Transition Probabilities and Branching Ratios

The probability of an individual transition J r f to occur is given by Equation 1.69. 

The correction factors for dielectric medium, x, used in this equation will depend on the transitions being absorption or emission. Further, since individual transitions will have different probabilities, it is possible to define a radiative branching ratio given by 

The radiative branching ratio can be calculated through the probabilities of the transitions, or, in the ease of emission, it can be determined experimentally from the emission spectra, where E JJ ) is the integrated emission spectrum of transition and J ) is the 

In the case of emission, A(J,J ) is also known as Einstein s coefficient of spontaneous emission, and the sum of all probabilities for all radiative transitions is equal to the inverse of the radiative rate constant, Icr, in turn the reciprocal of the emissive state lifetime, Tr. 

Werts and co-workers [59] demonstrated that for the purely magnetic dipole transition of Eu , Fj, the equation above can be rearranged to 

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Dysprosium ions Dy3+ can also be populated by direct absorption in the near U.V. part and blue part of the spectrum, or by energy transfer from U02+. The radiative transitions probabilities and branching ratios of Dy for tellurite and phosphate glasses have been calculated and measured51 and the corresponding values are given in Table 3. 

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