The status of theoretical K‐shell ionization cross sections by protons

Abstract

AbstractThe accuracy of PIXE analysis depends on inner‐shell ionization cross sections that are often calculated in the ECPSSR theory which accounts with analytical functions for the energy (E) loss and Coulomb (C) deflection of the projectile plus for the perturbed‐stationary state (PSS) and relativistic (R) nature of the target's inner shell. Although the ECPSSR is within 10% overall agreement with the K‐shell data—as the proton energy falls below 0.1 to 1 MeV, respectively, in ionization of light‐ to heavy‐target atoms—the ECPSSR increasingly overestimates the empirical database of Paul and Sacher (1989). Except for an enhancement of this overestimate at low energies, a modified ECPSSR based on the Chen–Crasemann (1985, 1989) plane wave Born approximation—evaluated with the exact limits for the momentum transfers and the Dirac–Hartree–Slater wavefunctions—yields cross sections that remain within 10% of the data and the ECPSSR theory. Codes that use only the exact limits instead of the energy‐loss function are confirmed to be improper for evaluation of the ECPSSR. Further enhancement of the cross sections at the low energies is limited to light target atoms after the function derived in the separated atom approach to account for the PSS effect is joined with an expression obtained in the united atom limit. An empirical database, updated with cross sections from post‐1989 publications, is normalized to the modified ECPSSR theory and various forms of the Coulomb deflection factor are revisited. Copyright © 2005 John Wiley & Sons, Ltd.