L-shell ionization probability of Pb by 2-, 3-, 6-MeV protons

The impact-parameter dependences of $L\alpha$, $L\beta$, and total $L$-shell x-ray production of Pb by 2-, 3-, and 6-MeV proton bombardment have been measured and compared with theoretical calculations based on the semiclassical approximation (SCA) and the binary-encounter approximation (BEA). The SCA satisfactorily reproduces the details of the ionization probabilities but overestimates the results at large impact parameters. The BEA does not predict the appropriate structure observed in the x-ray production probabilities. The BEA results are too low at small impact parameters, but in good agreement with measured values at large impact parameters. The behavior at large impact parameters explains the failure of the SCA in predicting the $L$-shell x-ray production total cross sections (the calculated values are too high), whereas the BEA cross sections are in close agreement with experiment.