Periodic Dependence of the Electronic Stopping Cross Section for Energetic Heavy Ions in Solids

Abstract

Measurements of the electronic stopping cross section for heavy ions in various substrates indicate a periodic dependence on the atomic number of the impinging ion. This work provides an explanation of the observed behavior. The periods are observed to correspond to unit steps in the principal quantum number of the outermost orbit of the incident ion, with a peak in the stopping cross section occurring roughly for the ion with a half-filled outer shell. As the number of electrons in the outermost shell is increased, the contribution to energy loss increases. However, beyond a certain point the increasing number of electrons in the outer shell is offset by the increased binding energy of the electrons and the decreased radii of the orbits, reducing the effective number of outer electrons. Use is made of the Firsov model with appropriate values for the effective charge to give stopping cross sections which agree rather well with channeling measurements in both crystalline silicon and tungsten. The same approach can be extended to explain similar behavior in amorphous as well as other crystalline substrates.