Rare-earth ion energy levels
Optical properties of rare-earth ions

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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