M-shell X-ray Production Cross Sections Research Articles

X-ray production cross sections induced by carbon ions

The K-shell of Ti, Cr, Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb x-ray production cross sections, L-shell x-ray production cross sections of Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, Ta, W, Pb, Bi and M-shell x-ray production cross sections of Ta, W, Pb and Bi were measured for 9.6–19.2 MeV 12C2+ ions and are compared to the ECPSSR and PWBA theories. The cross sections were calculated through the Rutherford backscattering cross section, which can be calculated from the Rutherford formula. The ECPSSR and PWBA calculations were performed with the ISICS11 code.

W and Tl M-shell X-ray production cross sections induced by carbon ions of energy between 1.56 MeV and 5 MeV

Although PIXE is usually performed with protons, PIXE with heavier ions can be useful in some specific cases. A number of Ion Beam Analysis (IBA) techniques, like ERDA (Elastic Recoil Detection Analysis), NRA (Nuclear Reaction Analysis), AMS (Accelerator Mass Spectrometry), or MeV-SIMS (MeV Secondary Ion Mass Spectrometry), require the use of heavier ions. In such cases the simultaneous use of PIXE could be beneficial. One of the prerequisites for such use of PIXE is good knowledge of X-ray production with heavier ions. In order to update the data base of heavy ion X-ray production cross sections, we have recently started with the systematic study of M-Shell X-ray production induced by carbon ions on heavy elements between W and Bi. Following previous works on Au and Pb (Haidra et al., 2018) and Pt and Bi (Haidra et al., 2019). In this work, we have measured particularly Mαβ, Mγ and total M-shell X-ray production cross section in tungsten and thallium induced by carbon ions of energy range 1.56 MeV to 5 MeV on respective thin targets. The obtained new experimental data are compared to the theoretical predictions given in the framework of the models Plane Wave Born Approximation (PWBA) (Brandt and Lapicki, 1981), ECPSSR (Brandt and Lapicki, 1981) and the Semi-Classical Approximation with united atom (SCA-UA) and separated atom (SCA-SA) correction (Bang and Hansteen, 1957) [5].

L-shell X-ray production cross sections of Ag and Au induced by carbon ions between 2 MeV and 5 MeV

In this work, we experimentally determined Ag and Au L-shell X-ray production and ionization cross sections, induced by 2–5 MeV carbon ions. The experiment was performed using the standard measurement setup already used to measure M-Shell X-ray production cross sections. Ag and Au thin targets, were used to measure L-shell X-ray spectra with Si(Li) and SDD X-ray detectors simultaneously with backscattered carbon ions from the targets by surface barrier detector. Experimental values are compared to the data available in the literature, as well as to the theoretical predictions of PWBA, ECPSSR and ECUSAR models. The analysis of data shows that the ECUSAR predictions are good at low carbon ion energies while the ECPSSR and PWBA predictions agree at the higher incident energies.

L- and M-shell X-ray production cross section measurements in 73Ta and 78Pt using B3+,4+-ions of energies below and above the potential barrier

In this paper, we report the L- and M-shell X-ray production cross sections in 73Ta and 78Pt caused by the bombardment of 35 to 60 MeV B3+,4+-ions. The energies of B-ions, below and above the potential barrier, were selected to study the effect on inner- and outer-shell ionization i.e. absolute X-ray production cross sections for various L- and M X-ray lines/group of lines (namely Lℓ, Lα2, Lα1, Lη, Lβ4,6, Lβ1, Lβ3, Lβ2,15, Lβ5,7,9,10, Lγ5, Lγ1, Lγ2,3,6, Lγ4,4′, Mξ2,1, Mδ + M3N1, Mα1,2 + M2N1, Mβ + Mη, Mγ, Mm11 (M3O1 + M3O4,5), Mm12 (M2N4 + M1N3), Mm21 (M2O1), Mm22 (M2O4 + M1O2,3) and the change in the intensity ratios due to multiple ionization of M- and higher-shells. The present measurements were carried out at 16UD Pelletron Accelerator at Inter-University Accelerator Centre (IUAC) Delhi. The ion beams were bombarded on thin targets evaporated on an ultrapure carbon backing of 10 μg/cm2. The targets fixed on a steel ladder were placed in an evacuated (<10−6 Torr) scattering chamber at 45° each to the beam direction and to the Si(Li) detector. The recorded L and M X-ray spectra were separately deconvoluted into various components of the L and M X-ray lines using the computer code after subtracting suitable background. The experimental results have been compared with the theoretical values by converting the L and M-subshell ionization cross sections based on the PWBA and ECPSSR direct-ionization theories taking into effect the sub-shell fluorescence yields, Coster-Kronig transition probabilities and transition rates based on Dirac-Fock and Dirac-Hartree-Slater models. In the present measurements (0.0641 ≤ Z1/Z2 ≤ 0.0685), the velocity ratios v1/v2pi and the reduced ion velocity ξpi = 2v1/(θpi.v2pi) for p = L- or M-shell are in the range of 0.309 ≤ v1/v2Li ≤ 0.435 and 0.913 ≤ ξLi ≤ 1.316 and the ratios v1/v2Mi and ξMi for M-shell are in the range of 0.555 ≤ v1/v2Mi ≤ 0.790 and 2.575 ≤ ξMi ≤ 3.779 respectively. To the best of our information, this study of B-ion impact on 73Ta and 78Pt, near the potential barrier of the system which falls in the fast (ξLi ≈ 1, ξMi > 1) collision regime, is being reported for the first time.

New measurements of Mαβ, Mγ and total M-shell X-ray production cross sections induced by carbon ions on Bi and Pt targets

In this work X-ray and elastic backscattered spectra from Pt and Bi thin targets were simultaneously measured using C4,3+ ions in the energy range 2.5 MeV to 5 MeV. Mαβ, Mγ and total M-shell X-ray production cross sections were extracted from collected X-ray and backscattered particle spectra using calibrated SDD X-ray and silicon solid state particle detectors. The obtained cross section values are compared to theoretical values employing commonly used datasets for fluorescence yields, emission rates, Coster-Kronig transitions and M-shell ionization cross sections based on the Semi-classical Approximation (United Atom and Separated Atom limits), PWBA (Plane Wave Born approximation), and ECPSSR models. The ISICS code was used for PWBA and ECPSSR calculations.

Measurements of the line resolved M-shell X-ray production cross sections for 79Au, 82Pb and 83Bi by 100 keV/u proton, C, N, O ions

The cross sections for production of the Mk (k=ξ, αβ, γ, m1) X-rays of 79Au, 82Pb and 83Bi induced by the 100keV/u proton, C4+, N5+ and O6+ ions have been measured in the present work. The experimental cross sections have been compared with the earlier reported values and those calculated using the ionization cross sections based on the ECPSSR model, the X-ray emission rates based on the Dirac-Fock model, the fluorescence and Coster-Kronig yields based on the Dirac-Hartree-Slater model. In addition, the present measured proton induced X-ray production cross sections have also been compared with those calculated using the Dirac-Hartree-Slater model based ionization cross sections. The intensity ratios among the Mk X-rays have been deduced and compared with the theoretical values. The present measured Mk (k=ξ, αβ, γ, m1) X-ray production cross sections are found to be very high as compared to the theoretical values. The total M X-ray production cross sections for the targets under investigation exhibited Zp2 dependence; Zp denotes the projectile atomic number.

Feasibility study of thin films deposited on a self-supporting carbon grid substrate target on the measurement of atomic inner-shell ionization cross-sections impacted by 3–30 keV electrons

In this paper, we have measured the , and X-ray production cross-sections of the W element and the K-shell ionization cross-sections of the Al element impacted by 3–30 keV electrons. A new kind of target consisting of a thin film deposited on a self-supporting carbon grid substrate has been used in this work. The self-supporting carbon grid substrate is made of several layers of super-aligned carbon nanotube arrays (the mass thickness of each layer of super-aligned carbon nanotube arrays is 20 μg/cm2). As a comparison, three kinds of targets consisting of a) the studied element deposited onto four layers of super-aligned carbon nanotube arrays and separated from each other by one layer of single carbon atoms, b) the studied element deposited directly onto four layers of super-aligned carbon nanotube arrays, and c) the studied element deposited directly onto two layers of super-aligned carbon nanotube arrays, were respectively prepared to figure out which type is fit for the measurement of inner-shell ionization cross-sections induced by 3–30 keV electrons. The experimental data are compared with the distorted-wave Born approximation (DWBA) theoretical predictions and with the available experimental data from other references. The results show that the first and the second targets are both suitable for the inner-shell ionization cross-section measurements by 3–30 keV electrons, but the third target is not. Besides, we present the M-shell X-ray production cross-sections of the W element by 5–30 keV electrons in this paper for the first time.

Relativistic calculations of K-, L- and M-shell X-ray production cross-sections by electron impact for Ne, Ar, Kr, Xe, Rn and Uuo

In this work, we derive X-ray production cross-sections from electron-impact ionization cross-sections for Ne, Ar, Kr, Xe, Rn, and Uuo, calculated in the modified relativistic binary-encounter-Bethe model, and using as the only input parameter the binding energies obtained in the Dirac-Fock approach. Radiative and radiationless transition probabilities necessary to compute the inter- and intra-shell atomic yields were calculated in the same approach. Shell electron-impact ionization cross-sections and X-ray production cross-sections are compared with the corresponding cross-sections retrieved from the National Institute of Standards and Technology Reference Database and available experimental data.

Empirical M X-ray production cross sections for heavy elements by proton impact within Z-dependence analysis

New empirical M-shell X-ray production cross sections have been deduced by introducing the dependence of the universal trend of the experimental data on the atomic number of the target, noted as "Z-dependence" for semiempirical cross sections in our previous work. For this effect, the updated experimental data (from 1980 to 2009) are used to calculate the empirical cross sections for heavy elements with 60 $\le $ Z $\le $ 90 by proton impact. Finally, a comparison is made between the deduced results and other earlier works.

Hafnium to thorium M-shell X-ray production cross sections by proton impact

Theoretical M-shell X-ray production cross sections have been calculated within the ECPSSR model. The semi-empirical cross sections are then deduced by fitting the available experimental data normalized to their corresponding theoretical values for elements with 72 ≤ Z ≤ 90 by proton in the energy range 0.1–4.0 MeV. Also, an analytical formula has been used to calculate the empirical X-ray production cross sections by direct fitting of the same experimental data, which are found to be universal, both for individual and collective fits. On the other hand, based on the individual fitting which gives the reliable cross sections, we attempt to deduce another new empirical cross sections by assuming that the ratio empirical to ECPSSR of the cross sections is roughly the same for all elements. In addition, our results are presented for selected heavy elements, namely 74W, 79Au and 83Bi, being the most extensively studied. Finally, a comparison is made between the different procedures followed here and the experimental data.

K-, L- and M-shell x-ray production cross sections by 1–1.3 MeV protons

In 2012, our institute had initiated a series of research activities aimed to measure the characteristic x-ray production cross-section, arising from interaction of accelerated particles with target atoms. This paper presents the data of x-ray production cross-sections under excitation of K-, L- and M-shells of target atoms in the range of mass from Mg to Bi by protons of the energies in the range of 1–1.3MeV. We used the approach based on calculation of x-ray production cross sections through the cross-section of Rutherford backscattering, which can be calculated with high accuracy from the Rutherford formula. Such approach reduces the measurement errors of x-ray cross-sections and thus improves the accuracy of the obtained data. It is further planned to expand the area of research to protons of other energies and heavy charged particles in the energy range of 0.5–1.7MeV/nucleon.

Z-dependence and collective analysis of M x-ray production cross sections for a wide range of elements (60≤Z≤90) by proton impact

Based on the remarkable spread of the ratios of the experimental to theoretical M-shell x-ray production cross section, where they are usually analyzed by a function depending only on the scaled velocity parameter, we attempt to deduce new semi-empirical cross sections by introducing the dependence of these ratios on the atomic number of the target, noted as “Z-dependence”. For this effect, the ECPSSR model and the updated experimental data (from 1980 till 2009) of the M-shell x-ray production cross sections are combined to calculate the semi-empirical cross sections for a wide range of heavy elements (60≤Z≤90) by proton impact. A brief discussion of the agreement between our results and earlier theoretical as well as experimental works has been demonstrated.

Thorium and uranium M-shell x-ray production cross sections by 4.5–11.3 MeV carbon ion and 4.5–13.5 MeV oxygen ion bombardment

The M-shell x-ray production cross sections for thorium and uranium have been measured for carbon ions with energies from 4.5 to 11.3 MeV with the charge state q increasing from 2 to 4, and oxygen ions with energies from 4.5 to 13.5 MeV with the charge state q increasing from 2 to 5. These cross sections are compared to the predictions of the first Born (PWBA+OBKN) and ECUSAR ionization theories, which were evaluated in a novel manner for the C+q and O+q energies and charge states of the data and converted to x-ray production cross sections with atomic parameters for a singly ionized M-shell and multiple ionization in the outer shells. Individual groups of M-shell transitions are also compared to the two ionization theories. The ECUSAR theory is shown to describe the measurements better than the first Born approximation. It is found to be in generally good agreement for all the total M-shell x-ray production and M-shell lines except for the Mγ cross sections. Reasons for the overestimation of the Mγ data are discussed.

Lower and upper bounds on M-shell X-ray production cross sections by heavy ions

In inner-shell ionization by heavy ions, a significant shift of X-ray lines to the higher energy side and broadening of the peaks indicate that simultaneous multiple ionization of the M and higher shells can dramatically change the values of the atomic parameters. 14 Si 3 , 4 + and 16 S 3 , 4 + ions in the energy range of 5–10 MeV were used to bombard gold (200 μg/cm 2) and bismuth (80 μg/cm 2) targets. Eight main M X-ray lines have been detected with a Si(Li) detector. Without a possibility for a realistic way to modify the atomic parameters and an accurate extraction of M-subshell ionization cross sections, theoretical cross sections for M-shell ionization are converted to X-ray production cross sections with two extreme choices that presume (i) no multiple ionization and (ii) the certainty that all shells outer to the M-shell are completely ionized in the full multiple ionization. These choices impose the lower and upper limits on theoretical predictions. The X-ray production data should be bracketed by the bounds calculated with any theory. We test this proposition by comparison of the measured cross sections for production of the main X-ray lines and their sum for the total M-shell X-ray production with the predictions of the First Born and ECUSAR [G. Lapicki, Nucl. Instrum. Meth. B 189 (2002) 8] theories in those two extreme limits. With the extreme assumption of no multiple ionization, the First Born approximation shows overall satisfactory agreement with the data while the ECUSAR theory drastically underpredicts our measurements. With the opposite extreme assumption of the full multiple ionization, the ECUSAR exhibits better agreement with the data than the First Born approximation. While neither agreement suggests sure preference for either of these theories, such extreme conversions – as they would have for of any ionization theories – set the lower and upper bounds on their predictions.

On the angular dependence of differential and total M-shell X-ray production cross-sections

The article “Differential and total M-shell X-ray production cross-sections of some selected elements between Au and U at 5.96keV”, published in NIMB 256 (2007) 581 claims that the measured data of differential photoelectric cross-sections for inner atomic shells has an angular dependence with the scattering angle. It is not possible to demonstrate the existence of a physical dependence on the angle between the paths of the incident and exiting X-ray beams from a sample based on this data with large experimental errors. A rigorous analysis of the article reveals that the description of the experimental set-up is deficient and incomplete, many assumptions are based on dubious grounds and the data reported is not statistically evaluated with the appropriate tools.

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.

M-shell X-ray production cross-sections for elements with 67 ⩽ Z ⩽ 92 at incident photon energies [formula omitted

The X-ray production cross-sections for the M k ( k = ξ, δ, α, β, ζ, γ, m 1 and m 2) groups of X-rays have been evaluated for all the elements with 67 ⩽ Z ⩽ 92 at incident photon energies ranging E M 1 < E inc ⩽ 150 keV using currently available theoretical data sets of different physical parameters, namely, partial photoionization cross-sections, X-ray emission rates, fluorescence and Coster–Kronig yields, and the K-shell/L j ( j = 1–3) subshell to the M i ( i = 1–5) subshell vacancy transfer probabilities, based on the independent particle models.

Measurement of M-shell X-ray production cross sections for the element 73 $\leqslant$ Z $\leqslant$ 83 using 5.96 keV photons

Total M-shell X-ray production cross sections (M XRF) of the some elements in the atomic number range \(73 \leqslant Z \leqslant 83\) were measured at 5.96 keV incident photon energy using a Si(Li) detector. The results are compared with the experimental and theoretical values in the literature.

Differential and total M-shell X-ray production cross-sections of some selected elements between Au and U at 5.96 keV

Differential M-shell X-ray production (MXRP) cross-sections for selected heavy elements between Au and U have been measured at 5.59keV incident photon energy, respectively at seven angles varying from 120° to 150° a Si(Li) detector. The differential M-shell X-ray production cross-sections have been derived, using M-shell fluorescence yields, experimental total M X-ray production cross-sections and theoretical M-shell photoionization cross-sections. The differential M-shell X-ray production cross-sections have been compared with the semi-empirical fits. The measured differential M X-ray production cross-sections have been found within experimental error. Differential M X-ray production cross-section can be fitted to the ∑nanZn (n=2) as a function of cosθ. Total M X-ray production cross-sections have been derived using the fitted values.

L-subshell and total M-shell X-ray production cross sections of Ta, W, Pt, Au, Pb and Bi by 0.7–2.4 MeV protons

The L-subshell and total M-shell X-ray production cross sections of Ta, W, Pt, Au, Pb and Bi have been measured by protons of energy between 0.7 and 2.4MeV. The obtained results for X-ray production cross sections have been compared with the existing experimental data, prediction of the ECPSSR theory and also with fitted empirical cross sections of Strivay and Weber.