Simple model for the resonant vibrational excitation of molecules and its application to Li2 and N2

A simple model for the resonant vibrational excitation of a molecule by electron impact is proposed in which the potential curves of the electronic states of the molecule and its resonant anion are replaced by those of linear harmonic oscillators of arbitrary frequencies and equilibrium internuclear separations. A closed-form expression for the excitation amplitude is derived. Useful recursion relations among amplitudes are obtained which allow convenient evaluation of cross sections for any inelastic or superelastic vibrational transition. The model is used to generate the cross sections for vibrational excitation of Li_2 and N_2 by the impact of low-energy electrons

Exact evaluation and recursion relations of two-center harmonic oscillator matrix elements

Using vibrational wave functions of two relatively displaced harmonic oscillators of arbitrary frequencies, Franck–Condon overlap integrals and matrix elements of x^l, exp(−2cx), and exp(−cx^2) (x is the internuclear separation) are obtained. Useful three‐term, four‐term, and five‐term recursion relations among these matrix elements are derived. It is shown that all of the relevant matrix elements can be obtained from a mere knowledge of the lowest two Franck–Condon overlap integrals. Results are illustrated by computation of Franck–Condon factors for the A ^1∑^+_u –X ^1∑^+_g and the B ^1Π_u –X ^1∑^+_g systems of ^7Li_2

Exact time-dependent evolution of electron velocity distribution functions in a gas using the Boltzmann equation

A numerical technique, starting from the Boltzmann equation, for obtaining the time-dependent behavior of the electron-velocity distribution function in a gas is presented. A unique feature of this technique is that, unlike previously used procedures, it does not make use of any expansion of the distribution function. This allows the full anisotropy of the distribution function to be included in the solution. Furthermore, the problem associated with multiterm-expansion techniques of choosing a sufficient number of terms for convergence is completely avoided. The distribution function obtained by the present method is exact and, in principle, contains all of the expansion terms of the previous procedures. Details of the algorithm, including stability conditions, treatment of the boundaries, and evaluation of the collision integrals, are presented. This technique has been applied for obtaining the time-dependent behavior of electron swarms in gaseous argon and neon for various values of E/N (the ratio of the applied uniform dc field to the gas density), and the corresponding results are presented

A novel algorithm for calculating the time evolution of the electron energy distribution function in gaseous discharges

We are presenting a novel numerical technique for obtaining the time evolution of the electron velocity and electron energy distribution functions in the presence of a uniform electric field. Using this technique, the various swarm parameters can be evolved for sufficiently long times so that equilibrium can be reached without incurring any numerical instabilities. Results are presented for electron swarms in gaseous neon for various values of E/N