Energy loss of atmospheric muons and the Bethe–Bloch formula

Abstract

The stopping power of atmospheric muons in silicon is studied by combining the Bethe-Bloch formalism with a semiconductor detector called MiniPix. The Bethe–Bloch formula was implemented numerically, correctly reproducing the characteristic energy loss regimes. The energy calibration was performed using the γ emission lines from a source of 241Am (59.54 keV and 26.34 keV). During a 15-hour acquisition period, 267 muon candidates were identified and selected for their linearity and track length. A numerical inversion of the Bethe–Bloch function was applied to reconstruct the energies of the muons from the measured stopping power values. The energies were found to be systematically underestimated, attributed to the geometric incompatibility between γ-based calibration and the extended charge deposition profile of muon tracks. Although a quantitative comparison with the Bethe–Bloch prediction could not be achieved, the tracks recorded are qualitatively consistent with the expected behavior of the muons, validating the detection methodology.