A perturbative solution of the transfer equations for the Stokes parameters in a magnetic field

The transfer equations for the Stokes parameters, as derived under the assumption of LTE and in the general case of anomalous Zeeman multiplet, are solved by a perturbative method that reduces the system of four coupled linear differential equations to an iterative series of well known linear differential equations. The perturbation parameter turns out to be of the order of magnitude of the ratio of the Larmor frequency to the line Doppler half-width, so that the method appears to be particularly suitable for small magnetic fields.Some qualitative results on the importance of Faraday rotation and the orders of magnitude of the line profiles of the Stokes parameters are obtained.