  We study the formation of the Stokes profiles of the He I multiplet at 10830
A when relaxing two of the approximations that are often considered in the
modeling of this multiplet, namely the lack of self-consistent radiation
transfer and the assumption of equal illumination of the individual multiplet
components. This He I multiplet is among the most important ones for the
diagnostic of the outer solar atmosphere from spectropolarimetric observations,
especially in prominences, filaments, and spicules. However, the goodness of
these approximations is yet to be assessed, especially in situations where the
optical thickness is of the order or larger than one, and radiation transfer
has a significant impact in the local anisotropy and the ensuing spectral line
polarization. This issue becomes particularly relevant in the ongoing
development of new inversion tools which take into account multi-dimensional
radiation transfer effects. To relax these approximations we generalize the
multi-term equations for the atomic statistical equilibrium to allow for
differential illumination of the multiplet components and implement them in a
one-dimensional radiative transfer code. We find that, even for this simple
geometry and relatively small optical thickness, both radiation transfer and
differential illumination effects have a significant impact on the emergent
polarization profiles. This should be taken into account in order to avoid
potentially significant errors in the inference of the magnetic field vector.
