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

TL;DR

This paper evaluates the accuracy of measuring charged particle energies via their path lengths in nuclear emulsion, demonstrating a method with approximately 2.7% precision for muons and potential for 5% accuracy in electron energy measurements.

Contribution

The study introduces a coordinate method for energy measurement in nuclear emulsion with quantified accuracy, applicable to muons and electrons in beta decay.

Findings

Muon energy measurement dispersion is 0.11 MeV, about 2.7% accuracy.

Method enables electron energy measurements in 2β decay with about 5% accuracy.

The developed technique improves precision in charged particle energy determination in nuclear emulsion.

Abstract

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%$.