Accurate Theoreticalβ-Decay Energy Spectrum of the Tritium Molecule and Its Neutrino Mass Dependence

Abstract

The $\beta$-decay energy spectrum which results from the decay of one of the nuclei in the ${\mathrm{T}}_2$ molecule has been computed. An accurate, explicitly correlated basis set was used to describe electronic states of both the parent and the daughter molecules, and effects of nuclear motion have been taken into account. All the channels which meaningfully affect the spectrum have been incorporated, including resonance and scattering channels. The spectra are presented for several neutrino masses. It is shown that the molecular effects are crucial for accurately determining the neutrino mass from a tritium $\beta$-decay experiment.