The Free-Ion Approach to Rare Earth

It turns out that another method exists where the approach has been to calculate so-called free-ion levels, so that the spin-orbit coupling factor, and the crystal field parameter, 4f, are not adjusted to give a satisfactory fit to the experimental data. ASfyboume (1963) and others have accomplished this task by using a Hartree-Fock approach (and a high speed computer) to calculate the energy levels of aU of the trivalent rare earth ions. 

These levels are shown in the following diagram, given on the next page as 6.8.39. In general, these levels show many similarities and only a few 

Relative Emission Intensities of the Trivalent Rare Earths 

Excitation of these ions using 40,000 cm i energy results in various excited states for each ion. Each state relaxes by phonon processes until the terminal excited state is reached, from which emission of a visible photon results. But we need to remember that any time we put a trivalent rare earth ion into a host crystal to form a phosphor, we will modify its free-ion energy levels, depending upon the site symmetry and crystal field strength. 

When the proper values are plotted vs the number of 4f electrons, the following curves result, as shown in 6.8.42., given on the next page. 

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