Abstract
The expression of the electron broadening operator including the effect of penetrating collisions, i.e., for which the incoming electron enters the extent of bound-electron wave-functions, is rather complicated, even for hydrogen. It involves integrals of special functions, the evaluation of which deserves scrutiny. We present a simple approximate form of the electron collision operator for hydrogen including penetration effects, both in direct and interference terms. The new expression is accurate and easy to compute. In the Penetration Standard Theory, the collision operator is convergent whatever the value of the maximum impact parameter. However, when penetration theory is not valid anymore, it should be questioned. We discuss the problem of strong collisions when penetration effects are taken into account.
Highlights
Line-shape profiles are important ingredients of opacity and emissivity calculations, as they often serve as a diagnostics of laboratory or astrophysical plasmas
We found an exact expression of such functions, which enabled us to derive a simple approximate form of the electron collision operator for hydrogen including penetration effects, both in direct and interference terms
A semi-classical model for the electron broadening operator including the effect of penetrating collisions on isolated lines of hydrogen, i.e., collisions in which the incoming electron enters the extent of bound-electron wave-functions, was developed by Alexiou and Poquérusse
Summary
Line-shape profiles are important ingredients of opacity and emissivity calculations, as they often serve as a diagnostics of laboratory or astrophysical plasmas. The computer-simulation methods based on the molecular-dynamics approach, have been successfully applied to calculate the spectral line shapes [7] In these computations, which are very efficient but expensive, the time-evolution operator for the simple model of the plasma is obtained by solving numerically the time-dependent Schrödinger equation accounting for the many-body interactions between the emitter and the surrounding moving particles. We found an exact expression of such functions, which enabled us to derive a simple approximate form of the electron collision operator for hydrogen including penetration effects, both in direct and interference terms.
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