Page 271 - Tunable Lasers Handbook

6 Transition Metal Solid-State Lasers 23 1

4F

-2 x I 63 cm-1
Central Mutual Spin Crystal
Potential Repulsion Orbit Field
FIGURE 5 Effect of various interactions on lanthanide series arom

With lanthanide series elements, the spin orbit interaction is next in order of
importance, sometimes equalling the strength of the mutual replsion of the
electrons. Through the spin orbit interaction, the total spin momentum and the
total orbital momentum are coupled to produce the total angular momentum,
characterized by the quantum number J. In cases where the mutual repulsion and
xhe spin orbit interaction are comparable, the same Russel Saunders nomencla-
ture is used to designate the states. Although J is an approximately good quan-
tum number. actual states can be composed of various combinations of states.
Fcr the lower levels, however. the states are primarily composed of states having
the same L and S quantum numbers.
Crystal field effects contribute only weakly to the energy levels of the Ian-
thanide series atoms embedded in a laser material. Although crystal field interac-
tions have a relatively small effect on the energy levels, they do split the levels
associated with a particular lsvel, lifting much of the degeneracy left after the
spin orbit coupling. Groups of energy levels. associated with a particular J quan-
tum number. are referred to as manifolds.
The nomenclature for the lanthanide series elements is similar to the nota-
tion used for Russel Saunders coupling. Energy manifolds, that is, closely
spaced groups of energy levels, are labeled