Spectral line broadening by plasmas can be computed by solving the equation of motion for the dipole of the radiating system perturbed by a fluctuating potential obtained from computer simulations. Such calculations have relied on the multipole expansion of the radiator-plasma interaction often keeping only the dipole term. With increasing density, however, higher multipoles as well as plasma perturbers overlapping the bound electron wave functions are expected to become important. For hydrogenic systems, the atomic matrix elements of the full Coulomb and screened Coulomb interactions are given by analytical formulas. Using these results, a computer simulation approach that accounts for the full radiator-plasma interaction is developed. One benefit is the removal of inherent strong collision divergences in the multipole expansion approximation. Furthermore, it yields the plasma polarization shift produced by perturbers penetrating the wave function of the radiator bound electrons. The model was applied to hydrogenic argon Ly-α, Ly-β, and Ly-γ spectral lines in a dense argon plasma at free electron densities of 10^{24} or 10^{25}cm^{-3} and temperature of 800eV relevant to plasma diagnostic techniques for inertial confinement fusion implosions.