Theory of Optical Transitions in Trivalent REE

The characteristic absorption and emission spectra of lanthanide compounds in the visible, near ultra-violet and infra-red is attributed to transitions between 4/ levels due to the fact that they present a sharp line with oscillators strengths typically of the order of 10 . These transitions are electric dipole forbidden but became allowed as forced electric dipole transitions. 

The forced electric dipole mechanism was treated in detail for the first time by Judd (1962) through the powerful technique of irreducible tensor operators. Two years later it was proposed by Jorgensen and Judd (1964) that an additional mechanism of 4/-4/ transitions, originally referred to as the pseudo-quadrupolar mechanism due to inhomogeneities of the dielectric constant, could be as operative as, or, for some transitions, even more relevant than, the forced electric dipole one. 

In the standard theory the integrated coefficient of spontaneous emission of a transition between two manifolds / and is given by 

The intensity parameters Qx depends on both the chemical environment and the lanthanide ion, and theoretically they are given by 

Here we are discussing only the static model and omit the vibronic interaction. 

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