Measurements of L-Subshell Ionization Cross Sections by energetic a particles for Ho, Er, and Tm

Abstract

The L-subshell ionization cross sections induced by 1 to 6 MeV a particles were measured for three elements of the rare earth group: holmium, erbium, and thulium. The measurements were performed by taking advantage of simultaneous PIXE and RBS detection. The measured data were compared with the theoretical calculations of the ECPSSR theory. The comparison shows that there are systematic discrepancies at low energies especially for L₂ subshell whereas better agreement is observed at high bombardment energies. When the effect of intra-shell transitions induced by the Coulomb field of the projectile (IS) was included in the ECPSSR formalism, the systematic discrepancies between the theoretical and the experimental values at low energies were reduced. However, the ECPSSR-IS predictions overestimates the experimental values over all the energy range 1-6 MeV for the three subshells. Using the ECPSSR-IS theory at binding energies corresponding to united atom (UA), the predictions of the modified model, ECPSSR-IS-UA, agrees exactly with the experimental values for L₂ and L₃ subshells over all energy range. Nevertheless, for L₁ subshell the discrepancies remain. The ECPSSR-IS-UA theory underestimates the experimental values of L₁ subshell at low energies and overestimates the experimental values at high energies. It is shown that at high energies the discrepancies for L₁ subshell are due to the screening effect of the electronic cloud, which reduces the effective charge of the projectile to values less than 2, but higher than 1. Possible reason of low energy discrepancies for L₁ subshell is referred to the necessity of using relativistic Dirac-Hartree-Slater wave function in the basic calculations of the ECPSSR instead of the adopted screened hydrogen-like wave function.