  A series of high presicion atomic experiments was carried out last decade to
get a better estimate for the electron (anti)neutrino mass $m_\nu$. The
reaction to be observed is molecular tritium $\beta$- decay. The $m_\nu$ value
serves as one of the tune parameters to fit $\beta$- electrons spectrum via
reference theoretical one. The unexpected message consists of that parameter
${m^2_\nu}$ has to be fixed at some negative value to get best statistically
reliable fit. Apart of some exotic scenarios suggested the problem remains
open. In this paper we tried to reanalyze ground features of the final states
spectrum (FSS) and its influence on the $\beta$- electrons spectrum. A new
approach has been developed which gives some hints to make proper modifications
to the tabulated FSS in the course of experimental fits.
