  The KArlsruhe TRItium Neutrino experiment (KATRIN) aims to determine the
effective mass of the electron antineutrino via a high-precision measurement of
the tritium beta-decay spectrum in its end-point region. The target
neutrino-mass sensitivity of 0.2 eV / c^2 at 90% C.L. can only be achieved in
the case of high statistics and a good control of the systematic uncertainties.
One key systematic effect originates from the calculation of the molecular
final states of T_2 beta decay. In the first neutrino-mass analyses of KATRIN
the contribution of the uncertainty of the molecular final-states distribution
(FSD) was estimated via a conservative phenomenological approach to be 0.02
eV^2 / c^4. In this paper a new procedure is presented for estimating the
FSD-related uncertainties by considering the details of the final-states
calculation, i.e. the uncertainties of constants, parameters, and functions
used in the calculation as well as its convergence itself as a function of the
basis-set size used in expanding the molecular wave functions. The calculated
uncertainties are directly propagated into the experimental observable, the
squared neutrino mass m_nu^2. With the new procedure the FSD-related
uncertainty is constrained to 0.0013 eV^2 / c^4, for the experimental
conditions of the first KATRIN measurement campaign.
