Intensity-average decay time

In this definition, each decay time is weighted by the corresponding fractional intensity. This average is called the intensity-averaged decay time (or lifetime). 

For the calculation of transfer efficiency, it is incorrect to use the intensity-averaged decay time (see Section 6.2.1 for... 

The definition used depends on the phenomenon under study. For instance, the intensity-averaged lifetime must be used for the calculation of an average colli-sional quenching constant, whereas in resonance energy transfer experiments, the amplitude-averaged decay time or lifetime must be used for the calculation of energy transfer efficiency (see Section 9.2.1). 

Fig. 11.10. Schematic illustration of fluorescence correlation spectroscopy. The autocorrelation function characterises the fluctuations of the fluorescence intensity its decay time expresses the average duration of a...

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

Figure 20. The phase-averaged mean decay time as a function of frequency of the driving signal for different values of noise intensity, kT = 0.3,0.1,0.05, A — 1. Solid hnes represent results of computer simulation, and dashed lines represent adiabatic approximation (6.15).

There should exist a correlation between the two time-resolved functions the decay of the fluorescence intensity and the decay of the emission anisotropy. If the fluorophore undergoes intramolecular rotation with some potential energy and the quenching of its emission has an angular dependence, then the intensity decay function is predicted to be strongly dependent on the rotational diffusion coefficient of the fluorophore.(112) It is expected to be single-exponential only in the case when the internal rotation is fast as compared with an averaged decay rate. As the internal rotation becomes slower, the intensity decay function should exhibit nonexponential behavior. 

Figure 7. Relative luminescence intensity and decay lifetime of Cu(I)Y during exposure to oxygen at 25°C and I atm. The decay times are average lifetimes except for the last point at which two distinct lifetimes, t = 28 /isec and r = 6 ysec (not shown here), were determined.

G (t) is a time average of the scatter intensity at time t, I(t), times the intensity at a time t later, or I (t + x) where x is on the order of msec or jxsec. The autocorrelation function is determined by the Coulter Model N4 for a number of values of x simultaneously, and the data is plotted as G (x) versus x. If the particles in the liquid are the same size and shape (i.e., spherical), and hence monodisperse, the curve of the autocorrelation function of the scattered light intensity is a single decaying exponential ... 

Of these absorptions the latter two produce most of the emission intensity so that we are concerned mainly with the v = 32 excited vibrational level. Detailed studies of single vibrational-rotational states show only slow variation of the relaxation constants with upper state J. Thus in this experiment it will be assumed that a single decay constant is sufficient to describe the average relaxation. This assumption has been validated by using a Nd YAG laser that had a single-frequency output, which was tunable to any of the three transitions the decay times vary by less than 10 percent among these three upper states. ... 

The radiative decay time of the red PL is of the order of several tens of microseconds in all cases. The lack of the blue shift in the compact films has been explained in terms of the surface state model [19]. The theory predicts an increase of the transition probability for absorption and PL with decreasing crystallite size [9, 10, 13]. Fig. 5 shows the measured dependence of the PL intensity on the average crystallite size in the compact ncSi/SiO films [19,25]. 

If the spontaneous emission of radiation of the appropriate energy is the only pathway for a return to the initial state, the average statistical time that the molecule spends in the excited state is called the natural radiative lifetime. For an individual molecule the probability of emission is time-independent and the total intensity of emission depends on the number of molecules in the excited state. In a system with a large number of particles, the rate of decay follows a first-order rate law and can be expressed as... 

Cf (ti 2.73 y) has found several uses. It decays to 3.1% by spontaneous fission (the main decay mode is through a emission) leading to a neutron emission rate of 2.3 X10 n s kg (average n-energy 2.35 MeV). The n-dose rate is 22 kSv h kg Cf is the only nuclide that can provide a useful neutron intensity over a sufficiently long half-life to make it a useful neutron source. The low rates of heat emission (38.5 kW/kg), y-radiation (initially 1.3 x 10 photons s kg, yielding an initial dose rate of 1.6 kGy h kg y-ray intensity increases with time due to fission product build-up) and helium evolution (from a decay) allow fabrication of simple, small Cf sources that require no external power... 

---