Improved Molecular Final-State Distribution of ${\mathrm{HeT}}^{+}$ for the $\mathit{\beta }$-Decay Process of $T_2$

An improved theoretical final-state distribution of ${\mathrm{HeT}}^{+}$ (and ${\mathrm{HeH}}^{+}$) resulting from the $\beta$ decay of molecular tritium ${\mathrm{T}}_2$ (HT) is presented to accommodate the needs of increased accuracy in the analysis of ongoing and future tritium neutrino-mass experiments. The previously available theoretical spectrum has been improved in many respects, and adopted approximations have been validated.