Radiative transition probabilities

As a matter of fact low-lying MMCT states can also influence radiative transition probabilities. The long decay time of the VO4 luminescence is considerably shortened by the presence of Bi " [27] due to a Bi(IV)-V(IV) MMCT state (see also above). Such effects are very well-known for LMCT states in case of transition-metal ions and lanthanide ions [6]. They will not be discussed here any further. 

In the first topic, we will briefly describe a semi-empirical method that is commonly nsed to estimate the radiative transition probabilities from energy levels of (RE) + ions in crystals. This is certainly very nsefnl in order to determine the efficiency of a (RE) + based system as a luminescent or laser material. In the previous chapter (Section 5.7), we have described a method for determining the qnantnm efficiency of a Inminescent system. However, the application of that method is limited to certain... 

In the absence of the reverse absorption the radiative transition probability fquantum yield of fluorescence qmC) and the decay constant l/r (C)= 2 [Pg.200]

It is interesting to note that the emission spectra of the terbium chlorides solvated with H20 and D20 show no discernible differences. Since the rare-earth chlorides solvated with D20 are isostructural with the chlorides solvated with H20 and since the emission spectra are essentially identical, Freeman et al believe that the variations in lifetime are not brought about by changes in the radiative-transition probabilities, but are a consequence only of changes in radiationless quenching efficiencies. They speculate that the decreased efficiency upon substitution of D20 for H20 must be related to the large changes in vibrational frequencies associated with substitution of the H atoms by the D atoms. 

It is quite interesting to note that the neodymium-decay time is 25 per cent larger in the coactivated glass than in the single activated glass. This could be due to changes in either radiative or non-radiative-transition probabilities. The authors do not give an explanation as to the nature of the increase. 

One explanation is that the radiative transition probabilities of the excimers are similar to those of the monomeric singlet states, but the excimers are formed in much lower yields. This could be the case if the initially excited state (the optically bright state populated by absorption) forms the excimer state in competition with other decay channels. An alternative explanation is that the excimer states are formed in high yield, but have low radiative transition probabilities (i.e. they are relatively dark in emission). 

The irregularity of the spectrum has consequences on the properties of the matrix elements of observables like the electric dipole moment and, thus, on the radiative transition probabilities. For radiative transitions, a single channel is open and the statistics of the intensities follow a Porter-Thomas or x2 distribution with parameter v = 1, as observed in NO2 [5, 6]. 

The absence of an enormous enhancement in radiative decay rates in the nanocrystals can also be verified by electronic absorption spectroscopy. The original claim stated that the Mn2+ 47) —> 6A1 radiative decay lifetime dropped from xrad = 1.8 ms in bulk Mn2+ ZnS to xrad = 3.7 ns in 0.3% Mn2+ ZnS QDs ( 3.0 nm diameter) (33). This enhancement was attributed to relaxation of Mn2+ spin selection rules due to large sp-d exchange interactions between the dopant ion and the quantum-confined semiconductor electronic levels (33, 124— 127). Since the Mn2+ 47 > 6Ai radiative transition probability is determined... 

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. 

Also in response theory the summation over excited states is effectively replaced by solving a system of linear equations. Spin-orbit matrix elements are obtained from linear response functions, whereas quadratic response functions can most elegantly be utilized to compute spin-forbidden radiative transition probabilities. We refrain from going into details here, because an excellent review on this subject has been published by Agren et al.118 While these authors focus on response theory and its application in the framework of Cl and multiconfiguration self-consistent field (MCSCF) procedures, an analogous scheme using coupled-cluster electronic structure methods was presented lately by Christiansen et al.124... 

The near equality of population in the two levels is an important factor in determining the intensity of the NMR signal. According to the Einstein formulation, the radiative transition probability between two levels is given by... 

The origin of this process may be seen in the following Let n = (na — np) be the difference in population let 0 = (na + np) let W+ be the probability for a nucleus to undergo a transition from the lower to the upper level as a result of an interaction with the environment, and let ILL be the analogous probability for the downward transition. Unlike the radiative transition probabilities, W+ and W are not equal in fact, at equilibrium, where the number of upward and downward transitions are equal,... 

Further quantum yield measurements (111) and emission lifetimes (111-113,115) have also been reported which demonstrate that the radiative transition probability from a vibronic state is determined by the combination of vibrational modes that have been excited. The transition rates that may be of interest in comparing data from all three phases are, of course, those from the lower levels of Sj, since relaxation in higher-pressure gases and condensed media will lead to these states. The data of Spears and Rice (111) show that the emission probability from the levels 0, 6 16 and 1 are 2.2 x lO s", 3.4 x 10 s l,... 

Ubrium nuclear configuration is smaU. The interaction V(Xeq + q, B) between the oscillator and the surrounding bath B can then be expanded in powers of q, keeping terms up to first order. This yields V = C — Fq where C = V(xeq, B) is a constant and F = —(9 E/9 ) =o- When the effective interaction —Fq is used in the golden rule formula (9.25) for quantum transition rates, we find that the rate between states i and j is proportional to qy This is true also for radiative transition probabilities, therefore the same formalism can be apphed to model the interaction of the oscillator with the radiation field. 

The quantum efficiency rj at a given wave-number of incoming photons is defined30 as the sum of probabilities of radiative transitions from the excited level 2Aj divided by the sum of radiative and non-radiative transitions probabilities... 

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... 

One important step is the choice of the gauge in which to express the two-body relativistic interaction. For the exact solution we know that the result should be gauge independent but this will not hold for approximate solutions (remember the length and velocity forms for dipole radiative transition probabilities). The final result for g(l,2) of Eq. (5) reads ... 

Highly-ionized atoms DHF calculations on isoelectronic sequences of few-electron ions serve as the starting point of fundamental studies of physical phenomena, though many-body corrections are now applied routinely using relativistic many-body theory. Relativistic self-consistent field studies are used as the basis of investigations of systematic trends in ionization energies [137-144], radiative transition probabilities [145-148], and quantum electrodynamic corrections [149-151] in few-electron systems. Increased experimental precision in these areas has driven the development of many-body methods to model the electron correlation effects, and the inclusion of Breit interaction in the evaluation of both one-body and many-body corrections. 

Table 4 Radiative transition probabilities for pyrene in various oxygen-free solvents at 25 °C... 

RADIATIVE TRANSITION PROBABILITIES FOR X-RAY LINES Ratios of Transition Probabilities for K X-Ray Lines... 

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