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%$.