Landau collision integral

Let us first consider Eq. (3.68) for the distribution function of free particles. The contribution of the two-particle collision then gives the well-known Landau collision integral... 

In principle, such approximations may serve as a basis of the description of partially ionized plasmas, if we have to take into account ionization and recombination. However, because of the long range of Coulomb interaction, the Landau collision integral (3.110) and such integrals of type (3.119) are divergent. Such divergencies may be avoided by an appropriate screening. The simplest way to do this is to replace the... 

The Chapman-Enskog procedure to approximate the distribution functions /j, /e by a linear perturbation ansatz, the Landau form of the Coulomb collision integral together with the small mass ratio me/m expansions in the classical work of Braginskii results in the friction term R... 

Here d,e is the classic Poisson bracket, e is the total energy with the accoimt of self-consistent field, l(p) is the collision integral of Boltzmann-Landau type, the kernel r(p,pf) and the collision cross-section in l( ) are expressed through the amplitude of binary quasiparticle scattering. 

Fig. 8. Relative velocity dependence of integral cross sections calculated for Na + O collisions for the indicated exit channels. The solid curve is the charge transfer cross section calculated using a multichannel Landau-Zener formalism (see text). The dashed curve is the two-state Landau-Zener cross section. Charge transfer calculations by van den Bos are indicated by triangles. Full circles and squares are the respective excitation channels as determined using the multichannel Landau-Zener model.

Paulsen et al. (1972) developed an optical model for vibrational relaxation in reactive systems. Only collinear atom-diatom collisions were considered, i.e. impact parameter dependencies were omitted. The model was applied to vibrational relaxation of electronically excited I2 in inert gases, in which case dissociation of I2 is responsible for flux loss. Olson (1972) used an absorbing-sphere model for calculating integral cross sections of ion-ion recombination processes A++B ->A + B + AE, with A or B atoms or molecules. He employed the Landau-Zener formula to obtain a critical crossing distance Rc, and assumed the opacity to be unity for distances... 

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