Predissociation radiative rate

Time-dependent picture. Experimental observations can be discussed in terms of a competition between two processes the radiative process (absorption or emission), characterized by a radiative rate r"1, and a nonradiative process, predissociation, characterized by a nonradiative rate. There are two possible decay pathways for the excited state,... 

Only the total lifetime r of a level can be measured, r is related to the rate of decrease of the number of molecules initially in a given level via both radiative and nonradiative routes. Let kr be the radiative rate constant (the probability per unit time that a molecule will leave the level as a result of emission of a quantum of light) and knr the predissociation rate (the dissociation probability per unit time). Recall that the pressure is assumed to be low enough that the rates are not affected by collisions. The number of molecules leaving the initial state during the time interval dt is given by... 

A relaxation process will occur when a compound state of the system with large amplitude of a sparse subsystem component evolves so that the continuum component grows with time. We then say that the dynamic component of this state s wave function decays with time. Familiar examples of such relaxation processes are the a decay of nuclei, the radiative decay of atoms, atomic and molecular autoionization processes, and molecular predissociation. In all these cases a compound state of the physical system decays into a true continuum or into a quasicontinuum, the choice of the description of the dissipative subsystem depending solely on what boundary conditions are applied at large distances from the atom or molecule. The general theory of quantum mechanics leads to the conclusion that there is a set of features common to all compound states of a wide class of systems. For example, the shapes of many resonances are nearly the same, and the rates of decay of many different kinds of metastable states are of the same functional form. 

Quenching half-pressure is equal lo (, t) 1 where kt is the rate constant for quenching reaction and r is the mean lifetime (radiative and predissociative) of excited NO. 

The measured lifetime t can be expressed by the pure radiative lifetime and the rate of predissociation kp... 

To take one example, let us consider the effects of rotational relaxation in BrF. The excited 53FI(0+) state in BrF is crossed by another 0+ state which leads to predissociation of the B state in vibrational levels 7 and 6. The initial study of the dynamics of the B state was carried out in a discharge flow system where the minimum operating pressure was 50 m Torr. The gas-kinetic collision rate coefficient at 298 K for He + BrF(B) collisions is 4.4 x 10-10 cm3 molecule-1 s-1. Thus, at the minimum pressure of 50 m Torr, the average time between collisions of excited BrF molecules and helium buffer gas is 1.5/us. This time is short compared with the radiative lifetime of BrF (42—56/ns [43]) and therefore significant redistribution in the excited state can occur before it radiates. 

The fluorescence decay curves for initial rotational states 17 < J < 28 were intermediate in behavior between those for stable and unstable states already described. As rotational energy was increased, the initial decay spike became more and more intense in relation to the subsequent slower rate. For the most part, the decay could be approximated by a double exponential. The question arose as to where the sharp onset of predissociation actually occurred, i.e. which was the first rotational level that had a radiative lifetime shorter than that of the stable levels. To answer this question, it was necessary to formulate a kinetic model for the excited state. 

Figure 2.3 Perturbations and predissociations affect absorption and emission line intensities in quite different ways. Two pairs of absorption and emission spectra are shown. The first pair illustrates the disappearance of a weakly predissociated line in emission without any detectable intensity or lineshape alteration in absorption. The second pair shows that emission from upper levels with slow radiative decay rates can be selectively quenched by collision induced energy transfer. The opposite effect, selective collisional enhancement of emission from perturbed, longer-lived levels, is well known in CN B2 +—X2 +(u = 0,v") emission spectra (see Fig. 6.14 and Section 6.5.5). (a) the CO B1S+—X1S+(1,0) band in emission (top) and absorption (bottom). The last strong lines in emission are 11(16) and P(18). Emission from levels with J > 17 is weak because the predissociation rate is larger than the spontaneous emission rate. (Courtesy F. Launay and J. Y. Roncin.) (6) The CO A ll—X1 + (0,0) band in emission (bottom) and absorption (top). The a 3 + —X1 +(8,0) band lines appear in absorption because the A1 FI a 3 + spin-orbit interaction causes a small amount of A1 character to be admixed into the nominal a 3 + levels. These a —X lines are absent from the emission spectrum because collisional quenching and radiative decay into a3II compete more effectively with radiative decay into X1 + from the long-lived a 3 + state than from the short-lived A1 state. In addition, collisions and radiative decay into a3II cause the P(31) extra line (E) (arising from a perturbation by d3A v = 4) to be weakened in emission relative to the main line (M). (Courtesy F. Launay, A. Le Floch, and J. Rostas.)...

The mechanism of a predissociation may be characterized by measurements of the lifetime, rv, of each vibrational level or, even better, tvj, of every rotational level, carefully extrapolated to zero pressure. When the two unknown rates that appear in Eq. (7.4.6) have similar magnitudes, it is necessary to partition the observed total decay rate into tt and rnr. If the radiative lifetime is known for a non-predissociated level of the same electronic state, rT can be calculated for predissociated levels assuming an //-independent value for the electronic transition moment. The nonradiative lifetime is then deduced by subtraction of 1 /tt from the experimental 1/t value as follows ... 

When the predissociation rate is so much larger than the radiative decay rate that the fluorescence quantum yield is too low to measure a radiative decay rate directly, it is possible to infer the decay rate of the parent molecule from the effect of a static magnetic field on the polarization of a photofragment (Buijsse and van der Zande, 1997). 

Collisions destroy the coherences associated with the initially prepared state and induce transitions between rotational levels. This results in redistribution of population between all interacting levels but the overall population (the trace of the density matrix) is not affected and decays only radiatively with the rate k Pss + Puu)- Collisions, thus, modify the form of the excited-state decay but the overall fluorescence yield remains equal to one unless the levels s, u, and/or /, m are subjected to additional nonradia-tive decay processes (e.g., in the case of predissociation). 

The absorption coefficient of Bt2 in the visible region is intermediate between those of Oi and l2- Hence for Bt2, fluorescence studies are more difficult, and bromine has only recently attracted attention. As for I2, large variations of lifetime and cross-sections as a function of v have been reported, and the short lifetime of the excited state (less than anticipated from the absorption coefficient) indicates that for Bt2 the radiative lifetime contributes little to the measured lifetime, and that non-radiative processes are very important. Capelle, Sakurai, and Broida suggest that the predissociation rate is proportional to the inverse square of the molecular mass. However, the relatively large bandwidth used by these workers (0.1—0.8 nm) makes such a conclusion doubtful, and the variation of lifetime with vibrational-rotational state would seem to be more complex, as recently found by McAfee and Hozack. ... 

The investigation of fast processes, such as electron motions in atoms or molecules, radiative or collision-induced decays of excited levels, isomerization of excited molecules, or the relaxation of an optically pumped system toward thermal equilibrium, opens the way to study in detail the dynamic properties of excited atoms and molecules. A thorough knowledge of dynamical processes is of fundamental importance for many branches of physics, chemistry, or biology. Examples are predissociation rates of excited molecules, femtosecond chemistry, or the understanding of the visual process and its different steps from the photoexcitation ofrhodopsin molecules in the retina cells to the arrival of electrical nerve pulses in the brain. 

Figure 7.14 clearly reveals the deviation from the expected, calculated radiative lifetime beyond v = 3. Using these calculated unperturbed values for T, the predissociation rate constants can be extracted from the measured radiative lifetime values (see Table 7.1 for a summary), and these in turn can be used to deduce information about the quantum-mechanical coupling matrix elements. 

Predissociation of molecules in excited states plays a very important role in atmospheric processes. Details of the competition between the radiative and radiationless transitions for 02 and OH are described in Hess et al. The potential curves for H states of NO are shown in Figure 12 together with the important perturber state a n which causes predissociation via spin-orbit coupling. The calculated data for the predissociation rate k, the lifetime, and the line width F for the low vibrational levels of Fl and two rotational levels N are given in Table 2. The calculations predict the predissociation process even at the v = 0 level to be distinctly faster than the radiative transition (r = 70 ns calculated. 

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