Judd-Ofelt treatment

In practice, two methods were supplementing the identification. One is to look for the maximum of (2J + 1) sub-levels induced in a level by the ligand field when q is even [for odd, q, at most (J + 5) Kramers doublets can be formed]. This technique was mainly explored by Hellwege and collaborators in Darmstadt after 1948. The other technique is to rely on the Judd-Ofelt treatment, expressing the oscillator strength P of each band (it can also be applied to luminescent transitions) as a function of the sum (Q2V2 + + Qf,V(,) involving three matrix elements U,... 

Judd-Ofelt treatment to obtain closure see Downer and Bivas (1983) and Judd and Pooler (1982). Similar work has been carried out on the Sq state of Pr " in various hosts and once again the modifications of the first-order Judd-Ofelt theory by Downer seem to be applicable, see Levey (1984) and Cordero-Montalvo and Bloemberger (1984). 

The n parameters for a given ion-host combination are derived from a least squares fit of calculated and observed intensities. The validity of the Judd-Ofelt treatment has been tested for most trivalent rare earths in both crystals and solutions and has been applied to rare earth molecular vapors. Peacock (1975) has presented a thorough review of the Judd-Ofelt theory and experimental results. 

We have mentioned several times that the Judd-Ofelt treatment is not numerically perfect. This can be seen from the number of measured P values, usually being well above 3, overdetermining eq. (5) for the evaluation of the three /2,. Various explanations have been proposed. In the original theory (Judd, 1962 Ofelt, 1962) the total width of the excited configuration of opposite parity mixing (to a very small extent) with 4f has to be negligible compared with the distance... 

The rationalization of absorption band intensities in lanthanide compounds (as developed since 1945) got in the Judd-Ofelt treatment a form in eq. (8) (see 2.5) directly involving the Einstein transition probabilities A J, / ). In the case of resonant absorption and emission being the only process occurring (like sodium atoms in yellow light), eq. (1) gives a direct relation between the (radiative) lifetime r and the oscillator strength P. As an important example of such a resonant situation can be mentioned r = 10.9 ms for the first excited state of gadolinium(III) aqua ions (Carnall, 1979) at 31200 cm of which three quarters... 

A recent development of interest in interpreting the absorption spectra of lanthanide ions has been a theory of absorption intensities developed independently by Judd (14) and by Ofelt (21) which represents an important advance from earlier treatments of this problem (3, 25). 

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