L-shell x-ray production for Rh, Ag, Cd, Sb and I with protons in the energy range from 1.6 to

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1 HOME SEARCH PACS & MSC JOURNALS ABOUT CONTACT US L-shell x-ray production for Rh, Ag, Cd, Sb and I with protons in the energy range from 1.6 to 5.2 MeV This article has been downloaded from IOPscience. Please scroll down to see the full text article J. Phys. B: At. Mol. Opt. Phys ( The Table of Contents and more related content is available Download details: IP Address: The article was downloaded on 15/12/2009 at 10:13 Please note that terms and conditions apply.

2 J. Phys. B: At. Mol. Opt. Phys. 29 (1996) Printed in the UK L-shell x-ray production for Rh, Ag, Cd, Sb and I with protons in the energy range from 1.6 to 5.2 MeV I Bogdanović and S Fazinić Ru der Bošković Institute, PO Box 1016, Zagreb, Croatia Received 1 September 1995 Abstract. Individual L α, L β1,3,4,6, L β2,15,7, L γ1,5 and L γ 2,3(4,4 ) x-ray production cross sections for the elements Rh, Ag, Cd, Sb and I have been measured by protons in the energy range 1.6 to 5.2 MeV. The experimental results for x-ray production cross sections and cross section ratios are compared with the RPWBA BC theoretical predictions and with the other available experimental data. The influence of using different databases for atomic parameters in the conversion of theoretical L-shell ionization cross sections to the L-shell x-ray production cross sections is discussed. 1. Introduction In the last few decades x-ray production in light ion atom collisions has been extensively studied from both experimental and theoretical points of view. Such studies have proven to be very important in understanding the complex mechanism of inner-shell ionization. At the same time, accurate knowledge of the ion-induced x-ray production cross sections for projectile energies of up to 5 6 MeV u 1 is important for ion beam applications (e.g. PIXE). A large portion of the experimental x-ray production cross section data published so far are on K and L shells ionized by protons. However, an extensive literature search for L x-ray studies with protons indicated that a very limited amount of data are available for elements lighter than Cs (Z = 55). For most of these elements only data about total L-shell x-ray production cross sections exist. Some data have been published only in graphical form. Some authors reported only L-subshell ionization cross sections, calculated from originally measured L-shell x-ray production cross sections with the help of the L-subshell vacancy decay yields. This practice of reporting only L-subshell ionization cross sections already makes the comparison of various experimental and theoretical results more difficult, and has been criticized (Cohen et al 1990). In this paper we report on the measurements of L-shell x-ray production cross sections for Rh, Ag, Cd, Sb and I in the proton energy range between 1.6 and 5.2 MeV. To facilitate conversion to ionization cross sections, the individual L- shell x-ray production cross sections for L α,l β1,3,4,6,l β2,15,7,l γ1,5 and L γ 2,3(4,4 ) x-ray lines have been derived and reported. The data about individual L-shell x-ray production cross sections for these elements are available in the literature only for Ag and Sb in the proton energy range between 0.4 and 2 MeV (Sow et al 1994). Most of the experimental data for L α and L total x-ray production cross sections published so far can be found in the compilation by Sokhi and Crumpton (1984) and in the recent compilation by Orlić et al (1994a). For L α x-ray production cross sections experimental data are available for Ag in the proton energy range between 0.25 and 1.75 MeV (Sarter et al 1981, Jesus et al 1986), /96/ $19.50 c 1996 IOP Publishing Ltd 2021

3 2022 I Bogdanović and S Fazinić for Cd in the proton energy range between 0.25 and 0.4 MeV (Sarter et al 1981), and for Sb in the proton energy range between 0.5 and 3.2 MeV (Jesus et al 1986, Braziewicz et al 1984). Rosato et al (1986) reported only L-shell ionization cross sections in graphical form for Ag and I for proton energies between 0.3 and 5 MeV. The results obtained are compared with other available experimental data and with theoretical predictions. Theoretical individual L-shell x-ray production cross sections have been calculated in the usual way from L-subshell ionization cross sections with the help of the atomic parameters as L-subshell fluorescence yields, Coster Kronig transition probabilities and x-ray emission rates. In the field of inner-shell ionization during ion atom collisions, several theories have been formulated. Inner-shell ionization theories very often used are the semiclassical approximation (SCA) (Bang and Hansteen 1959), and the socalled ECPSSR scheme of Brandt and Lapicki (1979, 1981). Cohen and Harrigan (1985) have published extensive tables based on the ECPSSR model using hydrogenic electron wavefunctions. Chen and Crasemann (1989) have published their tabulation based on the same model but using Dirac Hartree Slater (DHS) wavefunctions (RPWBA-BC model). Here relativistic (R) direct ionization cross sections have been evaluated in the frame of the plane-wave Born approximation (PWBA) with DHS wavefunctions, including binding (B), polarization and Coulomb deflection (C) corrections. The same DHS wavefunctions were used by Chen et al (1981) in a computation of L-subshell fluorescence and Coster Kronig yields. As stated by Campbell (1988), these RPWBA BC ionization cross sections, together with the L-subshell fluorescence and Coster Kronig yields calculated by Chen et al (1981), and the DHS x-ray emission rates of Scofield (1974a), provide a self-consistent theoretical database based on the DHS model. However, instead of DHS x-ray emission rates we have used Scofield s later Dirac Fock (DF) x-ray emission rates (Scofield 1974b) as tabulated by Campbell and Wang (1989). It has already been pointed out that these DF L-shell x-ray emission rates are more reliable than the DHS values (Campbell 1988). This self-consistent theoretical database has received wide acceptance in atomic physics and is used in this work for comparison with our experimental data. The other often used database for L-subshell fluorescence yields and Coster Kronig transition probabilities, based on some theoretical calculations and experimental pre-1979 data, has been published by Krause (1979). According to Krause s compilation there is a sharp break in the L 1 -subshell x-ray fluorescence yield ω 1 between In and Sn. The L 1 - subshell x-ray fluorescence yields ω 1 for the elements between 46 <Z<54 were studied by Rosato (1986). According to his semiempirical results, ω 1 increases smoothly with Z with no evidence of any jump. The DHS values of ω 1 calculated by Chen et al (1981) are in good agreement with the Krause s data for the elements with Z>49. But, in the case of Rh and Ag the ratio of Krause s and Chen s ω 1 is 1.41 and 1.40, respectively. Since Chen et al (1981) have calculated their results only for some elements, the interpolation scheme of Campbell and Wang (1989) has been used here. The influence of using different databases for atomic parameters in the conversion of theoretical L-shell ionization cross sections to L-shell x-ray production cross sections is discussed. 2. Experiment The proton beam was obtained from the EN tandem Van de Graaff accelerator at the Ru der Bošković Institute in Zagreb. All details about the experimental set-up can be found elsewhere (Fazinić et al 1994). The nominal thicknesses and compositions of the targets used for the measurements are given in table 1. All targets were deposited on 1 mg cm 2 Nucleopore backing, except for CdSe which was deposited on 20 µg cm 2 thin carbon

4 L-shell x-ray production for Rh, Ag, Cd, Sb and I 2023 Table 1. The nominal thickness and composition of targets used for the measurements. Element Nominal elemental composition Nominal target thickness (µg cm 2 ) Rh Rh 47.7 Ag Ag 45.7 Cd CdSe 20 Sb Sb 51 I RbI 96.3 Figure 1. Si(Li) detector efficiency. Circles represent experimental points obtained by measuring K x-rays emitted from selected thin targets. The full curve represents the calculated efficiency with a Si dead layer thickness of 260 nm, gold layer thickness 26 µg cm 2, Si crystal thickness of 3 mm, 12.5 µm thick beryllium window, 0.4 µm thick ice layer deposited on the surface of the detector crystal and 55 µm thick Kapton absorber between target and x-ray detector. foil. In order to avoid target damage and charge build up on the target, and to reduce dead-time correction and pile-up effect, the proton current was kept below 2 na all the time. The proton energies were varied in 0.4 MeV steps from 1.6 MeV to 5.2 MeV. The L x-rays were detected using a Link Analytical Si(Li) detector with nominal active area of 80 mm 2, Be window thickness of 12.5 µm and measured x-ray energy resolution (FWHM) of 150 ev at 5.9 kev. It was mounted inside the vacuum chamber at 135 to the beam axis. A thin Kapton film (55 µm) was placed in front of the detector to attenuate the intense M x-rays. Relative Si(Li) detector efficiency was determined from measuring the K x-rays emitted from a set of thin calibrating targets and using the method proposed by Lennard and Phillips (1979). To determine absolute efficiency, the radioactive calibrating source 55 Fe was used. Figure 1 shows the resulting detector efficiency. The full curve presents the efficiency which was calculated with the computer code TTPIXAN developed by Orlić et al (1990). In the x-ray energy region of interest the measured detector efficiency had an uncertainty of up to 6%, coming mainly from the uncertainties in the K-shell cross sections. Protons elastically scattered from the target were collected simultaneously with

5 2024 I Bogdanović and S Fazinić characteristic x-rays, and detected with an annular Si surface-barrier detector (active area 400 mm 2 ) positioned at 170 relative to the beam direction. To keep statistical errors below 2%, x-ray spectra were collected until the L γ 2,3(4,4 ) line intensity was more than 3000 counts. The non-linear least-square fitting routine AXIL (Van Espen et al 1985) was used for removing the background and for resolving the individual L-shell x-ray transitions in the measured spectra. The detector resolution allowed us to resolve L α,l β1,3,4,6,l β2,15,7,l γ1,5,l γ2,3(4,4 ) and L 1 x-ray lines. Corresponding L-shell x-ray production cross sections σli x were calculated according to the formula σli x = 4πY xσ p p F (E, E) (1) Y p ε x 1 + ((2 + β)/2)( E/E) F (E, E) = (2) 1 (α β + µ x) E/(2E) where Y x and Y p are x-ray and backscattered proton intensities corrected for dead-time, ε is the Si(Li) detector efficiency, x and p are x-ray and particle detector solid angles and σ p is the differential Rutherford cross section at an angle θ. The factor F (E, E) is the correction factor due to the self-absorption of the x-rays and proton energy loss inside the target (Pajek et al 1989). x = (E/S(E))(cos γ/cos δ), with γ being the angle between a normal to the target and ion beam axes, and δ the angle between a normal to the target and the x-ray detector direction. For our experimental set-up γ = 0 and δ = 45. F (E, E) was calculated using Ziegler et al (1985) data for the stopping power S(E), and Thin and Leroux (1979) data for the x-ray mass attenuation coefficients µ. F (E, E) was varying from 1% for Cd L α x-ray line to 9% for Rh L γ 2,3 x-ray line. At higher proton energies possible deviations from the Rutherford scattering can exist due to nuclear-force interactions between the projectile and target nucleus. A simple model developed by Bozonian et al (1990) was used to estimate the energy at which deviations from the Rutherford cross section are higher than 4%. It was found that for Rh, Ag, Cd, Sb and I these critical energies were 4.3, 4.5, 4.6, 4.9 and 5 MeV, respectively. Since these critical energies are within the studied energy interval, it was necessary to quantify possible non-rutherford effects. For this purpose, thin targets of all studied elements were covered with thin gold foil. These targets were irradiated with protons at the energies for which the x-ray measurements were done. Spectra of elastically scattered protons were collected by an annular Si surface-barrier detector at the same geometry. The cross sections for elastic scattering were obtained by normalization to the Au cross sections (they have Rutherford Table 2. Total experimental uncertainties for x-ray production cross sections (%). Proton energy Total experimental uncertainties (%) Element (MeV) L α,l β1,3,4,6,l β2,15,7,l γ1,5 L γ2,3(4,4 ) Rh Ag Cd Sb I

6 L-shell x-ray production for Rh, Ag, Cd, Sb and I 2025 values within the investigated proton energy range). From these measurements we found that Rh, Ag and Cd elastic scattering cross sections at the highest energies are lower than the Rutherford values. For an energy of 4.8 MeV the deviations are 8% for Rh and 7% for Ag. At 5.2 MeV the discrepancies are 13% for Rh, 8% for Ag and 11% for Cd. For Sb and I the deviations from the Rutherford cross sections were not observed. However, even for these cases we normalized our final results to the Rutherford cross sections and the observed deviations were incorporated in the total errors reported in table Results and discussion The measured L α,l β1,3,4,6,l β2,15,7,l γ1,5 and L γ 2,3(4,4 ) x-ray production cross sections for Rh, Ag, Cd, Sb and I, calculated by equation (1), are listed in table 3. Figure 2 shows the ratio between experimental and theoretical RPWBA BC predictions for L total x-ray production cross sections for all the elements from this study, as a function of the logarithm on the average reduced L-shell velocity parameter ξ L, which is defined as: ξ L = (ξ L1 + ξ L2 + 2ξ L3 )/4. Here ξ Li = 2v 1 n 2 /(θ Li Z 2L ), where v 1 is the velocity of the projectile, n is the principal quantum number of the L-shell electron, Z 2L is the effective nuclear charge of the target seen by an electron in the L shell (Z 2L = Z , Z 2 is the target atomic number), and θ Li = U Li n 2 /(Z2L 2 R ) is the scaled binding energy. U Li is the observed binding energy for the L i subshell, and R is the Rydberg constant. It can be seen that there is a good agreement between the RPWBA BC theory and the present experimental results for all the elements studied. Theoretical RPWBA BC L-subshell ionization cross sections were converted to individual L-shell x-ray production cross sections by the following relation: σli:p x = σ Li x F Li:p (3) Figure 2. Ratio of experimental L total x-ray production cross sections to the RPWBA BC predictions, as a function of the average reduced L-shell velocity parameter ξ L., Rh;, Ag;, Cd;, Sb;, I. Typical error bars are shown.

7 2026 I Bogdanović and S Fazinić Table 3. Proton-induced L-shell x-ray production cross sections a (in barns). Z Energy (kev) L α L β1,3,4,6 L β2,15,7 L γ 1,5 L γ 2,3(4,4 ) Rh Ag Cd Sb I a The uncertainties are given in table 2. where σli:p x are x-ray production cross sections for L p x-ray lines, F Li:p are fractional radiative widths involving the L i subshells, and σli x are x-ray production cross sections for the L i subshells (i = 1, 2, 3) expressed as σl1 x = σ L1ω 1 (4)

8 L-shell x-ray production for Rh, Ag, Cd, Sb and I 2027 Figure 3. Individual L-shell x-ray production cross sections for Ag as a function of proton energy., present measurements;, Sow et al (1994);, RPWBA BC theory. Figure 4. Individual L-shell x-ray production cross sections for Sb as a function of proton energy., present measurements;, Sow et al (1994);, Braziewicz et al (1984);, RPWBA BC theory. σl2 x = (σ L2 + σ L1 f 12 )ω 2 (5) σl3 x = (σ L3 + σ L2 f 23 + σ L1 (f 13 + f 12 f 23 + f 13 ))ω 3 (6) where σ L1, σ L2 and σ L3 are the L-subshell ionization cross sections, ω i are L-subshell fluorescence yields, f ij are Coster Kronig transition probabilities and f 13 is the radiative intra-shell vacancy transfer probability. It can be demonstrated that good agreement between present experimental results and RPWBA BC predictions exists for all the elements studied and for all x-ray lines reported except for the L γ 2,3(4,4 ) x-ray line. As an example, experimental L-shell x-ray production cross sections for Ag and Sb are given in figures 3 and 4. For comparison, other available experimental data as well as RPWBA BC theoretical predictions are given in the same figures. Our measured L γ 2,3(4,4 ) x-ray production cross sections are in good agreement with the values reported by Sow et al (1994) for the proton energies lower than 2 MeV. To the best of our knowledge, there are no published experimental data about individual L-shell x-ray production cross sections in the literature for the other elements (Rh, Cd, I). The L γ 2,3(4,4 ) x-ray lines correspond to the transitions to the L 1 subshell. From equations (3) and (4), production cross sections for these x-ray lines depend only on L 1 ionization cross section, ω 1 fluorescence yield and F L1:γ 2,3(4,4 ) fractional radiative width. It has already been pointed out that the agreement between the experimental results and theoretical predictions for the L 1 subshell ionization of atoms by protons is not as

9 2028 I Bogdanović and S Fazinić Figure 5. Ratio of experimental L γ 2,3(4,4 ) x-ray production cross sections to the RPWBA BC predictions, as a function of the reduced L-shell velocity parameter ξ L1. Theoretical values were calculated using (a) the x-ray fluorescence yield ω 1 compiled by Krause (1979) and (b) the interpolated theoretical DHS values of Chen et al (1981) supplied by the computer code GUPIX (Maxwell et al 1995). In both cases the DHF emission rates of Campbell and Wang (1989) were used., Rh;, Ag;, Cd;, Sb;, I. Typical error bars are shown. good as for the L 3 subshell (Orlić 1994b). A possible explanation of these discrepancies for the L 1 as well as for L 2 subshell could be the effect of collision-induced intra-shell transitions. According to Sarkadi and Mukoyama (1981) this effect plays a very important role in the ionization of L subshells by heavy ions, while it is less important in the case of proton bombardment, especially for ξ L1 1 as in our situation. Cohen (1990) pointed out that the choice of the database for fluorescence yields, Coster Kronig transition probabilities and fractional radiative widths used for conversion from x-ray production cross sections to the ionization cross sections can influence this disagreement. Figure 5 shows the ratio between experimental and RPWBA BC L γ 2,3(4,4 ) x-ray production cross sections for all the elements studied as a function of log ξ L1. Figure 5(a) shows this ratio obtained with the use of ω 1 given by Krause, while figure 5(b) shows the ratio between experiment and theory obtained with the use of ω 1 values calculated by Chen et al (1981). Since they published their values for fluorescence yields only for some elements, here we have used interpolated values supplied by the computer code GUPIX (Maxwell et al 1995). From these figures it can be seen that the agreement between

10 L-shell x-ray production for Rh, Ag, Cd, Sb and I 2029 Figure 6. Experimental L α /L γ 2,3(4,4 ) x-ray production cross section ratios divided by the corresponding RPWBA BC theoretical values, as a function of the proton energy. Theoretical values were calculated using (a) the x-ray fluorescence yields and Coster Kronig transition probabilities compiled by Krause (1979), and (b) the interpolated theoretical DHS values of Chen et al (1981) supplied by the computer code GUPIX (Maxwell et al 1995). In both cases the DHF emission rates of Campbell and Wang (1989) were used. 1: Rh; 2: Ag; 3: Cd; 4: In; 5: Sn; 6: Sb; 7: Te; 8: I. Typical error bars are shown. experimental values and RPWBA BC predictions is poor for Rh and Ag if Chen s values for ω 1 are used. The same is observed after the comparison of the experimental and RPWBA BC values for the L α /L γ 2,3(4,4 ) x-ray production cross section ratio. This ratio can be calculated by the following expression: ( σl3 σ L1 + σ L2 σ L1 f 23 + f 13 + f 12 f 23 + f 13 σlα x ) F L3:Lα ω 3 σlγ x =. (7) 2:3(4:4 ) F L1 :L γ2:3(4:4 ) ω 1 Figure 6 shows this ratio for eight elements between Rh and I. Experimental values for In,

11 2030 I Bogdanović and S Fazinić Table 4. Fluorescence yields and Coster Kronig transitions available in the literature. Target atom References ω 1 ω 2 ω 3 f 12 f 13 f 23 f 13 Rh a e-5 b e-4 d f Ag a e-5 b e-4 c d e Cd a e-4 b e-4 c d Sb a e-4 b e-4 c d I a e-4 b e-4 c d a Chen et al (1981). b Krause (1979). c Rosato (1986). d Xu and Rosato (1988). e Auerhammer et al (1988). f Markevich and Budick (1981). Sn and Te have been taken from Fazinić et al (1994). Figure 6(a) has been produced by using values for fluorescence yields and Coster Kronig transition rates from Krause (1979), while for figure 6(b) the corresponding values of Chen et al (1981) have been used. The observed disagreement between experimental and theoretical ratios for Rh and Ag is mostly influenced by the differences in Chen s and Krause s values for the ω 3 /ω 1 ratio for these two elements. The ratio of Chen to Krause ω 3 /ω 1 values is 1.53 and 1.57 for Rh and Ag, respectively. The difference in the values of the expression closed inside the brackets of equation (7), induced by choosing Chen s or Krause s values for f ij values, is less than 5%. The difference in the σ L3 /σ L1 ratio obtained by Cohen and Harrigan (1985) and the RPWBA BC treatment of Chen and Crasemann (1989) is less than 5% for 2 MeV protons and elements considered in this work. By increasing the proton energy this difference is becoming smaller. Table 4 shows fluorescence yields and Coster Kronig transitions for the studied elements available from the literature. It can be seen from this table that recently published experimental data for ω 1 fluorescence yields for Rh and Ag are almost twice the values calculated by Chen et al (1981). This is in agreement with our observations.

12 4. Conclusion L-shell x-ray production for Rh, Ag, Cd, Sb and I 2031 The individual L α,l β1,3,4,6,l β2,15,7,l γ1,5 and L γ 2,3(4,4 ) x-ray production cross sections for Rh, Ag, Cd, Sb and I have been measured for MeV protons. The results have been compared with the self-consistent theoretical database of RPWBA BC L-shell ionization cross sections, DHS fluorescence yields and Coster Kronig transition rates, and DF emission rates. Good agreement between present experimental results and theory has been found for all x-ray lines except for the L γ 2,3 line. The source of this disagreement can potentially be found in the too low values for L 1 subshell fluorescence yields ω 1 of Chen et al (1981), especially for Rh and Ag. In order to obtain more definite conclusions, more experimental data are needed for x-ray production cross sections, and a database is needed for necessary conversions. Acknowledgments The authors are indebted to their colleagues from the Laboratory for Nuclear Microanalysis for their help in running the accelerator. References Auerhammer J, Genz H and Richter A 1988 Z. Phys. D Bang J and Hansteen J M 1959 K. Dansk. Vidensk. Selsk. Mat.-Fys. Meddr Bozonian M, Hubbard K M and Nasstasi M 1990 Nucl. Instrum. Methods B Brandt W and Lapicki G 1979 Phys. Rev. A Phys. Rev. A Braziewicz J, Pajek M, Braziewicz E, Ploskonka J and Osetynski G M 1984 J. Phys. B: At. Mol. Phys Campbell J L 1988 Nucl. Instrum. Methods B Campbell J L and Wang J-X 1989 At. Data Nucl. Data Tables Chen M H and Crasemann B 1989 At. Data Nucl. Data Tables Chen M H, Crasemann B and Mark H 1981 Phys. Rev. A Cohen D D 1990 Nucl. Instrum. Methods B 49 1 Cohen D D and Harrigan M 1985 At. Data Nucl. Data Tables Fazinić S, Bogdanović I,Jakšić M, Orlić I and Valković V 1994 J. Phys. B: At. Mol. Opt. Phys Jesus A P, Pinheiro T M, Niza I A, Ribeiro J P and Lopes J S 1986 Nucl. Instrum. Methods B Krause M O 1979 J. Phys. Chem. Ref. Data Lennard W N and Phillips D 1979 Nucl. Instrum. Methods Markevich D and Budick B 1981 J. Phys. B: At. Mol. Phys Maxwell J A, Teesdale W J and Campbell J L 1995 Nucl. Instrum. Methods B Orlić I, Makjanić J, Tros G H J and Vis R D 1990 Nucl. Instrum. Methods B Orlić I, Sow C H and Tang S M 1994a At. Data Nucl. Data Tables Orlić I 1994b Nucl. Instrum. Methods B Pajek M, Kobzev A P, Sandrik R, Ilkhamov R A and Khusmurodov S H 1989 Nucl. Instrum. Methods B Rosato E 1983 Phys. Rev. A Sarkadi L and Mukoyama T 1981 J. Phys. B: At. Mol. Phys. 14 L225 Sarter W, Mommsen H, Sarkar M, Schürkes P and Weller A 1981 J. Phys. B: At. Mol. Phys Scofield J H 1974a At. Data Nucl. Data Tables b Phys. Rev. A Sokhi R S and Crumpton D 1984 At. Data Nucl. Data Tables Sow C H, Orlić I, Osipowicz T and Tang S M 1994 Nucl. Instrum. Methods B Thin T P and Leroux J 1979 X-Ray Spectrometry 8 85 Van Espen P, Janssens K and Nobles J 1985 Chemometrics Intell. Lab. Syst Xu J Q and Rosato E 1988, 1994 Nucl. Instrum. Methods B Ziegler J F, Biersack J P and Littmark U 1985 The Stopping and Range of Ions in Solids vol 1 (New York: Pergamon)