The theory of the pressure broadening of rotational spectra is described using (for the first time) the Magnus approximation to calculate the relevant S matrices. The latter's unitary character is thereby maintained. The relative contributions of the attractive and repulsive anisotropy terms in the interaction potential is investigated for the system of a linear molecule broadened by a noble gas atom. A ``centrifugal'' approximation is also introduced to write the linewidth expression in a closed analytic form and to simplify the computation. It is shown to be a good approximation for the systems investigated. An additional approximation described in an appendix can also be introduced, but it is valid only for systems in which the repulsive anisotropy does not make a significant contribution to the linewidth.
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