Contributions of Spin, Anomalous Magnetic Moment, and Form Factors to the Stopping Power of Matter for Protons and Muons at Extreme Relativistic Energies

The stopping power of matter for protons and muons is calculated without the usual restriction that γmM, where M is the rest mass of the proton or muon, m is that of the electron, γ=(1-β²)^-12, and β is the ratio of the speed of the proton or muon to the speed of light. The calculation includes the effects of the incident proton's spin, anomalous magnetic moment, and form factors, the muon being considered as a point particle that obeys the Dirac equation. The contributions of these effects to the stopping powers of aluminum, copper, and lead are evaluated numerically for protons and muons up to γ=10⁴ ({~}10⁴-GeV protons and {~}10³-GeV muons), where they amount to about 10%. Restricted energy-loss values with cutoff energies of 1.1 and 8.0 MeV are calculated for protons and muons in water.