Radiative relaxation time

The radiative relaxation time tt of a vibrational mode v is inversely proportional to the band strength S . (See, for example, R. M. Goody, Atmospheric Radiation I. Theoretical Basis, Oxford Univ. Press, Oxford, 1964.) Thus one finds, for example, that the radiative lifetime of the bending mode, v2, of H20 is about 0.07 sec. 

However, for excited atoms in coUisionless conditions only the radiative relaxation channel is open. Here coUisionless means that the time between colhsions is much longer than the radiative relaxation time. 

Figure J. 28. Globally averaged infrared radiative relaxation time deduced from data provided by UARS and LIMS. Note the increase in the lower stratospheric relaxation time in response to enhanced aerosol load after the eruption of Mt. Pinatubo (UARS measurements). From Mlynczak et al. (1999).

Using the above results of the lifetimes together with the radiative relaxation times estimatedfrom / and we can estimate the intensity ratio R(2 Ag/ BJ of the fluorescence from the 2 Ag level to that from the B level. The estimated value of 0.4 agrees with the experimental result of 0.8. The agreement supports the validity of the estimated above. 

The 300s oscillations have been mostly observed as velocity oscillations of 80+ 20m/s in photospheric spectral line profiles. Since they are not purely isothermal, they also appear as temperature fluctuations, and the comparison of phases between temperature and velocity can give indication on the propagation character of the waves. In the photosphere, the radiative relaxation time is of the order of Is and the wave is isothermal. 

This time increases with height and in the upper photosphere, HUDSON and LINDSEY (1974) have convincingly observed temperature fluctuations at the 300-s period, with an amplitude of 3.OK rms. This work has been repeated and extended by LINDSEY (1976) and results are summarized in Table 3. The main conclusions are toward a rather short radiative relaxation time compared to (300/2ir)s, and toward evanescent modes of the waves. 

Quantum well interface roughness Carrier or doping density Electron temperature Rotational relaxation times Viscosity Relative quantity Molecular weight Polymer conformation Radiative efficiency Surface damage Excited state lifetime Impurity or defect concentration... 

Here, a is a stretched factor, and Xdark is the characteristic time of the non-radiative relaxation. 

Trivalent samarium activated minerals usually display an intense luminescence spectrum with a distinct hne structure in the red-orange part of the spectrum. The radiating term 65/2 is separated from the nearest lower level 11/2 by an energy interval of 7,500 cm This distance is too large compared to the energy of phonons capable to accomplish an effective non-radiative relaxation of excited levels and these processes do not significantly affect the nature of their spectra in minerals. Thus all detected lines of the Sm " luminescence take place from one excited level and usually are characterized by a long decay time. 

At high viscosities or low temperatures, dielectric relaxation time xj may be larger than the mean radiative lifetime t/ of the molecule. This may decrease the O—O separation between absorption and emission. On the other hand, at high temperatures solvent relaxation may be promoted thermally decreasing xd and O—O separation may again decrease. A maximum value for Av (O—O) is expected at some intermediate temperatures. Besides the relaxation effects, the O—O separation can also be affected by environmental modification of the potential energy surfaces. 

It is possible to perturb a spin equilibrium by photoexciting one of the isomers. Among the possible radiative and nonradiative fates of the excited state is intersystem crossing to the manifold of the other spin state. Internal conversion within this manifold ultimately results in the nonequilibrium population of the ground state. If these processes are rapid compared with the relaxation time of the spin equilibrium, then the dynamics of the ground state spin equilibrium can be observed. This experiment was first performed for spin equilibria with a coordination-spin equilibrium of a nickel(II) complex (85). More recently a similar phenomenon has been observed in the solid state at low temperatures (41). The nonequilibrium distribution can be trapped for long periods at... 

This photoperturbation technique has been applied to a number of different spin-equilibrium complexes. Its success is apparently due to the fact that the relaxation times of the spin equilibria are longer in each case than the radiative and nonradiative processes in the excited states. 

The possibility of deactivation of vibrationally excited molecules by spontaneous radiation is always present for infrared-active vibrational modes, but this is usually much slower than collisional deactivation and plays no significant role (this is obviously not the case for infrared gas lasers). CO is a particular exception in possessing an infrared-active vibration of high frequency (2144 cm-1). The probability of spontaneous emission depends on the cube of the frequency, so that the radiative life decreases as the third power of the frequency, and is, of course, independent of both pressure and temperature the collisional life, in contrast, increases exponentially with the frequency. Reference to the vibrational relaxation times given in Table 2, where CO has the highest vibrational frequency and shortest radiative lifetime of the polar molecules listed, shows that most vibrational relaxation times are much shorter than the 3 x 104 /isec radiative lifetime of CO. For CO itself radiative deactivation only becomes important at lower temperatures, where collisional deactivation is very slow indeed, and the specific heat contribution of vibrational energy is infinitesimal. Radiative processes do play an important role in reactions in the upper atmosphere, where collision rates are extremely slow. 

To obtain the equilibrium result computationally, we repeat the procedure of Eq. (36) to Eq. (39) while explicitly taking into- aecount the M averaging. We note that the population after laser excitation, but before radiative relaxation, consists of the weighted sum of the results of 2 X (27 +1) computations NjJ (27 + 1) times the results of laser excitation starting solely with molecules in Z), M) for M = — 7,..., 7, plus NLf 2J +1) times the results of laser excitation starting solely with molecules in L, M) for M = — 7,. .., 7. 

From inspecting the atomic database of the EIRENE code [31], which is used in many applications to a large number of different tokamaks, including for the ITER design, in particular its collisional-radiative models for molecules, it was clear that matters can be more complicated. The relaxation time for establishing a vibrational distribution of the ground state molecule is comparable to the transport time of the molecule, hence the applicability of local collisional-radiative approximations is questionable. Furthermore, one of the two atoms created in dissociative recombination is electronically excited, and, hence, can be ionized very effectively even at low divertor plasma temperatures (instead of radiative decay). In this case, the whole chain of reactions would be just an enhanced ( molecular activated ) dissociation (MAD, i.e., dissociative excitation of those H]]", which have been produced... 

ADAS is centred on generalized collisional-radiative (GCR) theory. The theory recognizes relaxation time-scales of atomic processes and how these relate to plasma relaxation times, metastable states, secondary collisions etc. Attention to these aspects - rigorously specified in generalized collisional-radiative theory - allow an atomic description suitable for modeling and analyzing spectral emission from most static and dynamic plasmas in the fusion and astrophysical domains [3,4]. 

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