Communications in Theoretical Physics

Multiphonon Nonradiative Transition of Rare-Earth Ions

Ma Dong-Ping, Xu Yi-sun

Published Jan 1, 1985• 4 citations

Abstract

Based on the general theory, the formula of multiphonon nonradiative transition probability is derived by adopting simplified approximations involving single-frequency model. Satisfactory agreement is obtained through the comparison of theory and experiment. The principal differences between the present paper and relevant literatures as well as the validity of simplified approximation are discussed.

DOI: 10.1088/0253-6102/4/1/1

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Communications in Theoretical Physics

Multiphonon Nonradiative Transition of Rare-Earth Ions

Ma Dong-Ping, Xu Yi-sun

Published Jan 1, 1985• 4 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/4/1/1

Related papers

Effect of excited-state population density on nonradiative multiphonon relaxation rates of rare-earth ions

F. Pellé, Nicole Gardant, Francois E. Auzel

Multiphonon relaxation rate saturation is observed for rare-earth-doped glasses for high excited-state densities. This behavior is analyzed in a statistical approach; a theoretical model for the microscopic process is proposed. A phonon bottleneck effect on radiationless relaxation related to an accepting-modes saturation is suggested. At high excited-state density, ions in a phonon diffusion volume simultaneously fill the accepting modes. The critical distance below which excited ions share a common phonon bath is related to the phonon diffusion length in the host and deduced from our model. The results are in good agreement with the phonon mean free path independently deduced from sound velocity, thermal conductivity, and heat capacity.Multiphonon relaxation rate saturation is observed for rare-earth-doped glasses for high excited-state densities. This behavior is analyzed in a statistical approach; a theoretical model for the microscopic process is proposed. A phonon bottleneck effect on radiationless relaxation related to an accepting-modes saturation is suggested. At high excited-state density, ions in a phonon diffusion volume simultaneously fill the accepting modes. The critical distance below which excited ions share a common phonon bath is related to the phonon diffusion length in the host and deduced from our model. The results are in good agreement with the phonon mean free path independently deduced from sound velocity, thermal conductivity, and heat capacity.

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Cooperative radiationless relaxation

Marvin M. Miller, Francis K. Fong

The Journal of Chemical PhysicsAug 1, 19737 citations

Experimental demonstration of multiphonon-assisted anti-Stokes and Stokes excitation of rare-earth ions (

{R}^{3+}

) in different hosts, that is, in a weak-coupling ion-lattice interaction case, is obtained. An exponential behavior of excitation probabilities with respect to energy difference between excitation and electronic line is found, just as for multiphonon-assisted nonradiative decay and energy transfer. Exponential parameters ${\ensuremath{\alpha}}_{\mathrm{AS}}$ and ${\ensuremath{\alpha}}_{\mathrm{S}}$ for anti-Stokes and Stokes excitation are measured and linked to the Miyakawa-Dexter $\ensuremath{\alpha}$ parameter for decay, leading to estimates for Pekar-Huang-Rhys coupling parameter

{S}_{0}

of about 0.04, in agreement with values obtained from one-phonon spectra or nonradiative-decay measurements. A semiempirical formula is deduced to obtain $\ensuremath{\alpha}$ from only one parameter, an effective phonon energy.