Dipole Magnus approximation for electron-atom collisions: Excitation of the resonance transitions of Li, Na, and K

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Abstract
The Magnus expansion, to second order, has been used to solve the coupled-channel, symmetrized impact-parameter equations for electron-atom scattering. Collision integrals are evaluated in the dipole approximation, allowing both first- and second-order terms to be written in closed, analytic form. The numerical work is therefore essentially reduced to a matrix exponentiation for each value of the impact parameter, which can be efficiently carried out by the well-known diagonalization procedure. It thus becomes computationally feasible to handle problems involving a large number of closely coupled states. As a test case, the theory has been applied to electron-impact excitation of the resonance transitions of Li, Na, and K. The calculated cross sections were found to be in good agreement with experimental data over most of the intermediate-energy range. Thus far, the present method appears to be competitive with more sophisticated approaches and is readily applicable to complex processes, such as electron collisions with atoms in excited states.