Polynomial approximants for the calculation of polarization profiles in the He I 10830 Å multiplet

The He I multiplet at 10830 angstrom 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 similar to 10(-2) m angstrom in the component positions and similar to 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.