Determination of the accuracy of measuring the energy of charged particles by their path lengths in nuclear emulsion

The path lengths of monochromatic muons emerging in the $\pi \to \mu {\nu }_{\mu }$ decay were measured by the coordinate method with the view to determine their energy by path length. The dispersion of muon energy measurements by this method was ${\sigma }_{\mu }=(0.11\pm 0.01)$ MeV, which corresponds to the accuracy of $\sigma \approx 2.7$ of the energy of a charged particle estimated by its path length in nuclear emulsion. The developed method will enable measurements of electron energies in $2\beta$ decay ($\sim 3$ MeV) to an accuracy of $\sigma \approx 5$.