Characteristic X-Ray Production in AtomicLandMSubshells

Explicit formulas are obtained for atomic form factors describing the energy loss and momentum transfer of a charged particle to electrons in the subshells of the $L$ and $M$ shells. The Bethe-Born approximation is used with hydrogenic wave functions. Application is made to the $L_{\mathrm{III}}$ ionization cross section for protons incident on copper in the energy range from 0.5 to 1.7 MeV.