Classical-Path Calculation of the Impact-Broadening Operator for the Stark Broadening ofHα

The impact-broadening operator $\Phi$ for the hydrogen line ${\mathrm{H}}_{\alpha }$ is calculated by solving numerically for the $S$ matrices using the straight-line classical-path approximation. All contributing multipoles in the perturber- (free-electron-) atom interaction [$V\left(t\right)\mathrm{}$] are included; time ordering of the operators in the $S$ matrices is retained. The matrix elements are compared with previous approximations based on the same model; the effects on the ${\mathrm{H}}_{\alpha }$ line profile are considered.