  We discuss studies of polarization in astrophysical masers with particular
emphasis on the case where the Zeeman splitting is small compared to the
Doppler profile, resulting in a blend of the transitions between magnetic
substates. A semi-classical theory of the molecular response is derived, and
coupled to radiative transfer solutions for 1 and 2-beam linear masers,
resulting in a set of non-linear, algebraic equations for elements of the
molecular density matrix. The new code, PRISM, implements numerical methods to
compute these solutions. Using PRISM, we demonstrate a smooth transfer between
this case and that of wider splitting. For a J=1-0 system, with parameters
based on the $v=1, J=1-0$ transition of SiO, we investigate the behaviour of
linear and circular polarization as a function of the angle between the
propagation axis and the magnetic field, and with the optical depth, or
saturation state, of the model. We demonstrate how solutions are modified by
the presence of Faraday rotation, generated by various abundances of free
electrons, and that strong Faraday rotation leads to additional angles where
Stokes-Q changes sign. We compare our results to a number of previous models,
from the analytical limits derived by Goldreich, Keeley and Kwan in 1973,
through computational results by W. Watson and co-authors, to the recent work
by Lankhaar and Vlemmings in 2019. We find that our results are generally
consistent with those of other authors given the differences of approach and
the approximations made.
