Bremsstrahlung from muons scattered by atomic electrons

Bremsstrahlung from ultrarelativistic muons that is due to their interaction with atoms and which is accompanied by the excitation of atoms and by the knockout of delta electrons is considered. The process is described by diagrams of two types corresponding to photon emission by a muon or by an electron. For diagrams of the first type, the cross section is calculated with allowance for the binding of electrons in atoms, and a simple approximate formula is given. It is shown that the substitution Z(2) --> Z(Z + const), which is often used to take into account bremsstrahlung from muons scattered by atomic electrons, is incorrect. The contribution from diagrams of the second type is treated as an addition to elastic mu e scattering, important radiative corrections of order alpha(3) being included simultaneously. The distribution of energy lost by a muon in a collision and a correction to the mean energy loss by ionization are obtained.