Branching ratios radiative

In the case of luminescence transitions it is usually not appropriate to use the absolute intensities because non-radiative processes such as multiphonon decay or energy transfer processes can effectively change the observed intensities. Similarly, also the experimentally measured lifetime is not suitable because non-radiative processes can effectively shorten the lifetime. However, the radiative branching ratios (1r can still be compared with the calculations. These ratios denote the relative intensities for transitions from the same initial to different final multiplets. 

One can measure the site concentrations in absolute units to 25% by measuring the absorption coefficient and radiative transition probability (which in turn comes from the level lifetime, radiative quantum efficiency and radiative branching ratios) or to 15% by nonlinear regression fitting of relative intensities to total dopant concentration over a range of site distributions. 

As for absorption spectra, it is assumed implicitly that all the crystal-field components of the initial state are equally populated. If the lifetime of the state is long compared to the rate at which it is populated in the excitation process, thermal equilibrium at the temperature of the system can be achieved before emission takes place (Carnall 1979). Because an excited state WJ is relaxed to several lower-lying states J, the radiative branching ratio jSr is defined... 

It is useful to define in addition the radiative branching ratio, )8r, from the relaxing state (i/ /) to a particular final state... 

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... 

The observable kinetics of a luminescence can be derived from the energy diagram of Figure 3.32. This shows a simple example of two competing decay paths, fluorescence from Si to S0, and a non-radiative transition from Sj to Tj. These are two first-order processes of rate constants and kisc respectively so that the quantum yield of fluorescence is given by the branching ratio as... 

There are several considerations to bear in mind when using fluorescence detection. First, the approach is most useful when the photons to be detected have a vastly different wavelength than the exciting light and the most probable decay of the optically excited state, which need not be the same. Second, the branching ratio for the detected transition should be favorable. Third, the lifetimes of the initial and final state of the microwave transitions must be taken into account. If the microwaves are always on, at resonance, radiative decay occurs from the coupled pair of states. If the initial state of the microwave transition has a much... 

In most cases, the Judd-Ofelt parameters are calculated with good confidence considering that results from various laboratories are convergent. They are found to adequately predict the radiative properties — lifetimes and branching ratios — of several transitions especially for Ho3+, Er3+, and Tm3+ ions in ZBLAN as well as in fluoroindate glasses. 

Erbium ions in fluoride glasses possess several radiative transitions from the violet to the mid-IR (3.45 pm) as shown in Fig. 10. Their spectroscopic parameters such as radiative lifetimes and branching ratios were determined for several types of glasses based on zirconium, indium, aluminum or even zinc fluoride [31,98-100]. 

Radiative transition probabilities for Pr3+ in tellurite, borate and phosphate glasses have been calculated by the use of Judd-Ofelt theory50. These data together with the branching ratio and calculated multiphonon relaxation rates of various levels of Pr3+ bring us to the conclusion that the following transitions may be of interest in LSC in borate, phosphate and silicate glasses... 

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. 

Table 1. Radiative transition probabilities, branching ratios and integrated cross-sections for stimulated emission of the D2 excited state of Pr3+ in binary borate glasses... 

Despite the unfavourable branching ratio, interference processes can occur between autoionisation and radiative decay. These are discussed in detail in section 8.30. One should also note that, as a result of autoionisation, the remaining parent ion may find itself in an excited state which decays by fluorescence. Thus, the study of fluorescence at wavelengths different from the original excitation may actually be used to detect the presence of autoionisation into a specific channel. 

Transition probabilities have mainly been detemnined firom calculations and to a much smaller extend from experiments [18]. Accurate experimental data are needed for checking of theoretical models and methods. Furthermore, in many cases, especially for complex heavy atoms, the theoretical models are under development and calculations with sufficient accuracy cannot be performed yet. For such atoms, experimental data are of major importance in practice. Presently, one of the most accurate methods to determine transition probabilities is the use of radiative lifetintes in combination with branching ratios. 

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