Time-dependent formulation of the two-dimensional model of resonant electron collisions with diatomic molecules and interpretation of the vibrational excitation cross sections

Abstract

A two-dimensional model of the resonant electron-molecule collision processes with one nuclear and one electronic degree of freedom introduced by K. Houfek, T. N. Rescigno, and C. W. McCurdy [Phys. Rev. A 73, 032721 (2006)] is reformulated within the time-dependent framework and solved numerically using the finite-element method with the discrete variable representation basis, the exterior complex scaling method, and the generalized Crank-Nicolson method. On this model we illustrate how the time-dependent calculations can provide deep insight into the origin of oscillatory structures in the vibrational excitation cross sections if one evaluates the cross sections not only at sufficiently large time to obtain the final cross sections, but also at several characteristic times which are given by the evolution of the system. It is shown that all details of these structures, especially asymmetrical peaks, can be understood as quantum interference of several experimentally indistinguishable processes separated in time due to a resonant capture of the electron and the subsequent vibrational motion of the negative molecular ion. Numerical results are presented for the ${\mathrm{N}}_{2}$-like, NO-like, and ${\mathrm{F}}_{2}$-like models and compared with ones obtained within the time-independent approach and within the local complex potential approximation.