Lienard-Wiechert or retarded electric and magnetic fields are produced by moving electric charges with respect to a rest frame. In hot plasmas, such fields may be created by high velocity free electrons. The resulting electric field has a relativistic expression that depends on the ratio of the free electron velocity to the speed of light in vacuum c. In this work, we consider the semi-classical dipole interaction between the emitter ions and the Lienard-Wiechert electric field of the free electrons and compute its contribution to the broadening of the spectral line shape in hot and dense plasmas.

In this work, we have calculated the relativistic collision operator representing the line broadening, by collision with free electrons, of isolated lines emitted by hydrogen-like ions (Ly- α line [Formula: see text]) of hydrogenic ions FeXXVI, CrXXIV, and CoXXVII in the temperature range of [Formula: see text] to [Formula: see text] and electron densities of 1021 to [Formula: see text]. To accomplish this task, we have considered the fine structure of these ions and taking into account the relativistic effects related to the free electrons. Specifically, two relativistic effects are considered: the electric field of Liénard–Wiechert, created by the free electron at the emitter ion, and the modification of the hyperbolic trajectory due to the dependent mass on the free electron velocity. The average over the velocities of the free electrons is accomplished by using the Maxwell–Juttner distribution, which is more adequate for the fast (relativistic) electrons. The results are compared to the classical case (when the electric field is the Coulomb's field) to Doppler broadening and to some experimental results (K. Koyama and M. G. Haines) available in the literature. It turns out that, at high temperatures and high densities, the Stark broadening by the relativistic electrons overcomes the Doppler broadening.