A theory of multiphonon relaxation for electronically or vibrationally
excited impurities in crystals is developed. Two alternative approach
es within the static-coupling scheme are presented and their relative
importance is discussed. For each approach a closed-form analytical ex
pression for the relaxation rate is given as a function of energy gap
and temperature. We consider relaxation either by optical or acoustic
phonons. From the analytical expressions we derive approximate energy
gap laws for the zero-temperature rates, and discuss the origin and ap
plicability of a popular phenomenological assumption for the rate's te
mperature dependence. The predictions of the theory are compared with
energy gap- and temperature-dependent experimental data for various el
ectronic transitions of rare-earth impurities in YA1O(3). (C) 1995 Ame
rican Institute of Physics.