A Predictive Range Expression: Applications and Limitations
Gregory A Wilson, Anne C Starley, Lisa Montierth Phillipps, JR Dennison · Digital Commons - USU (Utah State University) · 2018
An empirical model of the approximate electron range of some common materials has been extended to predict the range for many diverse types of materials.The electron range of a material is the maximum distance electrons can travel through a material, before losing all of their incident kinetic energy.The original model used the Continuous Slow Down Approximation (CSDA) and the constant loss approximation (CLA) for energy deposition in a material to develop a composite analytical formula which estimated the range from 10 MeV with an uncertainty of ≲20% using a single empirical fitting parameter, 𝑵𝑵 𝑽𝑽 𝒆𝒆𝒆𝒆𝒆𝒆 .This effective number of valence electrons, was empirically calculated for >200 materials which have tabulated range and inelastic mean free path data in the NIST ESTAR and IMFP databases.Correlations of 𝑵𝑵 𝑽𝑽 𝒆𝒆𝒆𝒆𝒆𝒆 with common material properties (density, atomic number, atomic weight, and band gap) were established for this large set of materials, leading to the development of a predictive formula to accurately determine 𝑵𝑵 𝑽𝑽 𝒑𝒑𝒑𝒑𝒆𝒆 for arbitrary materials.This paper discusses the accuracy and limitations of the predictive formula and presents illustrative applications to several materials of interest.