Polynomial Approximants for the Calculation of Polarization Profiles in the He I 10830 Å Multiplet

The He I multiplet at 10830 Å is formed in the incomplete Paschen-Back regime for typical conditions found in solar and stellar atmospheres. The positions and strengths of the various components that form the Zeeman structure of this multiplet in the Paschen-Back regime are approximated here by polynomials. The fitting errors are smaller than ~10-2 mÅ in the component positions and ~10-3 in the relative strengths. The approximant polynomials allow for a very fast implementation of the incomplete Paschen-Back regime in numerical codes for the synthesis and inversion of polarization profiles in this important multiplet.