Lifetimes of states

Here, t is the time taken for to fall to 1 /e of its initial value (where e is the base of natural logarithms) and is referred to as the lifetime of state n. If spontaneous emission is the only process by which M decays, comparison with Equation (2.9) shows that... 

Where is the Hamiltonian for the interaction of the nucleus with the photon, /> is the initial (excited) state of the nucleus, g the final (ground) state and T the inverse of the natural lifetime of state /). We introduce an integral form of the denominator of Eq. (92) by ... 

Consider a sensor in dynamic equilibrium between phases or states A and B as illustrated in Figure 9.5. This situation may occur in pH sensors in which the lifetime of the ionized molecule is different from the lifetime of the neutral molecule. In this case a distinction needs to be made between the lifetimes of the individual states and the lifetimes measured. Let xA and xb be the lifetimes of states A and B, respectively. The measured lifetime values, t and n, are then given by the following equation 12 ... 

The coefficient Am tn is related to the lifetime of state m. Suppose we initially have Nm0 molecules in the excited state m and let no radiation be present. Assume that state n is the only available state to which the excited molecules can decay. Then the rate of decay is dNmf dt= — Am nNm. This equation integrates to... 

Suppose there are two protons, in environments A and B, in the system under investigation, and that they have resonances at frequencies 0 and cOo, respectively, with no spin coupling between them the kinetics of possible exchange between A and B are to be followed. Suppose also that the concentrations of A and B are equal (although this is not an important restriction since the treatment has been extended to the more general case where Cg). The observed spectrum comprises two lines of equal intensity separated by 8 = (Da —cogl, the chemical shift. The term t is now introduced, and this represents the mean lifetime of states A and B, or the time spent by the proton in the environments A and B. (If the concentrations o... 

The patterns shown here can be simulated, using density matrix equations, and from such modeling the relative lifetimes of states e and / can be deduced. 

When one remote perturber, j), dominates the radiative lifetime of state z), where the j —> X transition is allowed, the lifetime of the t) state, Tj, can be easily estimated using experimental data, by the formula ... 

Eig. 22 a and b. Determination of lifetime of states of O by recoil-distance method (Devons et al. [2d]), (a) Apparatus for pair emitting and gamma emitting states, (b) Results for 6.13 MeV level. 

Excitation and Deexcitation Lifetimes of States, Fluorescence, and Phosphorescence... 

Excited-state lifetime of state x (x = 1 for a singlet state, x = 3 for a triplet state etc.) Radiative lifetime of state x (x = 1 for a singlet state, x = 3 for a triplet state etc.) Chemical lifetime— the lifetime of a chemical species in the atmosphere Donor lifetime... 

An alternative approach to chemical kinetics uses the broadening of spectral lines to determine lifetimes of states and thus kinetics. In NMR, exchange processes can be used to determine lifetimes in the range of sec while in optical spectra, lifetimes can be determined which are on the order of picoseconds. Puls NMR techniques can be used to determine lifetimes which are on the order of nanoseconds. A recent review of the possibilities of NMR and references are given in the chapter on NMR and some in the chapter on ESR in the Techniques in Chemistry volumes (Swift 1974). 

With a traveling fellowship awarded by Harvard, Slater spent his first postdoctoral year at Cambridge. There, he developed a theory on radiative transitions in atoms. On discussing this idea with Neils Bohr and Hans Kramers, a joint paper on the quantum theory of radiation was published in 1924. However, Bohr and Kramers altered Slater s original idea by ascribing a virtual existence to the photons in the transitions— not the real photons that Slater believed in. In early 1925, Slater was back at Harvard and published further work of his own on radiative transitions. He presented a picture of absorption and emission of real photons coupled with energy conservation in transition processes. He also established a relationship between the width of spectral lines and the lifetimes of states. 

The UV-Vis spectroscopy of lanthanide and actinide elements directly reflects the electronic structure of the species involved. In oxidation states (III) and (IV), the ground-state electronic configuration is/", thus the low-lying spectrum is dominated by/-/ transitions that are strictly parity forbidden, and can also be spin-forbidden although spin-orbit coupling attenuates the selection rules. Nevertheless, both restrictions have important consequences, namely that these /-/ bands have very low absorption intensities, and the radiative lifetimes of/-/ states are often rather large (10 s) and sensitive to the environment. This is routinely used in Time-Resolved-Laser-Fluoresence-Spectroscopy (TRLFS) of Eu(III) and Cm(lII) at approximately 17000 [49-51]. Metal-centered/-rf transitions occur... 

The lowest electronic origins I and II of site B are found 19 and 18 cm , respectively, above the corresponding origins of site A. The emission intensities at the origins of site B are by more than an order of magnitude smaller than those of site A. Moreover, the emission decay measured at origin I at 17828 cm (site B) is mono-exponential over more than four lifetimes with r(B, 11) —> 10)) = 60 10 ns (Fig. 21c). This value is by a factor of about 4000 smaller than the usual lifetime of state I) at the same temperature of 1.2 K (r(A, I) 0)) =... 

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