Recoil effect in the $\beta$ decay of molecular tritium

In order to determine the electron (anti)neutrino mass $m_\nu$, a number of precise atomic experiments with gaseous and frozen targets of molecular tritium $T_2$ have been carried out in the last decade. The nonzero neutrino mass should be manifested in the form of fine features near the upper edge of the $\beta$-electron spectrum. The problem of calculating the spectrum of final excitations, which is of crucial importance for determining $m_\nu$, is discussed. An operator approach has been used for an analysis of spectral sums. This allows a number of effects that could not be considered earlier to be discussed, including the recoil effect, which can be of substantial importance in the interpretation of the current and future experiments.