Article | REF: E1980 V2

Optical properties of rare-earth ions

Authors: François AUZEL, Richard MONCORGÉ

Publication date: July 10, 2017

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2. Rare-earth ion energy levels

2.1 Electronic interactions in the free ion

The possible energy levels of the isolated ion (free ion) are due to the interactions between the N electrons of layer 4f with each other, on the one hand, and with the nucleus and electrons of the complete layers, on the other. Because of the large number of electrons involved, this problem can only be treated approximately. For this purpose, we consider the Schrödinger equation of the isolated ion:

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