Abstract
High-energy muons can travel large thicknesses of matter. For underground neutrino and cosmic ray detectors the energy loss of muons has to be known accurately for simulations. In this article the next-to-leading order correction to the average energy loss of muons through bremsstrahlung is calculated using a modified Weizsäcker–Williams method. An analytical parametrisation of the numerical results is given.
Highlights
The muon bremsstrahlung cross section has been studied extensively for many years [1, 2, 3, 4, 5]
Previous calculations took into account the modification of the Coulomb interaction with the nucleus by elastic and inelastic nuclear form factors, the contribution of atomic electrons as target
The calculation reported here is based on the Weizsäcker-Williams method [14, 15], which approximates the effect of a nucleus by a spectrum of equivalent photons. This method allows to express the bremsstrahlung cross section through the Compton cross section convolved with the equivalent photon flux
Summary
The muon bremsstrahlung cross section has been studied extensively for many years [1, 2, 3, 4, 5]. Together with the production of electron-positron pairs [6, 7, 8, 9] and the inelastic nuclear interaction [10, 11, 12] it describes the dominant contribution to the energy loss of high-energy muons. Muons with energies of tens to hundreds of TeV can travel distances of the order of several kilometers. It is necessary to know the average energy loss per unit length − dE dx =N Ev dσ dv dv (1). V = (E − E′)/E is the relative energy loss per interaction, and N is the number density of target atoms. Previous calculations took into account the modification of the Coulomb interaction with the nucleus by elastic and inelastic nuclear form factors, the contribution of atomic electrons as target
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