Sensitivity of optical-absorption intensities for rare-earth ions

A technique is presented that uses molecular-dynamics simulation to generate the atomic positions needed to calculate the crystal-field parameters used in a Judd-Ofelt (JO) analysis. A slightly modified theory is used that permits analysis of both π- and σ-polarized absorption spectra. Different temperatures and ranges of calculation (up to 8 Å) around one rare-earth ion are used in the simulation of our test compound, ${\mathrm{Nd}}_2$ ${\mathrm{O}}_3$. It is shown that as many of the surrounding ions as possible should be included in the calculations, and also that it is possible to probe the sensitivity of the different transitions in rare-earth-ion spectra. It is further shown that the behavior of the so-called hypersensitive transition for a rare-earth ion is a result of the sensitivity of the JO parameter ${\mathrm{\Omega }}_2$, which is proportional to the square of the electric field created by the surrounding ions.