Numerically solvable model for resonant collisions of electrons with diatomic molecules

Abstract

We describe a simple model for electron-molecule collisions that has one nuclear and one electronic degree of freedom and that can be solved to arbitrarily high precision, without making the BornOppenheimer approximation, by employing a combination of the exterior complex scaling method and a finite-element implementation of the discrete variable representation. We compare exact cross sections for vibrational excitation and dissociative attachment with results obtained using the local complex potential approximation as commonly applied in the "boomerang" model, and suggest how this two-dimensional model can be used to test the underpinnings of contemporary nonlocal approximations to resonant collisions.

Probing the nonlocal approximation to resonant collisions of electrons with diatomic molecules

“…In a previous paper [1] (referred to hereafter as I) we introduced a simple two-dimensional model of electron collisions with diatomic molecules which enabled us to study the dynamics of inelastic resonant processes such as vibrational excitation…”

Calculation of vibrational excitation cross-sections in resonant electron-molecule scattering using the time-dependent wave packet (TDWP) approach with application to the 2Π CO− shape resonance

“…It is, therefore, a very pleasant surprise that our results indicate that the experimental structure in vibrational excitation cross-sections in the resonant e-CO scattering do emerge from the simple SCF level local complex potentials utilized by us and the cross correlation functions provide an unequivocal affirmation of the boomerang classification for the 2 ΠCOshape resonance. [1][2][3][4][5][23][24][25][26] There has been much debate and skepticism about the applicability of LCPs in the treatment of short lifetime resonances, [16][17][18][19][20][21][22] but our results show that simple local complex potentials can do justice to almost all features of the vibrational excitation cross-section profiles not only for e-H 2 and e-N 2 scattering 12 but for the e-CO scattering as well.…”

“…If the lifetime of the resonant anionic state Ais smaller than its vibrational period, then the anionic wave function decays before it can rebound from the right turning point of Aand for the lowest vibrational excitations, the resonance scattering cross-sections only show broad smooth peaks as a function of energy. [1][2][3][4][5][12][13][14][15][16][17][18][19][20][21][22] Vibrational structure in this case occurs only for higher level excitations of the target A since the larger inter-nuclear span of higher vibrational states permits an increase of the traversal/decay time and thereby sampling of interference structure between the A and Avibrational levels. 3,4,12 The role of the impinging electron in this case is to provide an impulse for quick decay of the compound anion and the 2 Σ + u H -2 shape resonance in e-H 2 scattering provides an example of the impulse model 3,4,12,13 for resonance decay.…”

Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model

“…For the latter we choose to provide numerical evidence by comparing the results with benchmark data which are obtained with a numerically solvable model of H + 2 in two dimensions, with one electronic and one nuclear coordinate. The model is similar to the two-dimensional model of resonant electron-molecule collisions, which was introduced in [15] and used to test the local and nonlocal theory of nuclear dynamics of these collisions [15,16].…”