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

Abstract

The 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.

An improved version of ISICS: a program for calculating K-, L- and M-shell cross sections from PWBA and ECPSSR theory using a personal computer

“…A scaling function, hsR(ξ K /ζ K , Z 2 /137), given in Ref. [8], is employed to correct for the Dirac-Hartree-Slater nature of the K shell. In this case, the relativistic correction, R, of ECPSSR is not necessary, and the modified cross-sections, σ eECPSShsR K , are given by,…”

“…Lapicki [8] has promoted a modification of the ECPSSR K-shell ionization cross-sections based on calculations of Chen and Crassemann (CC) [9] for which relativistic Dirac-HartreeSlater wave functions were used in computing the form factors of the theory. A scaling function, hsR(ξ K /ζ K , Z 2 /137), given in Ref.…”

K X-ray production cross sections in aluminium for 15, 20 and 25keV protons

“…The situation is even worse when considering low-energy (tens of keV) incident particles since the experimental data available in the literature is scarce or even nonexistent and the cross sections predicted by the theoretical models differ widely in this low-energy range [8][9][10][11]. The accuracy in the characterization of material surfaces through the PIXE technique by using low-energy impinging particles is therefore greatly limited by the lack of this data in the literature, as pointed out by Lapicki [12]. We believe that the reason for this lack of available results is mainly due to the experimental difficulties associated with the detection of the very low X-ray yields resulting from the interaction of the incident particles with the target, since for these low energies the X-ray production cross sections involved are much lower than those for impinging particles in the 1-4 MeV energy range [2].…”

Theoretical total charge transfer cross sections and differential ionization cross sections for ion–atom collisions illustrated for the system

“…Calculating accurate cross sections for electron excitation, ionization and charge transfer produced in a fast ion-atom collision has been the aim of many authors in the last three decades (Lapicki, 2005;Crothers et al, 1996;Bradley et al, 2005;Olsen, 1996;Knoop et al, 2005;Ford and Reading, 1996). In this short article we chose to focus not on the success of these efforts but rather to concentrate on the difficulties still remaining.…”

“…The perturbed stationary state, PSS, approximation (Lapicki, 2005), modifies the unperturbed initial state approximation of the first Born approximation as does the continuum distorted wave (CDW) approximation (Crothers, 1996). Both approximate a quantum approach.…”