Exact expression of the impact broadening operator for hydrogen Stark broadening

Aims.Recent measurements on the Stark broadening of radio recombination lines show values and trends in disagreement with conventional theories. Different attemps to explain those disagreements have not been successfull for any of the employed theoretical models. In particular, the impact model that describes well the physical conditions at which the studied broadenings occur, shows a functional trend upon the principal quantum number of the studied transitions that does not correspond to the experimental observations. Methods.High values of the principal quantum number require computable formulas for the calculation of transition probabilities. Some of those expressions have been published, leading to approximate formulas on the dependence of the line width versus the principal quantum number of the upper level of the transition. Results.In this work an exact expression for the hydrogen Stark width in the frame of impact approximation is given