Theory of Effective Charge and Stopping Power for Heavy Ions

Abstract

A revision of the Knipp-Teller effective-charge theory for the electronic stopping power of media for heavy ions is described. In the new theory the ion velocity is related to the mean ionization energy of the most loosely bound medium electrons as calculated from the Thomas-Fermi atomic model. The effective charge ($\ensuremath{\gamma}z$, $0<\ensuremath{\gamma}<1$, where $\ensuremath{\gamma}$ is the effective-charge parameter) of an ion with atomic number $z$ is related to the ionic kinetic energy $\ensuremath{\epsilon}$(MeV/amu) through the equation $\frac{\ensuremath{\epsilon}}{{z}^{\frac{4}{3}}}=0.0277k[{f}_{0}(\ensuremath{\gamma})+\frac{{f}_{1}(\ensuremath{\gamma})}{z}]$ where $k$ is a constant, near unity, to be determined from the empirical data for the atomic-number region of interest. Curves for ${f}_{0}$ and ${f}_{1}$ as functions of $\ensuremath{\gamma}$ are presented and an overall value of $k=1.25$ is recommended. Calculated values of the effective-charge parameter are compared to experimentally measured values for a wide range of ions, ionic energies, and stopping media. For $z>10$ the agreement is very good from $\frac{\ensuremath{\epsilon}}{{z}^{\frac{4}{3}}}\ensuremath{\approx}0.001$, where exchange corrections (ignored in the Thomas-Fermi model) become important, to $\frac{\ensuremath{\epsilon}}{{z}^{\frac{4}{3}}}\ensuremath{\approx}0.1$, where a statistical theory is no longer valid.