Probabilities for Radiative and Nonradiative Decay of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Er</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>in La<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

The rates of radiative and nonradiative decay were determined for several excited states of ${\mathrm{Er}}^{3+}$ in La${\mathrm{F}}_{3}$ from calculated spontaneous emission probabilities and measured lifetimes. Electric-dipole, magnetic-dipole, and electric-quadrupole transition probabilities were evaluated using intermediate coupled states derived from computer diagonalization of the combined spin-orbit and electrostatic energy matrix. The required spin-orbit and Racah parameters for La${\mathrm{F}}_{3}$: ${\mathrm{Er}}^{3+}$ were obtained from a least-squares fit of experimental and theoretical energy levels. The probabilities for electric-dipole transitions were calculated using the theory of Judd and Ofelt; the phenomenological parameters needed in this approach were derived from measurements of integrated absorption coefficients. By comparing the total calculated radiative lifetimes and the observed lifetimes, the probabilities for nonradiative decay from nine different excited states were determined. The probability of nonradiative decay was found to be very dependent upon the proximity of lower energy levels, which for the levels investigated ranged from approximately 1600 to 6000 ${\mathrm{cm}}^{\ensuremath{-}1}$, and hence upon the number of phonons required to conserve energy. The rates of nonradiative transitions corresponding to the simultaneous emission of as many as five phonons were found to make significant contributions to the lifetimes of fluorescent states of rare earths in La${\mathrm{F}}_{3}$.