Standard line broadening impact theory for hydrogen including penetrating collisions

In recent years there has been significant interest in the emission spectra from high-density plasmas, as manifested by a number of experiments. At these high densities short range (small impact parameter) interactions become important and these cannot be adequately handled by the standard theory, whose predictions depend on some cutoffs, necessary to preserve unitarity, the long range approximation, and to ensure the validity of a semiclassical picture. Very recently, as a result of a debate concerning the broadening of isolated ion lines, the importance of penetration of bound electron wave functions by plasma electrons has been realized. By softening the interaction, penetration makes perturbative treatments more valid. The penetration effect has now been included analytically into the standard theory. It turns out that the integrations may be done in closed form in terms of the modified Bessel functions K0 and K1. This work develops the new theory and applies it to experimental measurements.