Collisional cross section 3 + 3 conditions

Ammonia (NH3) and formaldehyde (H2CO) are among the best species for probing the physical conditions as they have many accessible lines coupling levels of different excitation energies, and their collisional cross sections have been accurately computed [36, 37]. 

The kinetic temperature cannot be directly measured from the observations but can be deduced from the analysis of the line profiles and molecular excitatiOTi as the level populations are also sensitive to the temperature. For an accurate determination of the physical conditions, including the kinetic temperature, the full set of the statistical equilibrium calculations must be solved. There are some freely available numerical codes, such as RADEX ([38], http //www.strw.leidenuniv.nl/moldata/ radex.html). They make use of extensive data bases of collisional cross sections, LAMDA (Leiden Atomic and Molecular DAtabase http //www.strw.leidenuniv.nl/ moldata/), and BASECOL (http //basecol.obspm.fr/), that are now part of the European initiative VAMDC (Virtual Atomic and Molecular Data Center http // www.vamdc.eu/). 

Many optical studies have employed a quasi-static cell, through which the photolytic precursor of one of the reagents and the stable molecular reagent are slowly flowed. The reaction is then initiated by laser photolysis of the precursor, and the products are detected a short time after the photolysis event. To avoid collisional relaxation of the internal degrees of freedom of the product, the products must be detected in a shorter time when compared to the time between gas-kinetic collisions, that depends inversely upon the total pressure in the cell. In some cases, for example in case of the stable NO product from the H + NO2 reaction discussed in section B2.3.3.2. the products are not removed by collisions with the walls and may have long residence times in the apparatus. Study of such reactions are better carried out with pulsed introduction of the reagents into the cell or under crossed-beam conditions. 

Kohn-variational (12), Schwinger-variational, (13) R-Matrix (14), and linear algebraic techniques (15,16) have been quite successful in calculating collisional and phH oTo nization cross sections in both resonant and nonresonant processes. These approaches have the advantage of generality at the cost of an explicit treatment of the continuous spectrum of the Hamiltonian and the requisite boundary conditions. In the early molecular applications of these scattering methods, a rather direct approach based on the atomic collision problem was utilized which lacked in efficiency. However in recent years important conceptual and numerical advances in the solution of the molecular continuum equations have been discovered which have made these approaches far more powerful than those of a decade ago... 

In the previous sections a model of the frequency-dependent collisional friction has been derived. Because the zero-frequency friction for a spherical particle in a dense fluid is well modeled by the Stokes-Einstein result, even for particles of similar size as the bath particles, there has been considerable interest in generalizing the hydrodynamic approach used to derive this result into the frequency domain in order to derive a frequency-dependent friction that takes into account collective bath motions. The theory of Zwanzig and Bixon, corrected by Metiu, Oxtoby, and Freed, has been invoked to explain deviation from the Kramers theory for unimolec-ular chemical reactions. The hydrodynamic friction can be used as input in the Grote-Hynes theory [Eq. (2.35)] to determine the reactive frequency and hence the barrier crossing rate of the molecular reaction. However, the use of sharp boundary conditions leads to an unphysical nonzero high-frequency limit to Ib(s). which compromises its utility. 

The results of these studies were clear. At very low pressures (ca 0.01 torr) where the collision interval exceeds the lifetime ( 10 sec) by a factor of about 100, collisional influences on electronic relaxation disappear. Yet nonradiative decay still persists, and in fact about 70% of the decay from the isolated molecules uses that channel. Furthermore, observations of butene-2 isomerization - indicated that the triplet state is present under these conditions so that at least part of this isolated molecule relaxation is intersystem crossing. The thermal data described in preceding sections imply that the nonradiative channel may be entirely intersystem crossing, but the butene-2 method cannot confirm this. That method does not give quantitative results at very low pressures. ... 

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