Collective radiative effects

Ensembles of N Rydberg atoms prepared in the cavity also exhibit interesting effects. The atoms couple symmetrically to the field mode and collective radiative effects are observable even if the atomic sample is made of a few radiators only. Tests of superradiance theory and related radiative effects have been studied on these systems which-when N goes down to unity-constitute the smallest maser systems ever achieved. 

The effect of the substitution of a heavy-atom directly onto the nucleus of aromatic compounds (internal heavy-atom effect) on intercombinational radiative and nonradiative processes can be seen by examination of experimental data obtained for naphthalene and its derivatives. The data obtained by Ermolaev and Svitashev<104) and analyzed by Birks(24) to obtain individual rate constants for the various processes are collected in Table 5.9. 

When comparing different solar collectors it is important to take into account the different quantities of radiation collected in each case. For a given receiver, the radiative power collected increases with aperture size (i.e., with concentration). However, this is not a linear effect and, for instance, a CPC with a two suns concentration ratio provides twice the aperture area of a nonconcentrating CPC. Nevertheless the power received by the tubular absorber is not doubled, because the former CPC misses around half of the diffuse radiation. Other important consideration is the fact that concentrating reactors are faster simply because they collect more radiation, which is associated with larger collector area. 

Previous work has indicated that the physical state of the deposit can have a significant effect on the radiative properties, specifically molten deposits show higher emissivities/absorptivities than sintered or powdery deposits (1). Although thin, molten deposits are less troublesome from a heat transfer aspect than thick, sintered deposits, molten deposits are usually more difficult to remove and cause frozen deposits to collect in the lower reaches of the furnace where physical removal then becomes a problem for the wall blowers. 

From the best fits, the kinetic rate constants, and kb, and the ratio of the radiative rate constants, A/B, of the resonantly coupled spin levels could be obtained. The lifetimes of the triplet sublevels in the various chelates [56] are collected in Table 2. Evidently, the sublevel lifetimes are on the millisecond time scale, and about three orders of magnitude shorter than the phosphorescence lifetimes of the free ligand molecules (bpy Tp = 0.8 s phen Tp=1.4 s [60, 61]). For [Rh(bpy)3] (0104)3 the radiative rate constants are in the ratio T Ty. Tz= 10 1 2, showing that the sublevel is the most active in the radiative as well as non-radiative processes [62]. The shortening of the triplet state sublevel lifetimes for the Rh(III)-chelates as compared to the triplet sublevel lifetimes of the free ligand molecules is reminiscent of the heavy atom effect as, for example, observed for halonaphthalenes [33-35]. In the latter, the mixing of states with UTT and Vtt excitations is enhanced by SOC within the heavy atom. In... 

However, as mentioned above simple lifetime shortening cannot be responsible for the wide lines seen in other molecules. For example, in many fluorescent molecules the observed lifetimes are near the lifetime calculated from Eq. (5), yet the observed width of the optical transitions remain far broader than the natural width. A common dye molecule such as rhodamine 6G has very broad optical absorption bands with widths on the order of 1000 A, but it has a measured radiative lifetime on the order of 10 nsec. Homogeneous lifetime broadening is clearly not the reason that the transitions are broad. The line width of the dye electronic transition must be the result of some combination of heterogeneous environment, coupling to vibrational transitions, and large-scale collective modes. An important goal of some low-temperature studies has been to separate these effects, because each is affected rather differently by temperature. 

Atmospheric and oceanic scientists often use the word parameterization to describe this formalism. In our jargon, the goal is to parameterize the collective effects of small-scale processes on large-scale processes. Because small-scale processes are sundry, the parameterization problem is multifaceted. Typically, small-scale processes are broken down into distinct classes of problems—clouds, radiative transfer, hydrometeor interactions, surface interactions, small-scale turbulence, chemistry, and so on—processes that can be thought of as the atoms. Although one may be interested only in the net effect of all of these processes, atomization facilitates idealization and subsequent study. 

Collective effects near threshold in inner shell photoionization include along with RPAE corrections also relaxation processes. They are a consequence of the fact that near inner shell threshold the photoelectron leaves the atom slowly and all other electrons have sufficiently time to feel the field of the vacancy created as well as its decay-Auger or radiative. It is very essential that because the field variation takes place after vacancy creation, the photoelectron wave function must be ortogonalized to all other electron states of the atom - otherwise it includes the interaction with the final state of the ion before its formation. 

Other processes eventually give rise to non-diagram lines, usually very weak ones (collective excitation, radiative Auger effect, etc.). 

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