Measured X-ray Production Cross Sections Research Articles

Experimental and theoretical L-shell ionization cross sections of heavy atoms by impact of Si ions

We present a theoretical and experimental study of the subshell resolved L-shell ionization of relativistic targets such as 73Ta, 78Pt, 90Th, and 92U. The measurements of x-ray production cross sections by (84–140 MeV) Si+q ions (q = 8; 12), were held at the Inter-University Accelerator Centre of New Delhi. Multiple-hole fluorescence and Coster-Kronig yields were used to obtain the Li(i = 1–3) ionization cross sections from the measured x-ray production cross sections of Lℓ, Lα, and Lβ, Lη, and Lγ lines. The experimental results are compared with ab initio theoretical calculations by means of the shell-wise local plasma approximation (SLPA). This model uses the quantum dielectric formalism to obtain the total ionization cross sections from an initial ground state. The wave functions and binding energies of the different targets were obtained by solving the fully relativistic Dirac equation using the HULLAC code package. These calculations are based on first order perturbation theory with a central field, including Breit interaction and quantum electrodynamics corrections. The present SLPA ionization cross sections of the L-shell are found to be independent of the charge state of the Si ions. The experimental observations display also quite similar character if the correct mean projectile charge state inside the target is used for including the multiple ionization effect during ion-solid collisions. A general good agreement between the experimental measurements and full theoretical calculations supports the reliability of present results. The comparison also includes the well-known ECPSSR and ECUSAR semi empirical approximations. We noted that the ECUSAR results agree well with the SLPA, while the ECPSSR cross sections are rather low.

Heavy ion PIXE cross sections in Ti, Zn, Nb, Ru and Ta for 4.8–30.0 MeV oxygen and 3.0–12.0 MeV lithium beams

Heavy ion Particle Induced X-ray Emission (PIXE) spectroscopy offers a number of advantages over standard proton PIXE, such as higher yields and therefore higher sensitivity. However, in order to be able to use heavy ion PIXE more detailed measurements of the ionisation and X-ray cross sections for heavy ions are required. This issue was recognised by one of the Coordinated Research Projects (CRP) of the IAEA on MeV Secondary Ion Mass Spectrometry (SIMS). ANSTO took part in this CRP and we measured X-ray production cross sections on a range of samples for oxygen and lithium beam in the energy range of 4.8–30 MeV and 3–12 MeV, respectively. Here we report on these X-ray production cross section measurements and compare the results with theoretical models. Further energy shifts of the characteristic X-ray lines for the different ion-target combinations are presented and discussed.

L-shell X-ray production cross sections in metal oxide thin films due to 12C, 16O and 28Si ion beams at MeV SIMS energies

Successful co-implementation of different heavy ion beam nuclear analytical techniques such as heavy ion PIXE, ERDA, MeV SIMS and RBS hinges on the availability of accurate databases of fundamental ion beam-matter interaction parameters. We report on measurements carried out to determine L-shell X-ray production cross sections in 101Ru and 181Ta due to 12C, 16O and 28Si projectile ions in the 0.2 MeV/u–1.0 MeV/u energy range. Experimental data is compared to calculations by one of the most widely implemented X-ray ionisation theories in PIXE analyses – the ECPSSR theory in its modified United Atom (UA) version. Results show fairly good agreement between experiment and theory for the 181Ta target atoms, with the level of agreement improving as the Zion/Ztarget ratio decreases and as beam energy increases. For 101Ru target atoms theoretical predictions tend to underestimate experimental data and the discrepancies increase with projectile mass and decreasing energy. The contribution of projectile electron capture (EC) to the measured X-ray production cross sections is also considered in the data analysis and discussion.

Coupling and binding-saturation effects inL-subshell ionization of heavy atoms by 0.3–1.3-MeV/amu Si ions

The coupling and binding effects have been studied in $L$-subshell ionization of heavy Au, Bi, Th, and U atoms by an impact of ${^{28}\text{S}\text{i}}^{q+}$ ions in the energy range of 8.5--36.0 MeV. The measured $\mathit{L}$ x-ray spectra were analyzed taking into account the multiple ionization effects in outer $M$ and $N$ shells. The $L$-subshell ionization cross sections have been obtained from measured x-ray production cross sections using the $L$-shell fluorescence and Coster-Kronig yields which were modified for a reduced number of electrons and closed Coster-Kronig transitions in the multiply ionized atoms. The results are compared with the available calculations, which are based on the semiclassical approximation (SCA) as well as the plane-wave Born approximation (PWBA). We demonstrate that for silicon ion impact these theoretical approaches have to be modified to include the $L$-subshell coupling effect using the ``coupled subshell model'' (CSM) as well as the saturation of the binding effect at the united atom limit. The calculations modified for both effects are in much better agreement with the data. In particular, an order-of-magnitude improvement of agreement between the data and the SCA-CSM calculations including the binding-saturation effect is reported for low-energy Si ions for the ${L}_{2}$-subshell. The results are also compared with the predictions of the PWBA based ECPSSR and ECUSAR theories accounting for the energy-loss (E), Coulomb-deflection (C), and relativistic (R) effects treating the binding effect within the perturbed stationary state (PSS) approximation with correction for the binding-saturation effect introduced to describe the united-atom and separated-atom (USA) limits.

L-subshell ionization of heavy elements by S ions with energy of 0.4–3.8 MeV/amu

The L-shell X-ray production cross sections have been measured for sulphur ions in the energy range of 12.8–120MeV for Au and Bi elements. The experimental L X-ray spectra were analyzed using the method that takes into account the multiple ionization in outer shells. The L-subshell ionization cross sections have been obtained from measured X-ray production cross sections for resolved Lα1,2 Lγ1 and Lγ2,3 transitions using the L-shell fluorescence and Coster–Kronig yields modified by the multiple ionization effects in the M and N shells. The results are compared with the predictions of ECUSAR theory, which is the modified ECPSSR approach describing both direct ionization and electron-capture processes and the semiclassical approximation (SCA) calculations for direct ionization. These approaches were modified by the L-subshell coupling effects within the “coupled-subshell model” (CSM). Both modified approaches are in good agreement with the data. Remaining discrepancies are discussed in terms of the L-shell decay rates modified for the multiple ionization effects.

Measurements of L X-ray production cross sections, L subshell fluorescence yields and K to L shell vacancy transfer probabilities

L i X-ray production cross sections have been measured for Sm, Eu, Gd, Dy, Ho, Er, Pt, Au, Tl, Pb and Bi at 59.54 keV incident photon energy. The values of L i subshell fluorescence yields ( ω 1, ω 2 and ω 3) have been determined using the presently measured X-ray production cross sections and the theoretical L i subshell photoionization cross sections values, Coster–Kronig transition probabilities and radiative emission rates. Furthermore, K to L shell vacancy transfer probabilities η KL i ( i=1, 2, 3) for Sm, Eu, Gd, Dy, Ho, Er were determined by measuring the L X-ray production cross section and L subshell fluorescence yields. The measurements were performed using an Am-241 radioisotope as the photon source and a Si(Li) detector. The measured X-ray production cross sections, fluorescence yields and vacancy transfer probabilities were compared with the theoretical values. The results in the present paper are found to be in good agreement with the calculated values.

Measurements and calculations of M-shell X-ray production in Er, Yb and Lu by 0.75–6 MeV He ions

M-shell X-ray production cross sections for the light rare-earth elements of 68Er, 70Yb and 71Lu have been measured for incident 4He+ ions in the energy range from 0.75 to 6MeV. The measured X-ray production cross sections are compared to the predictions of the First Born approximation, the ECPSSR theory and the ECUSAR theory. A comparison of the ytterbium M-shell X-ray production cross sections with these theories is made for two different sets of fluorescence yields and Coster–Kronig factors that are further modified for multiple ionization.

Multiple ionization and coupling effects inL-subshell ionization of heavy atoms by oxygen ions

The multiple-ionization and coupling effects in L-shell ionization of atoms by heavy-ion impact have been studied by measuring the L x-ray production cross sections in solid targets of Au, Bi, Th, and U bombarded by oxygen ions in the energy range 6.4--70 MeV. The measured L x-ray spectra were analyzed using the recently proposed method accounting for the multiple-ionization effects, such as x-ray line shifting and broadening, which enables one to obtain the ionization probabilities for outer shells. The L-subshell ionization cross sections have been obtained from measured x-ray production cross sections for resolved $L{\ensuremath{\alpha}}_{1,2},$ $L{\ensuremath{\gamma}}_{1},$ and $L{\ensuremath{\gamma}}_{2,3}$ transitions using the L-shell fluorescence and Coster-Kronig yields being substantially modified by the multiple ionization in the M and N shells. In particular, the effect of closing of strong ${L}_{1}\ensuremath{-}{L}_{3}{M}_{4,5}$ Coster-Kronig transitions in multiple-ionized atoms was evidenced and discussed. The experimental ionization cross sections for the ${L}_{1},$ ${L}_{2},$ and ${L}_{3}$ subshells have been compared with the predictions of the semiclassical approximation (SCA) and the ECPSSR theory that includes the corrections for the binding-polarization effect within the perturbed stationary states approximation, the projecticle energy loss, and Coulomb deflection effects as well as the relativistic description of inner-shell electrons. These approaches were further modified to include the L-subshell couplings within the ``coupled-subshell model'' (CSM). Both approaches, when modified for the coupling effects, are in better agreement with the data. Particularly, the predictions of the SCA-CSM calculations reproduce the experimental L-subshell ionization cross section reasonably well. Remaining discrepancies are discussed qualitatively, in terms of further modifications of the L-shell decay rates caused by a change of electronic wave functions in multiple-ionized atoms.

Measurement of L X-ray production cross sections and Li subshell fluorescence yields

L i ( i=1, 2 and 3) X-ray production cross sections have been measured for 14 elements in the atomic number range 55≤ Z≤81 at 15.73 keV. The values of L i subshell fluorescence yields ( ω 1, ω 2 and ω 3) have been determined using the presently measured X-ray production cross sections and the theoretical L i subshell photoionization cross sections values, Coster–Kronig transition probabilities and radiative emission rates. The measured X-ray production (XRP) cross-sections and fluorescence yield values were compared with the theoretical and semi empirical values, respectively.

L i ( i=1,2,3) subshell X-ray production cross-sections and fluorescence yields for Ir, Pt, Pb and Bi

The L i ( i=1,2,3) subshell X-ray production (XRP) cross-sections were measured for 77Ir, 78Pt, 82Pb and 83Bi following direct ionization in the L i ( i=1,2,3) subshells by the 59.54 keV γ-rays and the L 3 subshell by the Br/Rb/Sr/Y K X-rays. The photon sources consisting of an 241Am source in (i) the direct excitation mode and (ii) the secondary excitation mode together with the KBr/RbNO 3/SrCO 3 /Y secondary exciter and an Si(Li) detector were used. The L i ( i=1,2,3) subshell fluorescence yields ( ω i ) for these elements were deduced using the measured XRP cross-sections and the L i subshell photoionization cross-sections based on the Hartree–Fock–Slater model. The measured ω 1 values are found to be higher upto 50% than those based on the relativistic Dirac–Hartree–Slater (RDHS) calculations, while the ω 2 and ω 3 values exhibit good agreement. The predicted jump in the RDHS based ω 1 values from 77Ir to 78Pt due to onset of intense L 1–L 3M 4 CK transition is not observed.

L-shell ionization study of indium, tin, and rhenium by low-energy electron impact

The $L\ensuremath{\alpha},$ ${L}_{\ensuremath{\beta}},$ and $L\ensuremath{\gamma}$ x-ray production cross sections of In, Sn, and Re by electron impact were measured at energies from near threshold to tens of keV. Thin targets with thick substrates were used in the experiments. We compare the experimental results of Sn x-ray production cross sections with data determined by Baxter and Spicer [Aust. J. Phys. 36, 287 (1983)] with a different method, and present some results. The measured x-ray production cross sections are also compared with the binary encounter approximation theory of Gryzinski [Phys. Rev. 138, A336 (1965)] and the atomic-rearrangement theory of McGuire [Phys. Rev. A 16, 73 (1977)]. It is found that the L-shell production cross sections do not exhibit a gradual increase with atomic number, a result observed by Park et al. [Phys. Rev. A 12, 1358 (1975)] in a systematic study of L-shell x-ray production cross sections by MeV electron impact. For the present measured L-shell data of In and Sn, it seems that, so far, none of the available theories can adequately interpret the L-shell results at low energies.

Measurement of M-shell X-ray production induced by protons of 0.3–0.7 MeV on W, Au, Pb, Bi, Th and U

M-shell X-ray production cross-sections of the elements 74 W, 79 Au, 82 Pb, 83 Bi, 90 Th and 92 U induced by protons were measured in the energy range 0.3–0.7 MeV in steps of 50 keV. X-rays were registered by a Si(Li) detector. Values measured for the cross-sections of the most intense M-shell X-ray lines are presented. The measured X-ray production cross-sections are compared with PWBA and ECPSSR theoretical calculations. Results indicate the ECPSSR theory underestimates the experimental cross-sections for low energy protons.

L-subshell ionization studies in Au and Bi for 19F and 28Si large-ion bombardment.

{ital L} x-ray production and subshell ionization cross sections of Au and Bi have been measured for the bombardment of {sup 19}F and {sup 28}Si ions in the energy range 30{endash}57 MeV and 36{endash}84 MeV, respectively. Comparison of the {ital L}{alpha} x-ray production cross sections of Au with the earlier data by Malhi and Gray [Phys. Rev. A {bold 44}, 7199 (1991)] shows reasonable agreement for {sup 19}F impact and their data are consistently higher for {sup 28}Si at all energies. The measured {ital L}{alpha} line energy shows a shift towards higher energy, which appears to be proportional to the square of the projectile atomic number at all impact energies. This shift suggests the presence of multiple ionization in the {ital L} and {ital M} shells with a simultaneous production of four {ital M} holes in Au at the impact energy of 3 MeVu{sup {minus}1} of {sup 28}Si. The {ital L}-subshell ionization cross sections obtained from the measured x-ray production cross sections have been compared with the semiclassical approximation and perturbed stationary state theory with energy loss, Coulomb deflection, and relativistic correction for the electron motion calculations, which show large deviations for the {ital L}{sub 1} subshell. The {ital L}{submore » 2}- and {ital L}{sub 3}-subshell ionization cross sections are underestimated by both the theories by a factor of 1.2{endash}4.0 for {sup 28}Si impact whereas for the {sup 19}F case there is reasonable agreement for the {ital L}{sub 3} cross section but the {ital L}{sub 2} cross section is underestimated by 20{endash}30{percent}. {copyright} {ital 1996 The American Physical Society.}« less

L-subshell ionization studies in Ta, Au and Pb excited by 59.54 keV γ-rays

Measurement of L X-ray production cross sections and their relative intensities with respect to L α are reported for Ta, Au and Pb. Using the measured X-ray production cross sections, L- subshell ionization cross sections have been evaluated for different decay yield data sets and compared with the theoretical predictions of Scofield [Lawrence Livermore Laboratory report No. UCRL-51236, 1973 (unpublished)]. The comparison shows inadequacy of some of the decay yield parameters in providing good agreement with the theroetical predictions. It is also found that the present X-ray production cross sections are somewhat higher than the theoretical predictions, a trend similar to the results observed by Rao et al. [Phys. Rev. A 74 (1993) 1087] at lower photon energy. The intensity ratios, however, are found to be in good agreement with theoretical predictions obtained by using certain decay yield data.

M-shell ionization of rare earth elements by proton impact in the energy range 0.6–4.6 MeV

M-shell X-ray production cross sections of the rare-earth elements 57La, 60Nd, 62Sm, 63Eu, 64Gd, 66Dy, 67Ho, 66Dy, 67Ho, 68Er, 70Yb, 71Lu, and 72Hf were measured for proton bombardment in the energy range 0.6–4.6 MeV. The efficiency of the windowless Si(Li) detector for X-rays in the energy range 0.5–5.0 keV was determined by using the known atomic-field bremsstrahlung cross sections for low energy electron beams, K-shell X-ray measurements with protons, and calibrated radioactive sources. The measured X-ray production cross sections are compared to the predictions of the first Born approximation and the ECPSSR theories.

L-Subshell X-Ray Production Cross Sections of Ba, La and Ce for Proton Energies from 0.25 to 2.00 MeV

Protons from the University of Texas at Arlington's 2 MV Van de Graaff accelerator were used to produce characteristic L x-rays from thin targets of Ba, La and Ce. The incident proton energy was varied from 0.25 to 2.00 MeV. The x-rays were detected by a detector mounted at 90° to the incident beam direction. Measured x-ray production cross sections were converted to ionization cross sections by the use of subshell fluorescence yields and Coster-Kronig transition probabilities taken from Bambynek. Inflection points are found in the L1-subshell ionization cross section for all three elements. Although the theoretical plane-wave Born approximation (PWBA) curves do have inflection points (whereas the binary encounter approximation (BEA) curves do not), the PWBA theory does not correctly predict the proton energies at which these occur for all three elements.

L-Shell Ionization Cross Sections of BA, CE, ND, SM and DY for Proton Energies from 0.5 to 2.0 MeV

Protons from the University of Texas at Arlington's 2 MV Van de Graaff accelerator were used to produce characteristic L x-rays from thin targets of Ba, Ce, Nd, Sm and Dy. Incident proton energies were varied from 0.5 to 2.0 MeV. The x-rays were detected by an ORTEC High Purity Germanium Low Energy Photon Spectrometer (LEPS) mounted at 90° to the beam direction. The incident proton beam was monitored by a particle detector also mounted at 90° to the beam direction. The measured x-ray production cross sections were converted to ionization cross sections by the use of subshell fluorescence yields and Coster-Kronig transition probabilities taken from Bambynek. Comparison of these ionization cross sections as well as the ratios of selected subshell x-ray yields with the predictions of the Plane Wave Born Approximation (PWBA) and the Binary Encounter Approximation (BEA) show that the PWBA predictions fit the experimental results much better than the BEA predictions.

L-subshell ionization cross sections for Au, Pb, and Bi by 60?600 keV electron impact

TheL1-,L2- andL3-subshell ionization cross sections of Au, Pb and Bi by 60–600 keV electron impact have been determined from the measured x-ray production cross sections. The experimental results have been compared with the relativistic PWBA, the Binary Encounter Approximation (BEA) and the Kolbenstvedt Approximation (KA) calculations. These calculations, especially the relativistic PWBA, give good agreement with the experimental data for theL3-subshell. For theL1- andL2-subshells there are some deviations and these can explain the disagreement observed for theLα/Lχ- andLγ/Lχ intensity ratios.

SiK-shell ionization and electron transfer cross sections: Solid targets

The Si K x-ray production cross sections for F/sup q/+(q = 3--9) ion impact in the energy range of 0.4--2.2 MeV/amu are determined in the limit of a vanishingly thin target from the observed target thickness dependence of the x-ray yields. The ionization cross sections are deduced from the measured x-ray production cross sections using an average fluorescence yield (omega-tilde = 1.5..omega../sub 0/, where ..omega../sub 0/ is the fluorescence yield for an atom with single K vacancy) determined from high-resolution x-ray spectra and configuration fluorescence yields. For F/sup q/+ (q < or = 6) ion impact, the measured ionization cross sections are compared with the plane-wave-Born-approximation prediction with and without the Coulomb deflection and increased-binding-energy effects. The Si K shell to F K shell electron-transfer cross sections are determined from the difference between the ionization cross sections for F/sup 9 +/ ions and those for F/sup q/+ ions (q < or = 6). The results are compared with the prediction based on the two-state atomic-expansion method and that based on the modified Oppenheimer-Brinkman-Kramers approximation. A comparison is also made between the Si solid-target measurements with those obtained for gaseous Ne and Ar gas targets. The solid-target and gas-target data aremore » consistent at 1.58 MeV/amu. Finally, from a comparison between the measured equilibrium x-ray yields and the calculated x-ray yields using the equilibrium charge distribution of projectiles after passing through foils, it is found that the projectiles have a considerably larger number of K-shell vacancies inside solids than after passing through solids at lower-impact energies.« less

L-subshell ionization of Au, Tl, Pb, Bi, Th, and U by protons

$L$-subshell ionization cross sections for Au, Tl, Pb, Bi, Th, and U by proton impact have been determined over the projectile range 0.5-3.5 MeV. The measured x-ray production cross sections of the total $L$ shell and of some well resolved lines or groups of lines are consistent with those obtained by different authors in the same regions of bombarding energies and atomic numbers. Ionization cross sections were obtained by using the above results and experimental values for the relative radiative transition probabilities, fluorescence yields, and Coster-Kronig factors. The branching ratios of radiative transitions were measured and are in good agreement with the widely used theoretical calculations of Scofield, Rosner, and Bhalla. The values of fluorescence and Coster-Kronig yields were taken from previously published experiments performed in our laboratories. The influence of these experimental data on the shape of cross section versus proton energy curves is discussed. Comparisons of the experimentally determined $L$-subshell ionization cross sections are made with calculations in the plane-wave Born (PWBA), semiclassical, and binary-encounter approximations. The large effect of binding-energy, trajectory, and relativistic corrections on the PWBA calculations invalidates quantitative conclusions regarding agreement between experimental and theoretical values. Semiclassical arguments are presented, however, to explain some general aspects of the ionization cross-section curves.