The energy spectrum of the F-7(3) multiplet of a Tb3+ ion in one of the non
-equivalent positions (of D-2 symmetry) occupied by a rare-earth ion in the
Y3Al5O12 crystallographic garnet structure is calculated. The energy spect
rum of the F-7(3) state is characterized by the presence of quasi-doublet s
tates formed by closely located Stark singlet states, that are effectively
"mixed" in an external magnet field H. This inference is seriously confirme
d by results of experimental studies of magneto-polarized luminescence on t
he radiative D-5(4) --> F-7(3) 4f-4f transition in Y3Al5O12:Tb3+. The optic
al transitions are identified, and the components of the g-factor of the F-
7(3)(Gamma(2), Gamma(4)) quasi-doublets in the Y3Al5O12 structure are deter
mined.