Stopping power and ranges of fast ions in heavy elements.

Abstract

For the calculation of stopping power and ranges with the method suggested by Bethe, functions expressing the binding of the electrons in the atoms (``shell corrections'') are needed. Here, shell corrections calculated with hydrogenic wave functions have been employed. By using experimental atomic energy levels as parameters for them, I have found good agreement between experimental and calculated values of stopping power for elements with atomic number Z>56. Only for the mean ionization energy I there was no simple relation to atomic properties, and a considerable dependence of the Bloch parameter b=I/Z on Z has been found. Calculated values of stopping power and ranges agree with experimental values for protons with kinetic energies T above 0.5 MeV, for ions (with z protons and M\ensuremath{\le}40 nucleons) above T/M\ensuremath{\sim}(z-1.5) MeV, well within the uncertainty of the experiments, but an approximately 1% discrepancy for several hundred MeV protons remains.