A Hard Sphere Model for Bimolecular Recombination of Heavy Ions

We propose a hard sphere model of bimolecular recombination RM+ + X– → MX + R, where M+ is an alkali ion, X– is a halide ion, and R is a neutral rare gas or mercury atom. Calculations are carried out for M+ = Cs+, X– = Br–, R = Ar, Kr, Xe, Hg, for collision energies in the range from 1 to 10 eV, and for distributions of the RM+ complex internal energy corresponding to temperatures of 500, 1000, and 2000 K. The excitation functions and opacity functions of bimolecular recombination in the hard sphere approximation are found, and the classification of the collisions according to the sequences of pairwise encounters of the particles is considered. In more than half of all the cases, recombination occurs due to a single impact of the Br– ion with the R atom. For the recombination XeCs+ + Br–, the hard sphere model enables one to reproduce the most important characteristics of the collision energy dependence of the recombination probability obtained within the framework of quasiclassical trajectory calculations.

Time Delay in Electron Collision with a Spherical Target as a Function of the Scattering Angle

We have studied the angular time delay in slow-electron elastic scattering by spherical targets as well as the average time delay of electrons in this process. It is demonstrated how the angular time delay is connected to the Eisenbud–Wigner–Smith (EWS) time delay. The specific features of both angular and energy dependencies of these time delays are discussed in detail. The potentialities of the derived general formulas are illustrated by the numerical calculations of the time delays of slow electrons in the potential fields of both absolutely hard-sphere and delta-shell potential well of the same radius. The conducted studies shed more light on the specific features of these time delays.

Turbulence in Large-Scale Two-Dimensional Balanced Hard Sphere Gas Flow

In recent works, we developed a model of balanced gas flow, where the momentum equation possesses an additional mean field forcing term, which originates from the hard sphere interaction potential between the gas particles. We demonstrated that, in our model, a turbulent gas flow with a Kolmogorov kinetic energy spectrum develops from an otherwise laminar initial jet. In the current work, we investigate the possibility of a similar turbulent flow developing in a large-scale two-dimensional setting, where a strong external acceleration compresses the gas into a relatively thin slab along the third dimension. The main motivation behind the current work is the following. According to observations, horizontal turbulent motions in the Earth atmosphere manifest in a wide range of spatial scales, from hundreds of meters to thousands of kilometers. However, the air density rapidly decays with altitude, roughly by an order of magnitude each 15–20 km. This naturally raises the question as to whether or not there exists a dynamical mechanism which can produce large-scale turbulence within a purely two-dimensional gas flow. To our surprise, we discover that our model indeed produces turbulent flows and the corresponding Kolmogorov energy spectra in such a two-dimensional setting.