Molecular effects in tritium beta decay. III. Electronic resonances of the HeT+ ion and dependence of neutrino mass on the accuracy of the theoretical model.

Abstract

The theoretical aspects of the \ensuremath{\beta}-decay process in ${\mathrm{T}}_{2}$ as they relate to neutrino-mass experiments are discussed. We present new results from stabilization method calculations for the resonance states of the daughter ${\mathrm{HeT}}^{+}$ ion. The probabilities for this system to be found in various final shake-off states after the ${\mathrm{T}}_{2}$ decay have been calculated. The \ensuremath{\beta}-decay energy spectra are generated using probability distributions of various accuracies. It is shown that, if the actual neutrino mass were 30 eV, one would obtain masses of 6 and 25 eV using spectra of the bare tritium nucleus and the tritium atom, respectively, for analyzing the data. If the nuclear motion effects were neglected, the obtained mass would be 30 eV but the end-point energy would be shifted by 1.5 eV. For a 30-eV mass the accuracy of our calculations is much better than necessary: Substituting our data by those obtained with a very poor basis set changed the neutrino mass only by about 1 eV. For a 1-eV mass, however, the less accurate calculation would introduce a substantial error. In particular, including the effects of nuclear motion is important to correctly determine a 1-eV mass. The accuracy with which resonance states of the daughter ion are determined has practically no influence on the final result. We argue that most solid-state effects will lead to corrections small compared to the expected experimental errors.