Radiative collisions theory

Specifically, the collision-induced absorption and emission coefficients for electric-dipole forbidden atomic transitions were calculated for weak radiation fields and photon energies Ha> near the atomic transition frequencies, utilizing the concepts and methods of the traditional theory of line shapes for dipole-allowed transitions. The example of the S-D transition induced by a spherically symmetric perturber (e.g., a rare gas atom) is treated in detail and compared with measurements. The case of the radiative collision, i.e., a collision in which both colliding atoms change their state, was also considered. 

Fig. 15.10 Cross sections as a function of rf field strength for the first four orders of sideband resonances of the K 29s + K 27d radiative collisions in a 4 MHz rf field, (a) The zero-photon resonant collision cross section, (b) the +1 sideband resonance, (c) the —2 sideband resonance, and (d) the +3 sideband resonance. The solid line shows the experimental data, the bold line indicates the prediction the Floquet theory, and the dashed fine is the result of numerical integration of the transition probability (from ref. 17).

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]. 

Using gas kinetic molecular theory, show that under typical atmospheric conditions of pressure and temperature corresponding to an altitude of 5 km (see Appendix V) collisional deactivation of a C02 molecule will be much faster than reemission of the absorbed radiation. Take the collision diameter to be 0.456 nm and the radiative lifetime of the 15-/rm band of C02 to be 0.74 s (Goody and Yung, 1989). 

Arnold et al.24 have calculated radiative lifetimes for the various collision complexes of singlet molecular oxygen on the basis of a collision time of 10"13 sec. The data for wavelengths and transition probabilities are presented in Table III. A recent paper25 describes the theory of double electronic transitions, and gives calculated oscillator strengths for the oxygen systems. 

The fluorescence yield values (tu ) of the L-subshell and the Coster-Kronig transition probabilities (/y) are listed by Krause (1979). The relative radiative transition probabilities Fij) of the ith subshell contributing to the jth peak can be taken from Cohen (1990). The ionization cross-sections can be theoretically calculated using the ECPSSR theory (see Sect. 1.11.3 for different theories on ion-atom collision). 

In this period there was a great attention about the molecularity of mechanisms and of particularly interest was a debate about unimolecular reactions. The debate was that about the so called Radiative Theory (King Laidler, 1984), proposed mainly by Jean Baptiste Perrin (1870-1942), around 1917. Perrin propwsed that unimolecular processes was activated only by blackbody radiation. The hypwthesis, fallacious, continued for nearly ten years involving many and important figures as Einstein for example. Even being wrong Radiative Theory represents an interesting case study and boosted the research on different activation causes other than thermal collisions. 

Radiative processes and rotational excitation collisions preserve the para or ortho character of the Hj molecule due to the conservation of the total parity of the system (AJ even selection rule). However, at low collision energies, H, (J) collide with in a reactive process which proceeds through the strongly coupled intermediate complex I which leads to a redistribution of the rotational states of Hj without any selection rule on J and induces ortho-para transitions. This is the most simple reactive collision system for which the corresponding electronic potential surface is known (Giese Gentry, 1974). A most dynamically biased (MDB) statistical theory has been developed (Schlier, 1980) which has been tested to be... 

Under normal circumstances, this occurs by collisions with a third-body species and the reaction rate therefore depends on total pressure. Such a mechanism is impossible in the super-rarified environment of interstellar space. However, the kinetics of such reactions are of indirect interest to astrochemists on two counts. First, treatments of radiative association [22], which is implicated in the formation of molecular species in interstellar clouds, have much in common with those of three-body association [23]. Second, the rate constants for radical association in the limit of high pressure correspond to those for formation of the energised associated molecule, since all such species are collisionally stabilised in the limit of high pressure. Consequently, the values of kggg and how they vary with temperature provide an important test of theories of reactions occurring over attractive potential energy surfaces [6]. 

Although radiative association has been occasionally studied in the laboratory (e.g., in ion traps ), most experiments are imdertaken at densities high enough that ternary association, in which collision with the background gas stabihses the complex, dominates. A variety of statistical treatments, such as the phase-space theory, have been used to study both radiative and ternary association. These approximate theories are often quite reliable in their estimation of the rate coefficients of association reactions. In the more detailed treatments, microscopic reversibility has been applied to the formation and re-dissociation of the complex. Enough experimental and theoretical studies have been undertaken on radiative association reactions to know that rate coefficients range downward from a collisional value to one lower than lO cm s and depend strongly on the lifetime of the complex and the frequency of photon emitted. The... 

The broadening Fj is proportional to the probability of the excited state k) decaying into any of the other states, and it is related to the lifetime of the excited state as r. = l/Fj . For Fjt = 0, the lifetime is infinite and O Eq. 5.14 is recovered from O Eq. 5.20. Unfortunately, it is not possible to account for the finite lifetime of each individual excited state in approximate theories based on the response equations (O Eq. 5.4). We would be forced to use a sum-over-states expression, which is computationally intractable. Moreover, the lifetimes caimot be adequately determined within a semiclassical radiation theory as employed here and a fully quantized description of the electromagnetic field is required. In addition, aU decay mechanisms would have to be taken into account, for example, radiative decay, thermal excitations, and collision-induced transitions. Damped response theory for approximate electronic wave functions is therefore based on two simplifying assumptions (1) all broadening parameters are assumed to be identical, Fi = F2 = = r, and (2) the value of F is treated as an empirical parameter. With a single empirical broadening parameter, the response equations take the same form as in O Eq. 5.4 with the substitution to to+iTjl, and the damped linear response function can be calculated from first-order wave function parameters, which are now inherently complex. For absorption spectra, this leads to a Lorentzian line-shape function which is identical for all transitions. 

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