Radiative decay rate

In (8), the solvent-independent constants kr, kQnr, and Ax can be combined into a common dye-dependent constant C, which leads directly to (5). The radiative decay rate xr can be determined when rotational reorientation is almost completely inhibited, that is, by embedding the molecular rotor molecules in a glass-like polymer and performing time-resolved spectroscopy measurements at 77 K. In one study [33], the radiative decay rate was found to be kr = 2.78 x 108 s-1, which leads to the natural lifetime t0 = 3.6 ns. Two related studies where similar fluorophores were examined yielded values of t0 = 3.3 ns [25] and t0 = 3.6 ns [29]. It is likely that values between 3 and 4 ns for t0 are typical for molecular rotors. 

Herein, F is the radiative decay rate and km is the nonradiative decay rate, which comes from quenching. It has been demonstrated that silica nanomatrixes can change the fluorescence quantum yield and lifetime of fluorophores. Several groups have reported that both quantum yield and lifetime of fluorophores increased in DDSNs [27, 28, 52, 65-67]. However, the mechanisms regarding this enhancement were reported differently. 

The geometry of the nanoscaled metals has an effect on the fluorescence enhancement. Theoretically, when the metal is introduced to the nanostructure, the total radiative decay rate will be written as T + rm, where Tm corresponds to the radiative decay rate close to the metal surface. So, (1) and (2) should be modified and the quantum yield and lifetime are represented as ... 

From the practical point of view, the radiative decay rate kr may be assumed to be independent of the external parameters surrounding the excited sensor molecule. Its value is determined by the intrinsic inability of the molecule to remain in the excited state. The radiative decay rate kr is a function of the unperturbed electronic configuration of the molecule. In summary, for a given luminescent molecule, its unperturbed fluorescent or phosphorescent decay rate (or lifetime) may be regarded to be only a function of the nature of the molecule. 

It is of interest to correlate the above results with experimental quantities such as the integrated quantum yield of fluorescence. The observed radiative decay rate of the excited molecule is given by... 

In Chapter 3 we considered briefly the photoexcitation of Rydberg atoms, paying particular attention to the continuity of cross sections at the ionization limit. In this chapter we consider optical excitation in more detail. While the general behavior is similar in H and the alkali atoms, there are striking differences in the optical absorption cross sections and in the radiative decay rates. These differences can be traced to the variation in the radial matrix elements produced by nonzero quantum defects. The radiative properties of H are well known, and the radiative properties of alkali atoms can be calculated using quantum defect theory. 

From Eq. (4.8) we see that the A values contain a factor of co3, which generally means that the transition with the highest frequency contributes the most to the radiative decay rate and therefore dominates the overall dependence on n. 

In any low angular momentum state the radiative decay rate is usually dominated by the high frequency transitions to low lying states, and as a result it is impossible to control completely the decay rate using a millimeter wave cavity. In a circular i = m = n - 1 state the only decay is the far infrared transition to the n — 1 level, and Hulet et al. have observed the suppression of the decay of this level.26 They produced a beam of Cs atoms in the circular n = 22, = m = 21 state by pulsed laser excitation and an adiabatic rapid passage technique.27 The beam of circular state atoms then passed between a pair of plates 6.4 cm wide, 12.7 cm long, spaced by 230.1 jum, and held at 6 K. The 0 K radiative lifetime is 460ps, and... 

In light alkali atoms, Li and Na, the fine structure splitting of a low state is typically much larger than the radiative decay rate but smaller than the interval between adjacent states. In zero field the eigenstates are the spin orbit coupled tsjnij states in which and s are coupled. However, in very small fields and s are decoupled, and the spin may be ignored. From this point on all our previous analysis of spinless atoms applies. How the passage from the coupled to the uncoupled states occurs depends on how rapidly the field is applied. It is typically a simple variant of the question of how the m states evolve into Stark states. When... 

Here Wn is the average energy of the two fine structure levels. The real numerical coefficients a and b, where a2+b2=1, depend on the polarizations used in the excitation scheme, but are constant in time. Thus the relative amounts of d5/2 and d3/2 states do not change with time but simply decay together at the radiative decay rate T. However, the relative amounts of m character oscillate at the fine structure frequency, and this oscillation is manifested in any property which depends upon m, such as the fluorescence polarized in a particular direction, or the field ionization signal due to a particular value of m. This fact becomes more apparent... 

Level crossing spectroscopy has been used by Fredriksson and Svanberg44 to measure the fine structure intervals of several alkali atoms. Level crossing spectroscopy, the Hanle effect, and quantum beat spectroscopy are intimately related. In the above description of quantum beat spectroscopy we implicitly assumed the beat frequency to be high compared to the radiative decay rate T. We show schematically in Fig. 16.11(a) the fluorescent beat signals obtained by... 

Table 22.1. Perturber fractions obtained from the radiative decay rates, photoionization cross sections, and QDT analysis of the optical spectrum.

Experimental radiative decay rates" Experimental photoionization cross sections6 QDT three channel model 6s jj2, 5d5/2 limits"... 

With the exception of [Ir(ppy)2en] +, where we have a very big uncertainty in the estimated absorption intensity, the correlation between the calculated radiative and observed lifetimes at low temperatures is excellent. This proves that at low temperatures the lifetime of the excited state is mainly governed by its radiative decay rate [26]. 

When decay curves were analyzed using a biexponential function, the nonradiative decay rate tsnr 1 of the slow component was evaluated by subtracting the radiative decay rate from the slow fluorescence decay rate. Figure 10 shows... 

Second, Eq. (46) is ready to deduce excitonic augmented radiative decay rates since the matrix element (i U c(t,i) n) fully account for the excitonic coupling among different chromophores (for details we refer to [46]). 

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... 

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