G. Lapicki

The status of theoretical L-subshell ionization cross sections for protons

Accuracy of PIXE analyses depends on inner-shell ionization cross sections. These cross sections are often calculated in the ECPSSR theory; results of its variant (that uses DHS wavefunctions) are employed in the GUPIX package. While the ECPSSR theory agrees well with massive compilations of K x-ray production, it deviates systematically from Lsubshell data – in particular, L1 and L2 cross sections. Various modifications of the ECPSSR theory and their results are reviewed versus the empirical database from Orlic for 0.3–3.5 MeV protons on 45 6 Z2 6 92 targets. Comparison with this database does not give a clear choice between the ECPSSR and the ECPSSR with all modifications. Independently of the chosen theory and because of the increasing scatter in the data with the decreasing proton energy, PIXE packages that may rely on reference cross sections for L1 x-ray production in lanthanides by 0.2-MeV protons could err by an order of magnitude in the determination of the concentration of these elements. 2002 Elsevier Science B.V. All rights reserved.

Scaling of analytical cross sections for K-shell ionization by nonrelativistic protons to cross sections by protons at relativistic velocities

A procedure is given by which nonrelativistic cross sections are scaled to the K-shell ionization cross sections by protons of any velocity up to the speed of light. To perform this scaling in an analytical manner, the ECPSSR theory of Brandt and Lapicki (1981 Phys. Rev. A 23 1717) and its recent modifications that go beyond the plane wave Born approximation with exact (e) limits on the energy and momentum transfers (ePWBA) are formulated analytically. They are expressed in terms of a formula that fits numerically evaluated ePWBA to within 3% for carbon and all heavier elements. With an extension to GeV protons, the ECPSSR and its relativistic modifications are reviewed to untangle consequences of various relativistic treatments of protons and different methods to account for the relativistic nature of the K-shell electron. The adequacy of the scaling to obtain the relativistic K-shell ionization cross sections is scrutinized through departures of the developed theories from a comprehensive compilation of the data. Excellent agreement with 1 GeV data of Vodopyanov et al (1996 J. Phys. B: At. Mol. Opt. Phys 29 2543) is demonstrated, and an apparent discrepancy with 4.88 GeV data of Anholt et al (1976 Phys. Rev. A 14 2103) is examined in light of other theories.

M-SHELL X-RAY PRODUCTION CROSS SECTIONS FOR PIXE APPLICATIONS

M-shell X-ray production cross sections by protons of energies 0.1–4.0 MeV are reported for the most intense Mαβ(M4,5N6,7), Mγ(M3N4,5) and M3O4,5 M-X ray transitions appearing in PIXE spectra. The cross sections have been measured systematically for selected heavy elements between Ta and Th (Z2=73–90). Measured M-X-ray production cross sections were found to be universal with respect of M-shell scaled velocity ξM. The data are compared with available theoretical calculations of M-shell ionization by charged particles based on the plane-wave Born approximation (PWBA) and the semiclassical approximation (SCA), as well as the ECPSSR theory and relativistic RPWBA-BC which are going beyond the first order treatment. Simple parameterization of experimental proton induced M-X-ray cross sections is proposed for PIXE applications. This parameterization, being accurate within ±5%, can be used for precise determination of heavy metal concentrations by PIXE technique.

M-shell X-ray production in heavy elements by low-energy protons

Measurements of M-shell X-ray production cross sections in selected heavy elements (73 ≤ Z2 ≤ 90) have been performed for proton impact of energy 0.1–0.6 MeV. X-rays were collected by a Si(Li) detector, carefully calibrated for low-energy efficiency, and they were normalized to the projectiles that were elastically scattered into the surface barrier detector. The measured M-X-ray production cross sections are compared with the predictions of the first Born approximation, the semiclassical approximation, and the ECPSSR theory which corrects for energy loss, Coulomb deflection, binding-polarization and relativistic effects. The comparison of the present data with our earlier measurements and the data reported by other authors is discussed in detail. Strong underestimation (up to a factor of about 5) of experimental data by the ECPSSR theory is observed for the lowest energies.

Importance of subshell coupling in L-shell ionization by low-velocity heavy ions

Abstract Data for available L-subshell ionization caused by slow and heavy ions (Z 1 = 6, 7 and 8) are compiled and compared with the prdictions of the ECPSSR theory with and without the intra-shell (IS) coupling. It has been observed that the standard ECPSSR without Is is inadequate to predict quantitatively the L-subshell cross section data at low projectile velocities. The inclusion of the IS effect somewhat worsens agreement with experiment for the L 1 -subshell ionization, substantially improves it for the L 2 subshell, and plays essentially no role in an analysis of L 3 -subshell data which are fairly well predicted by the standard ECPSSR theory. The quantitative validity of such conclusions may be questioned because they rely on an approximate treatment of the IS effect.

Evaluation of cross sections for Lα x-ray production by up to 4 MeV protons in representative elements from silver to uranium

Over the last two decades, Lα x-ray production cross sections have been fitted with a number of empirical formulae. Cross sections obtained from these formulae are averaged and fitted to a new empirical formula. These new empirical cross sections are compared with the results of the plane-wave Born approximation and the ECPSSR theory of Brandt and Lapicki (1981 Phys. Rev. A 23 1717). They are also gauged by the ECPSSR theory that has been corrected with a united atom approach in slow collisions, evaluated with Dirac–Hartree–Slater instead of screened hydrogenic wavefunctions, modified for intra-shell couplings as well as the change of the atomic parameters due to multiple ionizations. The effects of appropriately normalized intra-shell coupling factors and of multiple ionization were found to be small and essentially offset each other. The role of different sets of atomic parameters in conversion of the predictions of these ionization theories for Lα x-ray production in elements from the 47 ≤ Z2 ≤ 92 range of target atoms bombarded by up to 4 MeV protons is examined, and the selection of the optimal combination of ionization theory and atomic parameters for a reliable data base for PIXE analysis of elements heavier than palladium is discussed.

L x-ray production in lanthanide elements by 1 - 5 MeV helium ions

L x-ray production in and was measured for bombardment in the energy range 1 - 5 MeV. Very thin target foils were used, and x-ray yields were measured simultaneously with elastically scattered ions. The L-shell and individual and production cross sections and their ratios were extracted. These cross sections are compared to the results of the ECPSSR theory (energy-loss and Coulomb deflection effects, perturbed stationary state approximation with the relativistic correction), its united-atom (UA) extension UA-ECPSSR and the UA-ECPSSR-MI, which also accounts for multiple ionization (MI). With a few exceptions, the standard ECPSSR appears to be better than its modifications when and ratios are analysed. and and total L x-ray production cross sections, however, are in the best overall agreement with the UA-ECPSSR-MI theory.

M-shell X-ray production in gold, lead, bismuth, thorium and uranium by 70–200 keV protons☆

Abstract M-shell X-ray production cross sections have been measured for thin-foil targets (thickness in μg/cm2) of 79Au (7.0), 82Pb (10.6), 83Bi (4.1), 90Th (7.9) and 92U (8.8) for 70–200 keV incident protons. These data are compared to other measurements at higher energies and to the first Born (plane-wave Born approximation for direct ionization and Oppenheimer-Brinkman-Kramers-Nikolaev approximation for electron capture) and ECPSSR (energy-loss and Coulomb deflection effects, perturbed stationary state approximation with relativistic correction for both direct ionization and electron capture) theories. The electron capture, included for completeness, contributed less than 1%. The ECPSSR underpredicts the data at all energies, while the first Born, which overpredicts the data, seems to approach agreement for low Z2. The data follow a trend established in this laboratory by earlier work [R. Mehta et al., Phys. Rev. A26 (1982) 1883] at higher energies.

Thorium and uranium M-shell x-ray production by 0.4?4.0 MeV protons and 0.4?6.0 MeV helium ions

M-shell x-ray production cross sections for thorium and uranium have been determined for protons of energies 0.4–4.0 MeV and helium ions of energies 0.4–6.0 MeV. The M-shell line and total M-shell x-ray production cross sections are compared to the predictions of the first Born approximation and ECUSAR ionization theory using recently recommended atomic parameters. Both theories are in good agreement with the data for protons and He ions above 1 MeV. The data of others for energies above 1 MeV protons on uranium, however, fall significantly under the present measurements. Below 1 MeV, with decreasing energy of these projectiles, the first Born approximation increasingly overestimates our measurements while the ECUSAR theory underestimates them to a similar degree. The same trends are seen versus the data of others.

K X-RAY PRODUCTION CROSS SECTION OF GE AND AG BY 3.7-11.1 MEV CARBON IONS

Abstract K X-ray production cross sections of Ge and Ag by 3.7–11.1 MeV carbon ions have been measured. After necessary corrections for projectile slowing down and X-ray self absorption, the data have been compared with the theoretical predictions of the ECPSSR and of the 1s σ molecular orbital theory.