Mean excitation energy for the stopping power of light elements

We have evaluated the mean excitation energy or I value for Coulomb excitations by swift charged particles passing through carbon, aluminum and silicon. A self-consistent Kramers–Kronig analysis was used to treat X-ray optical spectra now available from synchrotron light sources allowing us to carry out Bethe’s original program of evaluating I from the observed dielectric response. We find that the K and L shell are the dominant contributors to I in these light elements and that the contribution of valence electrons is relatively small, primarily because of their low binding energy. The optical data indicate that Si and Al have nearly equal I values, in contrast to Bloch’s Thomas–Fermi result, I ∝ Z. The optically based I values for C and Al are in excellent agreement with experiment. However, the dielectric-response I value for Si is 164 ± 2 eV, at variance with the commonly quoted value of 173 ± 3 eV derived from stopping-power measurements.