Semi-classical Stark broadening calculations of HeI lines in a non-ideal plasma

New semi-classical collision functions are used to compute the inelastic contribution to the impact electronic total width, by considering three interaction potentials (Coulomb Debye, Cut-off, and Ion Sphere). Numerical results are calculated for the neutral helium 6678 Å ($2^{1}\rm P\degr{-}3^{1}D$) and 5876 Å ($2^{3}\rm P\degr{-}3^{3}\rm D$) visible lines. The lines corresponding to these transitions are isolated, and the plasma is weakly non-ideal for all temperatures and electronic densities of interest. For electronic collisions, semi-classical perturbation theory is sufficient and the impact approximation is well satisfied. The ion effects can be treated within the quasistatic approximation, and the quasistatic ionic contribution is dominated by the polarization (or quadratic) $r_{\rm p}^{-4}$-interaction. To consider both the electron and the ion effects, the microfield distributions and the complete reduced Stark profile of isolated line are calculated using different methods. The computed total widths corresponding to the three interaction potentials are compared to the available experimental widths and then approximated by appropriate formulae. The data we obtained provide an opportunity to test various approximations included in the semi-classical perturbation formalism. They are also of interest for stellar spectroscopic diagnosis in dense atmospheres (white dwarfs for instance)