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Total photoionization cross-sections of Ar and Xe in the energy range of 2.1–6.0 keV
Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 143–147
Total photoionization cross-sections of Ar and Xe in the energy range of 2.1–6.0 keV Lei Zheng, Mingqi Cui ∗ , Yidong Zhao, Jia Zhao, Kai Chen Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, PR China Received 21 November 2005; received in revised form 26 April 2006; accepted 27 April 2006 Available online 4 May 2006
Abstract Total photoionization cross-sections of Ar and Xe have been accurately measured in the photon energy region of 2.1–6.0 keV, using a fourelectrode ion chamber with monochromatized synchrotron radiation. Experimental data are presented in both graphical and tabular forms and compared with previous data reported in the literatures. © 2006 Elsevier B.V. All rights reserved. Keywords: Photoionization cross-sections; Argon; Xenon; Synchrotron radiation
1. Introduction Photoionization cross-section is a fundamental physical quantity characterizing the interaction between photons and materials [1–4]. Accurate experimental data are necessary for verifying the validity of various theoretical models of the photoabsorption process [5,6]. In addition, accurate photoionization cross-sections are required for investigating the effects of solar radiation on a planetary atmosphere. Further the photoionization cross section of a rare gas is useful in obtaining the absolute or relative intensity of a source with radiation from VUV to soft X-ray using a rare-gas ion chamber [7,8]. Until now, many measurements of the photoionizaiton crosssection have been performed for rare gas atoms [5,6,9–23]. For Ar and Xe, the majority of cross-section data reported previously are in the photon energy region from vacuum ultraviolet to sub-keV [5,6,9–19]. But for higher photon energy, the measurement for cross-sections of Ar and Kr were less [20–23]. Among of them, Bearden [20] measured cross-sections of Ar in the energy range from 852 eV to 40 keV using monochromatized Bremsstrahlung radiation, as did Wuilleumier [23] for Xe from 0.8 to 8.0 keV. Using radioisotopes as light sources, McCrary et al. [22] measured photoionization cross-sections of Ar and Xe at 4508 and 5895 eV. In addition, Marr and West ∗
Corresponding author. Tel.: +86 10 88235986; fax: +86 10 88200395. E-mail address: [email protected] (M. Cui).
0368-2048/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2006.04.006
[3,4] critically evaluated and compiled most of the previously measured photoionization cross-sections of He, Ne, Ar, Kr, and Xe from a number of experiments, and presented tabulations of recommended values. Most recently, Henke et al. [1] provides a thorough analysis of the currently available theoretical predictions and experimental photoionization cross-sections over a wide energy range for atoms, which are now maintained by Gullikson [2] on World Wide Web. In the present work, total photoionization cross-sections of Ar and Xe have been measured in the energy range of 2.1–6.0 keV using a four-electrode ion chamber. Synchrotron radiation was used as a light source and monochromatized with higher spectral purity. Experimental data are discussed in comparison with reported data available in literatures. 2. Experimental Measurements were performed on beamline 3B3 [24] of the Beijing Synchrotron Radiation Facility (BSRF) at the Institute of High Energy Physics. Monochromatic X-ray radiation in the region of 2.1–6.0 keV was obtained using a doublecrystal monochromator equipped with a pair of Si(1 1 1) crystals. The energy resolution power (E/E) was higher than 5000 at 3206 eV and 1800 at 5465 eV. The pre-mirror system of the beamline 3B3 mainly consists of a water-cooled plane mirror and a toroidal mirror, and both of them are coated with nickel. The grazing angles of the incident photons on the two mirrors are
144
L. Zheng et al. / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 143–147
Fig. 1. Schematic of the four-electrode ion chamber with its cross-section.
fixed at 0.55◦ . Considering the reflectivity of the nickel coated pre-mirror system and photon flux from the bending magnet, the available photon energy of the beamline is about 6.0 keV. Note that the second (or even) order harmonic X-rays diffracted by the Si(1 1 1) crystal in monochromator are not allowed because of the annihilation rule, which results in highly pure monochromatic photons at the experimental station [9]. The ratios of higher order harmonics to the first order light were measured using a Si(Li) detector and evaluated to be less than 0.016% in the whole region except for about 0.05% at the photon energy 6.0 keV [24]. The beamline is evacuated by ion-sputtering pumps. The photon beam is introduced into an ion chamber, passing through a four-jaw diaphragm. The schematic illustration of the four-electrode ion chamber is shown in Fig. 1. An entrance aperture of the ion chamber is sealed by an Au-coated polyimide film with a diameter of 1 mm, which prevents rare gas from flowing into the beamline, and also, effectively suppresses the low energy stray light. The first and the fourth electrodes 100 mm in length keep the electric field uniformity in the effective region, and the second and third ones 350 mm in length collect the ions. These electrodes 6 mm in diameter are made of copper rods coated with Au and maintained at ground potential. The cylindric anode 903 mm in length is held at a positive potential in the ion chamber cylinder and has inside and outside diameters of 50 and 56 mm, respectively. These electrodes and anode are electrically insulated with Teflon. The incidence beam passes through the central axes of the ion chamber cylinder, which is not coaxial with the cylindric anode, as also shown in Fig. 1. The sensitive area is near the cylindric anode, where the electric field is weaker than that near the electrodes. In this way the photoelectrons produced by ionization can quickly be collected by the cylindric anode, without receiving extra energy from the electric field. Before filled with rare gas for measurement, the ion chamber was evacuated with a turbo-molecular pump. The ion currents of two collector electrodes were measured with an electrometer (Model 6517A, KEITHLEY, USA), which also supplied the bias for the cylindric anode and detected the gas temperature. A personal computer controls the energy scan of the monochromator and has a real-time data acquisition from an electrometer using the LabVIEW system. A diaphragm capacitance transducer (CPCA-130Z, ShangHai ZhenTai Instruments Co. Ltd., PR China) was used to measure the absolute gas pressure. When the two collector electrodes of the ion chamber have identical length, the total photoionization cross-section of a rare
Fig. 2. Ion currents of two collector electrodes versus bias of cylindric anode. The pressure of Xe gas in ion chamber is 1185.8 Pa, and the photon energy is 4.0 keV. Open circles denote the data of ion current (i1 ) for the second electrode; filled circles denote the third (i2 ).
gas can be expressed as follows by the Beer–Lambert law: i1 kT (1) ln σ= PL i2 where σ denotes the total photoionization cross-section, i1 and i2 are the ion currents measured from the two collector electrodes, which have the same length L. k is the Boltzman constant. P and T denote the pressure and temperature of the gas under study, respectively. The relationship between ion currents of the two collector electrodes and bias of cylindric anode for Xe gas are shown in Fig. 2. These data were obtained at the photon energy of 4.0 keV with gas pressure of 1185.8 Pa in the ion chamber. The ion current of the third electrode increases when the bias is added, then keeps constant as the bias exceeds 100 V, while for the second electrode the bias must be larger than 180 V to collect all the photoelectrons. In order to satisfy the complete collection for the two collector electrodes in the photon energy from 2.1 to 6.0 keV, the bias of 250 V was applied for Xe gas, while for Ar gas, the bias of 150 V was enough for the whole energy region at the pressure of 2371.4 Pa in the ion chamber. The factors producing uncertainties for cross-sections are as follows. The measured ion current has some relative fluctuation about 1% or less, and the manufacturer’s specification of our eletrometer gives an accuracy of 0.2%, which results in an uncertainty less than that of current fluctuation. Consequently, the relative uncertainty for the measured result of the ion current is estimated to be 1.0%. For the length of the electrodes, the relative uncertainty of measurement is about 0.3%. The uncertainty for temperature measurement is supposed to be about 1.0%. It is rational that the gas pressure has a relative uncertainty of about 1.0% according to the fact that the diaphragm capacitance transducer has a factory quoted accuracy of 0.5% and the gas in the chamber is not absolutely uniform. As mentioned above, the higher order harmonics were less than 0.05% of the first order light, indicating that the monochromatic light is highly pure enough to disregard the uncertainty resulting from the impurity of incidence photons. All of the uncertainties are
L. Zheng et al. / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 143–147
transferred to the total photoionization cross-sections through the equation as followed: u2σ = u2L + u2P + u2T +
u2i1 + u2i2 [ln(i1 / i2 )]
2
(2)
where uσ , uL , uP , uT , ui1 and ui2 denote the relative uncertainties of σ, L, P, T, i1 , and i2 in formula (1), respectively. Note that the relative uncertainty uσ of σ has a significant relationship with ln(i1 /i2 ) except for those uncertainties, as mentioned in reference [5]. In order to reduce the uncertainty due to ln(i1 /i2 ), the choice of gas pressure must insure the ratio of i1 to i2 big enough [5]. Therefore, the gas pressure of 2371.4 and 1185.8 Pa were adopted for Ar and Xe, respectively, in our experiments, satisfying i1 /i2 > 1.22 for Ar gas and i1 /i2 > 1.67 for Xe gas in this energy region. 3. Results and discussion 3.1. Ar The experimental data of the total photoionization crosssections for Ar in the photon energy region of 2.1–6.0 keV are given in Table 1. Comparison of our data with that reported previously [1–3,20–22] is shown in Fig. 3a, together with the calculated data from FFAST [25] and XCOM database [26]. In
Fig. 3. Total photoionization cross-sections for Ar vs. photon energy. Plot (a) is given for photon energy from 2.1 to 6.0 keV with an interval of 100 eV; plot (b) is given for the photon energy near K-edge with an interval of 0.2 eV. Filled circles denote our experimental data; the data of McCrary et al. [22] (circles), Marr and West [3] (squares), Bearden [20] (triangles), Millar and Greening [21] (pentagram), CXRO database (maintained by Gullikson) [1,2] (solid line) are also shown with that calculated from FFAST [25] (dotted line) and XCOM [26] (dashed line) database.
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Table 1 Total photoionization cross-sections of Ar and Xe in the region of 2.1–6.0 keV with uncertainties (unit: 1 Mb = 10−22 m2 ) Photon energy (eV)
Ar
Xe
Cross-section (Mb)
Uncertainty (%)
Cross-section (Mb)
Uncertainty (%)
2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500 5600 5700 5800 5900 6000
2.97E-02 2.62E-02 2.29E-02 2.05E-02 1.80E-02 1.61E-02 1.46E-02 1.31E-02 1.17E-02 1.07E-02 9.51E-03 1.05E-02 8.97E-02 7.94E-02 7.27E-02 6.76E-02 6.26E-02 5.82E-02 5.42E-02 5.05E-02 4.74E-02 4.44E-02 4.16E-02 3.90E-02 3.67E-02 3.47E-02 3.27E-02 3.09E-02 2.92E-02 2.77E-02 2.61E-02 2.50E-02 2.36E-02 2.24E-02 2.11E-02 2.02E-02 1.90E-02 1.81E-02 1.66E-02 1.57E-02
2.8 3.0 3.4 3.7 4.1 4.6 5.0 5.5 6.1 6.7 7.5 6.8 1.6 1.7 1.7 1.8 1.8 1.9 1.9 2.0 2.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.3 3.4 3.6 3.7 3.9 4.1 4.4 4.7
4.19E-01 3.75E-01 3.36E-01 3.03E-01 2.73E-01 2.47E-01 2.24E-01 2.04E-01 1.86E-01 1.71E-01 1.57E-01 1.44E-01 1.33E-01 1.23E-01 1.14E-01 1.06E-01 9.85E-02 9.19E-02 8.56E-02 8.00E-02 7.49E-02 7.00E-02 6.55E-02 6.15E-02 5.79E-02 5.41E-02 5.08E-02 1.51E-01 1.41E-01 1.35E-01 1.28E-01 1.68E-01 1.62E-01 1.55E-01 1.71E-01 1.63E-01 1.56E-01 1.50E-01 1.44E-01 1.38E-01
1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.9 2.0 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.0 3.1 1.7 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.8
general, our data are 4–10% lower than the values compiled by Henke et al. [1,2] and much lower than the data compiled by Marr and West [3] in this energy region. In the region of 2100–2700 eV, our results are in good agreement with the data from XCOM database but 5–10% larger than the data from FFAST database. In particular, our measured data agree very well with those data from XCOM and FFAST database in the spectral region of 3900–5600 eV. The photoionization cross-sections in XCOM database were obtained by a phaseshift calculation with a central potential and a Hartree–Slater atomic model. The values in the FFAST database were calculated within a self-consistent Dirac–Hatree–Fock framework. Thus, the results are quite dependent on the method adopted, especially near the absorption edges [26,27]. It is obviously shown in Fig. 3a that large discrepancies appear between cited
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data in the vicinity of the K-edge, where our data are closer to the values of FFAST than those of XCOM. The uncertainty of cross-sections obtained from FFAST and XCOM database is within 10% [27] in the region of 3300–3900 eV, while ours is only about 1.6–1.9%, as given in Table 1. More detailed cross-sections are shown with additional isolated points scanning the incident energies from 3202 to 3265 eV in Fig. 3b, where the K + M double excitation 1s3p → 4p2 [28] is clearly observed. The most pronounced feature is that the region above K-edge contains the well-known resonances associated with the 1s → np (n ≥ 4) Rydberg states [28], as shown in the inset of Fig. 3b. In addition, it is also indicated that our results are within 9% higher than those of Henke et al. [1,2] in the region of 3206–3390 eV. Bearden [20] measured cross-sections at selected photon energies using an X-ray tube with various anode materials. The photons were monochromatized by crystal X-ray monochromator and detected by an Ar–CH4 proportional counter. A gaseous absorber was positioned between the monochromator and the detector. He used narrow slits to insure that the detector did not receive scattered or fluorescent radiation. But his data have obviously large deviations from others. At 4508 eV, the measurements of both McCrary et al. [22] and Millar and Greening [21] have good agreement with the result reported here with deviation less than 1.6%. They adopted different experiment designs. McCrary et al. employed radioisotope sources, 49 V and 55 Fe, to provide photons whose energies were 4508 and 5895 eV, respectively. Instead of monochromator, filters were used to improve the Kα -to-Kβ intensity ratios and the purity of photons. The detector used in the experiment was a NaI (Tl) counter. Using X-ray tube with a tungsten target as a primary radiation to excite secondary fluorescence from Ti and Cr, Millar and Greening obtained photons in the energy of 4508 and 5411 eV, respectively. A LiF single-crystal spectrometer was introduced to determine cross-sections. At photon energy of 5411 eV, the cross-section by Millar and Greening is about 5% higher than ours and close to that of Henke et al. Above 5600 eV, the present data are typically 3–8% lower than cited data. 3.2. Xe The experimental data of the total photoionization crosssections for Xe in the photon energy region of 2.1–6.0 keV are also listed in Table 1. Comparison of our data with that reported previously [1,2,4,22,23] is shown in Fig. 4a and b, where the calculated results from FFAST [25] and XCOM database [26] are also shown. Below L3 edge, our data are about 11.4% higher than those synthesized by West and Morton [4] and the data compiled by Henke et al. [1,2] are 1.2–7% higher than ours except for data in the region of 2100–2500 eV. However, above L3 edge West and Morton’s data [4] agree well with the data by Henke et al. [1,2] and are about 4–9% higher than the present ones. Our data have better agreement with the data calculated from XCOM database than from FFAST database below L3 edge of Xe, but between L3 edge and L2 edge our results are closer to FFAST’s data than those from XCOM. Furthermore, it is clearly
Fig. 4. Total photoionization cross-sections for Xe vs. photon energy from 2.1 to 4.0 keV in plot (a) and from 4.0 to 6.0 keV in plot (b). Filled circles denote our experimental data; the data of West and Morton [4] (circles), Wuilleumier [23] (squares), McCrary et al. [22] (triangles), CXRO database (maintained by Gullikson) [1,2] (solid line) are also shown with that calculated from FFAST [25] (dotted line) and XCOM [26] (dashed line) database.
shown in Fig. 4b that there are excellent agreements between the present data and the data from XCOM database above L2 edge. Wuilleumier [23] investigated previously the absorption coefficients between 0.8 and 8.0 keV. He used an X-ray tube with a tungsten anode as light source. Continuous energy analysis of gas absorption spectrums was assured by a vacuum spectrograph with a bent quartz crystal and a photographic detection. His results differ from ours by 6% at most above L3 edge and only are in good agreement with our data in the range from 4200 eV to L3 edge. The experimental data by McCrary et al. [22] have only two points: one is 5.3% higher than the present one at 4508 eV; the other has good agreement with ours with deviation only 1.7% at 5895 eV. Table 1 also lists the uncertainties of photoionization cross-sections for Xe, and an energy step space of 100 eV is adopted. 4. Conclusions Total photoionization cross-sections of Ar and Xe have been accurately measured in the photon energy region of 2.1–6.0 keV, using a four-electrode ion chamber with tunable and monochromatized synchrotron radiation. Experimental data are compared with the results reported previously in the literatures and those calculated from FFAST and XCOM database. In particular, the present data for both Ar and Xe are in excellent agreement with those calculated from XCOM database in most
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photon energies. Furthermore, our results are in general lower than those compiled by Gullikson not only for Ar but also for Xe. Acknowledgements We would like to thank the staff of soft X-ray group in Beijing Synchrotron Radiation Facility for their assistance. This work was supported by the National Natural Science Foundation of China (No. 10374088). References [1] B.L. Henke, E.M. Gullikson, J.C. Davis, At. Data Nucl. Data Tables 54 (1993) 181. [2] E.M. Gullikson, http://www.cxro.lbl.gov/optical constants/. [3] G.V. Marr, J.B. West, At. Data Nucl. Data Tables 18 (1976) 497. [4] J.B. West, J. Morton, At. Data Nucl. Data Tables 22 (1978) 103. [5] J.A.R. Samson, L. Yin, J. Opt. Soc. Am. B6 (1989) 326. [6] J.A.R. Samson, W.C. Stolte, J. Electron Spectrosc. Relat. Phenom. 123 (2002) 265. [7] J.A.R. Samson, J. Opt. Soc. Am. 54 (1964) 6. [8] N. Saito, I.H. Suzuki, J. Synchrotron Rad. 5 (1998) 869.
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[9] I.H. Suzuki, N. Saito, J. Electron Spectrosc. Relat. Phenom. 129 (2003) 71. [10] I.H. Suzuki, N. Saito, Radiat. Phys. Chem. 73 (2005) 1. [11] D.L. Ederer, Phys. Rev. Lett. 13 (1964) 760. [12] R.D. Deslattes, Phys. Rev. Lett. 20 (1968) 483. [13] R. Haensel, G. Keitel, P. Schreiber, C. Kunz, Phys. Rev. 188 (1969) 1375. [14] J. Lang, W.S. Watson, J. Phys. B 8 (1975) L339. [15] D.R. Denne, J. Phys. D 3 (1970) 1392. [16] W.S. Watson, J. Phys. B 5 (1972) 2292. [17] R.W. Carlson, D.L. Judge, M. Ogawa, L.C. Lee, Appl. Opt. 12 (1973) 409. [18] J.B. West, G.V. Marr, Proc. R. Soc. Lond. A 349 (1976) 397. [19] B.X. Yang, J. Kirz, Appl. Opt. 26 (1987) 3823. [20] A.J. Bearden, J. Appl. Phys. 37 (1966) 1681. [21] R.H. Millar, J.R. Greening, J. Phys. B 7 (1974) 2332. [22] J.H. McCrary, L.D. Looney, C.P. Constanten, H.F. Atwater, Phys. Rev. A 2 (1970) 2489. [23] F. Wuilleumier, Phys. Rev. A 6 (1972) 2067. [24] J. Zhao, M.Q. Cui, Y.D. Zhao, et al., HEP&NP 12 (2005) 1209. [25] http://physics.nist.gov/PhysRefData/FFast/Text/cover.html. [26] http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html. [27] http://physics.nist.gov/PhysRefData/XrayNoteB.html. [28] R.D. Deslattes, R.E. LaVilla, P.L. Cowan, A. Henins, Phys. Rev. A 27 (1983) 923.
Total photoionization cross-sections of Ar and Xe in the energy range of 2.1–6.0 keV Lei Zheng, Mingqi Cui ∗ , Yidong Zhao, Jia Zhao, Kai Chen Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, PR China Received 21 November 2005; received in revised form 26 April 2006; accepted 27 April 2006 Available online 4 May 2006
Abstract Total photoionization cross-sections of Ar and Xe have been accurately measured in the photon energy region of 2.1–6.0 keV, using a fourelectrode ion chamber with monochromatized synchrotron radiation. Experimental data are presented in both graphical and tabular forms and compared with previous data reported in the literatures. © 2006 Elsevier B.V. All rights reserved. Keywords: Photoionization cross-sections; Argon; Xenon; Synchrotron radiation
1. Introduction Photoionization cross-section is a fundamental physical quantity characterizing the interaction between photons and materials [1–4]. Accurate experimental data are necessary for verifying the validity of various theoretical models of the photoabsorption process [5,6]. In addition, accurate photoionization cross-sections are required for investigating the effects of solar radiation on a planetary atmosphere. Further the photoionization cross section of a rare gas is useful in obtaining the absolute or relative intensity of a source with radiation from VUV to soft X-ray using a rare-gas ion chamber [7,8]. Until now, many measurements of the photoionizaiton crosssection have been performed for rare gas atoms [5,6,9–23]. For Ar and Xe, the majority of cross-section data reported previously are in the photon energy region from vacuum ultraviolet to sub-keV [5,6,9–19]. But for higher photon energy, the measurement for cross-sections of Ar and Kr were less [20–23]. Among of them, Bearden [20] measured cross-sections of Ar in the energy range from 852 eV to 40 keV using monochromatized Bremsstrahlung radiation, as did Wuilleumier [23] for Xe from 0.8 to 8.0 keV. Using radioisotopes as light sources, McCrary et al. [22] measured photoionization cross-sections of Ar and Xe at 4508 and 5895 eV. In addition, Marr and West ∗
Corresponding author. Tel.: +86 10 88235986; fax: +86 10 88200395. E-mail address: [email protected] (M. Cui).
0368-2048/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2006.04.006
[3,4] critically evaluated and compiled most of the previously measured photoionization cross-sections of He, Ne, Ar, Kr, and Xe from a number of experiments, and presented tabulations of recommended values. Most recently, Henke et al. [1] provides a thorough analysis of the currently available theoretical predictions and experimental photoionization cross-sections over a wide energy range for atoms, which are now maintained by Gullikson [2] on World Wide Web. In the present work, total photoionization cross-sections of Ar and Xe have been measured in the energy range of 2.1–6.0 keV using a four-electrode ion chamber. Synchrotron radiation was used as a light source and monochromatized with higher spectral purity. Experimental data are discussed in comparison with reported data available in literatures. 2. Experimental Measurements were performed on beamline 3B3 [24] of the Beijing Synchrotron Radiation Facility (BSRF) at the Institute of High Energy Physics. Monochromatic X-ray radiation in the region of 2.1–6.0 keV was obtained using a doublecrystal monochromator equipped with a pair of Si(1 1 1) crystals. The energy resolution power (E/E) was higher than 5000 at 3206 eV and 1800 at 5465 eV. The pre-mirror system of the beamline 3B3 mainly consists of a water-cooled plane mirror and a toroidal mirror, and both of them are coated with nickel. The grazing angles of the incident photons on the two mirrors are
144
L. Zheng et al. / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 143–147
Fig. 1. Schematic of the four-electrode ion chamber with its cross-section.
fixed at 0.55◦ . Considering the reflectivity of the nickel coated pre-mirror system and photon flux from the bending magnet, the available photon energy of the beamline is about 6.0 keV. Note that the second (or even) order harmonic X-rays diffracted by the Si(1 1 1) crystal in monochromator are not allowed because of the annihilation rule, which results in highly pure monochromatic photons at the experimental station [9]. The ratios of higher order harmonics to the first order light were measured using a Si(Li) detector and evaluated to be less than 0.016% in the whole region except for about 0.05% at the photon energy 6.0 keV [24]. The beamline is evacuated by ion-sputtering pumps. The photon beam is introduced into an ion chamber, passing through a four-jaw diaphragm. The schematic illustration of the four-electrode ion chamber is shown in Fig. 1. An entrance aperture of the ion chamber is sealed by an Au-coated polyimide film with a diameter of 1 mm, which prevents rare gas from flowing into the beamline, and also, effectively suppresses the low energy stray light. The first and the fourth electrodes 100 mm in length keep the electric field uniformity in the effective region, and the second and third ones 350 mm in length collect the ions. These electrodes 6 mm in diameter are made of copper rods coated with Au and maintained at ground potential. The cylindric anode 903 mm in length is held at a positive potential in the ion chamber cylinder and has inside and outside diameters of 50 and 56 mm, respectively. These electrodes and anode are electrically insulated with Teflon. The incidence beam passes through the central axes of the ion chamber cylinder, which is not coaxial with the cylindric anode, as also shown in Fig. 1. The sensitive area is near the cylindric anode, where the electric field is weaker than that near the electrodes. In this way the photoelectrons produced by ionization can quickly be collected by the cylindric anode, without receiving extra energy from the electric field. Before filled with rare gas for measurement, the ion chamber was evacuated with a turbo-molecular pump. The ion currents of two collector electrodes were measured with an electrometer (Model 6517A, KEITHLEY, USA), which also supplied the bias for the cylindric anode and detected the gas temperature. A personal computer controls the energy scan of the monochromator and has a real-time data acquisition from an electrometer using the LabVIEW system. A diaphragm capacitance transducer (CPCA-130Z, ShangHai ZhenTai Instruments Co. Ltd., PR China) was used to measure the absolute gas pressure. When the two collector electrodes of the ion chamber have identical length, the total photoionization cross-section of a rare
Fig. 2. Ion currents of two collector electrodes versus bias of cylindric anode. The pressure of Xe gas in ion chamber is 1185.8 Pa, and the photon energy is 4.0 keV. Open circles denote the data of ion current (i1 ) for the second electrode; filled circles denote the third (i2 ).
gas can be expressed as follows by the Beer–Lambert law: i1 kT (1) ln σ= PL i2 where σ denotes the total photoionization cross-section, i1 and i2 are the ion currents measured from the two collector electrodes, which have the same length L. k is the Boltzman constant. P and T denote the pressure and temperature of the gas under study, respectively. The relationship between ion currents of the two collector electrodes and bias of cylindric anode for Xe gas are shown in Fig. 2. These data were obtained at the photon energy of 4.0 keV with gas pressure of 1185.8 Pa in the ion chamber. The ion current of the third electrode increases when the bias is added, then keeps constant as the bias exceeds 100 V, while for the second electrode the bias must be larger than 180 V to collect all the photoelectrons. In order to satisfy the complete collection for the two collector electrodes in the photon energy from 2.1 to 6.0 keV, the bias of 250 V was applied for Xe gas, while for Ar gas, the bias of 150 V was enough for the whole energy region at the pressure of 2371.4 Pa in the ion chamber. The factors producing uncertainties for cross-sections are as follows. The measured ion current has some relative fluctuation about 1% or less, and the manufacturer’s specification of our eletrometer gives an accuracy of 0.2%, which results in an uncertainty less than that of current fluctuation. Consequently, the relative uncertainty for the measured result of the ion current is estimated to be 1.0%. For the length of the electrodes, the relative uncertainty of measurement is about 0.3%. The uncertainty for temperature measurement is supposed to be about 1.0%. It is rational that the gas pressure has a relative uncertainty of about 1.0% according to the fact that the diaphragm capacitance transducer has a factory quoted accuracy of 0.5% and the gas in the chamber is not absolutely uniform. As mentioned above, the higher order harmonics were less than 0.05% of the first order light, indicating that the monochromatic light is highly pure enough to disregard the uncertainty resulting from the impurity of incidence photons. All of the uncertainties are
L. Zheng et al. / Journal of Electron Spectroscopy and Related Phenomena 152 (2006) 143–147
transferred to the total photoionization cross-sections through the equation as followed: u2σ = u2L + u2P + u2T +
u2i1 + u2i2 [ln(i1 / i2 )]
2
(2)
where uσ , uL , uP , uT , ui1 and ui2 denote the relative uncertainties of σ, L, P, T, i1 , and i2 in formula (1), respectively. Note that the relative uncertainty uσ of σ has a significant relationship with ln(i1 /i2 ) except for those uncertainties, as mentioned in reference [5]. In order to reduce the uncertainty due to ln(i1 /i2 ), the choice of gas pressure must insure the ratio of i1 to i2 big enough [5]. Therefore, the gas pressure of 2371.4 and 1185.8 Pa were adopted for Ar and Xe, respectively, in our experiments, satisfying i1 /i2 > 1.22 for Ar gas and i1 /i2 > 1.67 for Xe gas in this energy region. 3. Results and discussion 3.1. Ar The experimental data of the total photoionization crosssections for Ar in the photon energy region of 2.1–6.0 keV are given in Table 1. Comparison of our data with that reported previously [1–3,20–22] is shown in Fig. 3a, together with the calculated data from FFAST [25] and XCOM database [26]. In
Fig. 3. Total photoionization cross-sections for Ar vs. photon energy. Plot (a) is given for photon energy from 2.1 to 6.0 keV with an interval of 100 eV; plot (b) is given for the photon energy near K-edge with an interval of 0.2 eV. Filled circles denote our experimental data; the data of McCrary et al. [22] (circles), Marr and West [3] (squares), Bearden [20] (triangles), Millar and Greening [21] (pentagram), CXRO database (maintained by Gullikson) [1,2] (solid line) are also shown with that calculated from FFAST [25] (dotted line) and XCOM [26] (dashed line) database.
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Table 1 Total photoionization cross-sections of Ar and Xe in the region of 2.1–6.0 keV with uncertainties (unit: 1 Mb = 10−22 m2 ) Photon energy (eV)
Ar
Xe
Cross-section (Mb)
Uncertainty (%)
Cross-section (Mb)
Uncertainty (%)
2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000 5100 5200 5300 5400 5500 5600 5700 5800 5900 6000
2.97E-02 2.62E-02 2.29E-02 2.05E-02 1.80E-02 1.61E-02 1.46E-02 1.31E-02 1.17E-02 1.07E-02 9.51E-03 1.05E-02 8.97E-02 7.94E-02 7.27E-02 6.76E-02 6.26E-02 5.82E-02 5.42E-02 5.05E-02 4.74E-02 4.44E-02 4.16E-02 3.90E-02 3.67E-02 3.47E-02 3.27E-02 3.09E-02 2.92E-02 2.77E-02 2.61E-02 2.50E-02 2.36E-02 2.24E-02 2.11E-02 2.02E-02 1.90E-02 1.81E-02 1.66E-02 1.57E-02
2.8 3.0 3.4 3.7 4.1 4.6 5.0 5.5 6.1 6.7 7.5 6.8 1.6 1.7 1.7 1.8 1.8 1.9 1.9 2.0 2.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.3 3.4 3.6 3.7 3.9 4.1 4.4 4.7
4.19E-01 3.75E-01 3.36E-01 3.03E-01 2.73E-01 2.47E-01 2.24E-01 2.04E-01 1.86E-01 1.71E-01 1.57E-01 1.44E-01 1.33E-01 1.23E-01 1.14E-01 1.06E-01 9.85E-02 9.19E-02 8.56E-02 8.00E-02 7.49E-02 7.00E-02 6.55E-02 6.15E-02 5.79E-02 5.41E-02 5.08E-02 1.51E-01 1.41E-01 1.35E-01 1.28E-01 1.68E-01 1.62E-01 1.55E-01 1.71E-01 1.63E-01 1.56E-01 1.50E-01 1.44E-01 1.38E-01
1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.9 2.0 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.0 3.1 1.7 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.8
general, our data are 4–10% lower than the values compiled by Henke et al. [1,2] and much lower than the data compiled by Marr and West [3] in this energy region. In the region of 2100–2700 eV, our results are in good agreement with the data from XCOM database but 5–10% larger than the data from FFAST database. In particular, our measured data agree very well with those data from XCOM and FFAST database in the spectral region of 3900–5600 eV. The photoionization cross-sections in XCOM database were obtained by a phaseshift calculation with a central potential and a Hartree–Slater atomic model. The values in the FFAST database were calculated within a self-consistent Dirac–Hatree–Fock framework. Thus, the results are quite dependent on the method adopted, especially near the absorption edges [26,27]. It is obviously shown in Fig. 3a that large discrepancies appear between cited
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data in the vicinity of the K-edge, where our data are closer to the values of FFAST than those of XCOM. The uncertainty of cross-sections obtained from FFAST and XCOM database is within 10% [27] in the region of 3300–3900 eV, while ours is only about 1.6–1.9%, as given in Table 1. More detailed cross-sections are shown with additional isolated points scanning the incident energies from 3202 to 3265 eV in Fig. 3b, where the K + M double excitation 1s3p → 4p2 [28] is clearly observed. The most pronounced feature is that the region above K-edge contains the well-known resonances associated with the 1s → np (n ≥ 4) Rydberg states [28], as shown in the inset of Fig. 3b. In addition, it is also indicated that our results are within 9% higher than those of Henke et al. [1,2] in the region of 3206–3390 eV. Bearden [20] measured cross-sections at selected photon energies using an X-ray tube with various anode materials. The photons were monochromatized by crystal X-ray monochromator and detected by an Ar–CH4 proportional counter. A gaseous absorber was positioned between the monochromator and the detector. He used narrow slits to insure that the detector did not receive scattered or fluorescent radiation. But his data have obviously large deviations from others. At 4508 eV, the measurements of both McCrary et al. [22] and Millar and Greening [21] have good agreement with the result reported here with deviation less than 1.6%. They adopted different experiment designs. McCrary et al. employed radioisotope sources, 49 V and 55 Fe, to provide photons whose energies were 4508 and 5895 eV, respectively. Instead of monochromator, filters were used to improve the Kα -to-Kβ intensity ratios and the purity of photons. The detector used in the experiment was a NaI (Tl) counter. Using X-ray tube with a tungsten target as a primary radiation to excite secondary fluorescence from Ti and Cr, Millar and Greening obtained photons in the energy of 4508 and 5411 eV, respectively. A LiF single-crystal spectrometer was introduced to determine cross-sections. At photon energy of 5411 eV, the cross-section by Millar and Greening is about 5% higher than ours and close to that of Henke et al. Above 5600 eV, the present data are typically 3–8% lower than cited data. 3.2. Xe The experimental data of the total photoionization crosssections for Xe in the photon energy region of 2.1–6.0 keV are also listed in Table 1. Comparison of our data with that reported previously [1,2,4,22,23] is shown in Fig. 4a and b, where the calculated results from FFAST [25] and XCOM database [26] are also shown. Below L3 edge, our data are about 11.4% higher than those synthesized by West and Morton [4] and the data compiled by Henke et al. [1,2] are 1.2–7% higher than ours except for data in the region of 2100–2500 eV. However, above L3 edge West and Morton’s data [4] agree well with the data by Henke et al. [1,2] and are about 4–9% higher than the present ones. Our data have better agreement with the data calculated from XCOM database than from FFAST database below L3 edge of Xe, but between L3 edge and L2 edge our results are closer to FFAST’s data than those from XCOM. Furthermore, it is clearly
Fig. 4. Total photoionization cross-sections for Xe vs. photon energy from 2.1 to 4.0 keV in plot (a) and from 4.0 to 6.0 keV in plot (b). Filled circles denote our experimental data; the data of West and Morton [4] (circles), Wuilleumier [23] (squares), McCrary et al. [22] (triangles), CXRO database (maintained by Gullikson) [1,2] (solid line) are also shown with that calculated from FFAST [25] (dotted line) and XCOM [26] (dashed line) database.
shown in Fig. 4b that there are excellent agreements between the present data and the data from XCOM database above L2 edge. Wuilleumier [23] investigated previously the absorption coefficients between 0.8 and 8.0 keV. He used an X-ray tube with a tungsten anode as light source. Continuous energy analysis of gas absorption spectrums was assured by a vacuum spectrograph with a bent quartz crystal and a photographic detection. His results differ from ours by 6% at most above L3 edge and only are in good agreement with our data in the range from 4200 eV to L3 edge. The experimental data by McCrary et al. [22] have only two points: one is 5.3% higher than the present one at 4508 eV; the other has good agreement with ours with deviation only 1.7% at 5895 eV. Table 1 also lists the uncertainties of photoionization cross-sections for Xe, and an energy step space of 100 eV is adopted. 4. Conclusions Total photoionization cross-sections of Ar and Xe have been accurately measured in the photon energy region of 2.1–6.0 keV, using a four-electrode ion chamber with tunable and monochromatized synchrotron radiation. Experimental data are compared with the results reported previously in the literatures and those calculated from FFAST and XCOM database. In particular, the present data for both Ar and Xe are in excellent agreement with those calculated from XCOM database in most
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photon energies. Furthermore, our results are in general lower than those compiled by Gullikson not only for Ar but also for Xe. Acknowledgements We would like to thank the staff of soft X-ray group in Beijing Synchrotron Radiation Facility for their assistance. This work was supported by the National Natural Science Foundation of China (No. 10374088). References [1] B.L. Henke, E.M. Gullikson, J.C. Davis, At. Data Nucl. Data Tables 54 (1993) 181. [2] E.M. Gullikson, http://www.cxro.lbl.gov/optical constants/. [3] G.V. Marr, J.B. West, At. Data Nucl. Data Tables 18 (1976) 497. [4] J.B. West, J. Morton, At. Data Nucl. Data Tables 22 (1978) 103. [5] J.A.R. Samson, L. Yin, J. Opt. Soc. Am. B6 (1989) 326. [6] J.A.R. Samson, W.C. Stolte, J. Electron Spectrosc. Relat. Phenom. 123 (2002) 265. [7] J.A.R. Samson, J. Opt. Soc. Am. 54 (1964) 6. [8] N. Saito, I.H. Suzuki, J. Synchrotron Rad. 5 (1998) 869.
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