Transition radiation

Various attempts have been made to measure the formation of peroxides in isolated proteins and low density lipoproteins upon exposure to various oxidizing agents including ionizing radiation, transition metals involved in Fenton reaction, peroxyl radicals, photosensitizers and enzymatic oxidative systems (for reviews see References 195, 234 and 241). 

Furthermore the dipole transition 2p-ls ean oeeur. The ealculated value for the prohahility of this transition is / i=7.910 s. This value is signifieantly higher than the eorresponding non-relativistie value [3], It is important to note that the value P3 is larger than the probability of the radiation transition pm-psn and that of the non-radiative transition pia - fm. The next transition p a fm oeeurs without radiation during the time 10 s, with ejeetion of the muon. 

From the data of Hoogschagen and Gorter (104), the oscillator strength of the 5D4-+7F6 transition was obtained. By means of the Ladenburg formula, the spontaneous coefficient A46 was calculated. Using the relative-emission intensities, the rest of the A4J spontaneous-emission coefficients could be calculated. From these and a measured lifetime of 5.5 x 10 4 sec at 15°C, he calculated a quantum efficiency of 0.8 per cent. Kondrat eva concluded that the probability of radiationless transition for the trivalent terbium ion in aqueous solution is approximately two orders of magnitude greater than for the radiation transition. 

A molecule could also relax from S, or T, to S0 by emitting a photon. The radiational transition Sj —> S0 is called fluorescence (Box 18-2), and the radiational transition T, —> S0 is called phosphorescence. The relative rates of internal conversion, intersystem crossing, fluorescence, and phosphorescence depend on the molecule, the solvent, and conditions such as temperature and pressure. The eneigy of phosphorescence is less than the energy of fluorescence, so phosphorescence comes at longer wavelengths than fluorescence (Figure 18-14). 

The photon hvx emitted in a radiating transition is reabsorbed with a certain probability by another molecule X or Y. By absorbing the photon the molecule makes a transition into the excited states X and Y, respectively. Thus the Y molecules are excited only by the radiating and nonradiating transfer of the excitation energy. The photons hvY emitted in a radiating transition which do not undergo self-absorption leave the scintillator. 

The values in this equation which depend on the concentration c of the Y molecules are obtained by a simple calculation from the process scheme. On the condition that the radiating transitions are not temperature dependent and the nonradiating transitions satisfy a Boltzmann distribution... 

Fig. 1.1. Scheme of optical pumping (orientation) of the 2 51/2-state the figures show the relative probabilities of radiational transition. 

From the form of Eq. (2.33) it becomes understandable why the anisotropy of polarization 7Z is sometimes called the degree of alignment. From the point of view of the determination of the magnitude of the polarization moments bPo the measurement of 71 is preferable, as compared with that of V, all the more so if one bears in mind that the population bPo appears only as a normalizing factor for all other bPQ and does not influence the shape of the probability density p(B,multipole moment dependence of V and 71 for various types of radiational transition (A = 0, 1) can be obtained using the numerical values of the Clebsch-Gordan coefficient from Table C.l, Appendix C. 

In a similar way the whole population is transferred from the magnetic sublevels of state J to state J" according to the scheme in Fig. 3.16, under conditions of intensive stimulated radiational transitions. As a result, all magnetic sublevels Mjn, except Mjn = J", will be equally populated, whilst the sublevels Mjn = J" will be completely empty . In this situation we have a picture which is directly opposite to that of the J" level, where only the sublevels Mjn = J" are populated. The alignment... 

The intensity of the fluorescence appearing in the radiational transition of the molecule from level J upon level J (see Fig. 3.14) may be calculated by means of the formula [133]... 

With regard to these radiation transitions, the Hamiltonian of the system available in the direct external electric field can be written in the small carrier concentration approximation as... 

Normal direct-line emission occurs when an atom is in a higher excited state and undergoes a radiational transition to a lower excited state above the ground state. The radiation in this process will be of longer wavelength than the radiation absorbed. 

Thermally assisted stepwise line emission may occur in atoms radiationally excited to a metastable state above the ground state and then thermally excited to an upper excited state, which subsequently undergoes a radiational transition to the ground state or to an excited state of energy lower than that of the radiation-ally excited state. The emitted radiation has a shorter wavelength than the absorbed radiation. 

If a sample of molecules with inverted populations is placed in an optical cavity which may consist, for instance, of two suitably aligned mirrors (see next section), induced radiation can change the densities N and N of Eq. (1). The interaction of a system with population inversion with a radiation field of the right frequency v can be described in the so-called rate equation approximation. The simplified rate equations for the laser are obtained as follows if two states Ni, Na are considered with the energy difference AE =hvia connected by a radiational transition (13). 

In direct-line fluorescence, an atom is excited (usually from the ground state) by a radiation source, and then undergoes a direct radiational transition to a metastable level above the ground state. An example is absorption at the 283.31 nm line by ground-state lead atoms, with subsequent emission at 405.78 nm. Xs with resonance fluorescence, direct-line fluorescence may be excited by absorption of a nonresonance line (e.g., tin fluorescence at 333.06 nm). 

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