In our earlier papers on theoretical analysis of fluorescent cooling

it is pointed out that there are two kinds of basic physical mechanism-anti-Stokes fluorescent cooling in single center(ASFCSC)and anti-Stokes fluorescent cooling by energy transfer(ASFCET).Doubtless

ASFCSC is an important process and dominants in fluorescent cooling of solid

but ASFCET can exist at the same time.Actually

the excitation transfers of rare-earth ions have been studied a lot even for ytterbium ions in fluoride glasses.Many experiment Phenomena show it is possible for ASFCET to realize.In this paper

we discussed the most cooling efficiency in ASFCET

which is a fluorescent cooling mechanism based on energy transfer among the centers within the inhomogeneously broadened spectral profile.A model was developed to evaluate the fluorescent cooling under the mechanism.We discussed it in two situations: two-phonon-assisted energy transfer process with small energy mismatch and one-phonon-assisted energy transfer process with large energy mismatch.The dependence of the most cooling efficiency on excitation photon energy and temperature was given.When the inhomogeneous line width is narrow

the best pump light frequency does not change with temperature and the most cooling efficiency is proportional to the cube of temperature.When the inhomogeneous line width is wide

the difference between the best pump light frequency and the center frequency of the inhomogeneous line gets wider as the temperature goes lower.The difference changes rapidly at low temperature.The most fluorescent cooling efficiency produced by energy transfer tends to lower with temperature decreasing

and trends to zero finally.The regularities by which fluorescent cooling efficiency lower with temperature are correspond to the results obtained in experiments.