Orbiting collisions

Figure 10. Comparison of the velocity dependence of the disappearance cross-section of CHa+, formation cross-section of CH0 +, and Langevin orbiting collision cross-section, all as a function of reciprocal average kinetic energy of ions in the mass spectrometer source...

Orbiting collisions, in the sense that the polar angle changes >71 and the azimuth changes >2it, are not found. These types of collisions are not found with molecules that are only polarizable and also they are unimportant when the dipole term dominates. 

In the classical theory orbiting collisions are defined by the radicant in Eq. 2.2 having exactly two roots. Normally, at a fixed, low enough energy Et and small b, three roots, Rq > Rq > Rq, exist and x is finite. If the... 

The Solar System is not stable, neither is our planet. Both are chaotic, in which luck may allow a certain degree of stasis. Thus orbital collisions occur until there are few bodies left, and interactions become so infrequent that the large planets seem to have attained stability in orbit. On a planet, geochemistry and heat production sort themselves out until the structure of the planet and its tectonic behaviour seem stable. But neither orbits nor tectonics are truly stable. Catastrophic events can and will occur that can upset the system. Planets collide. The Earth has precipitated a core, probably frozen a magma ocean, and will eventually freeze and be still. To stabilize the surface of a planet such that life can exist for 4Ga surely needs restorative feedbacks, and perhaps luck also. 

We can estimate the rate constant for the collisional stabilization process, Reaction (7), by assuming that only those hard-core collisions that result from the long-range polarization force between the ion and the neutral molecule are important and that orbiting collisions have unit effectiveness for stabilizing the complex. Thus the rate constant of this reaction is estimated to be 1.1 X 10 cm mole sec from the expression... 

In order to extend the corresponding-states correlations to lower and higher temperatures, it is important to know the asymptotic forms of the that are dictated by the limiting forms of U(r) given in equations (11.12) and (11.13). The low-temperature asymptotic form can be found, from dimensional analysis and an argument based on capture cross sections due to orbiting collisions, to be... 

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