\delta \pm 1$, the other one by $\epsilon$. Breaking off the series expansion for $\frac{1}{r_{FG}}$ in the electrostatic interaction after the second term gives for $\delta$ and $\epsilon$ only the values 0, ±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.