We report on the investigation of the photon energy dependence of double 1s photoionization of light atoms and compare the cross sections for hollow atom and He-like ion production. Measurements of the Kα hypersatellite x-ray spectra of Mg, Al, and Si were carried out using the Fribourg high-resolution x-ray spectrometer installed at the ID21 and ID26 beam lines at the ESRF. The double-to-single photoionization cross section ratios were derived as a function of the incident photon beam energy and compared to convergent close-coupling (CCC) calculations for He-like ions. The dynamical electron-electron scattering contribution to the DPI cross-sections was found to be more important for neutral atoms than for the He isoelectronic serie

Berset, M.

Bray, I.

Cao, W.

Dousse, J.-Cl

Fennane, K.

Hoszowska, J.

Kavčič, M.

Kayser, Y.

Kheifets, A. S.

Szlachetko, J.

Szlachetko, M.

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Eur. Phys. J. Special Topics 169, 23–27 (2009)c© EDP Sciences, Springer-Verlag 2009DOI: 10.1140/epjst/e2009-00968-9THE EUROPEANPHYSICAL JOURNALSPECIAL TOPICSRegular ArticleDouble K-shell photoionization of low-Z atomsand He-like ionsJ. Hoszowska1,a, A.S. Kheifets2, M. Berset1, I. Bray5, W. Cao1, J.-Cl. Dousse1, K. Fennane1,M. Kavcˇicˇ4, Y. Kayser1, J. Szlachetko1,3, and M. Szlachetko11 Physics Department, University of Fribourg, 1700 Fribourg, Switzerland2 Research School of Physical Sciences, Australian National University, ACT 0200 Canberra, Australia3 European Synchrotron Radiation Facility, 38043 Grenoble, France4 J. Stefan Institute, 1001 Ljubljana, Slovenia5 ARC Centre for Matter-Antimatter Studies, Curtin University, WA 6845 Perth, AustraliaAbstract. We report on the investigation of the photon energy dependence ofdouble 1s photoionization of light atoms and compare the cross sections for hollowatom and He-like ion production. Measurements of the Kα hypersatellite x-rayspectra of Mg, Al, and Si were carried out using the Fribourg high-resolutionx-ray spectrometer installed at the ID21 and ID26 beam lines at the ESRF. Thedouble-to-single photoionization cross section ratios were derived as a functionof the incident photon beam energy and compared to convergent close-coupling(CCC) calculations for He-like ions. The dynamical electron-electron scatteringcontribution to the DPI cross-sections was found to be more important for neutralatoms than for the He isoelectronic series.1 IntroductionThe double photoionization (DPI) process provides a measure of the importance of electron cor-relations [1]. This is because the single-photon absorption and two-electron ejection is inducedby only one single interaction of the photon with the bound electron and it would not occurin the independent electron picture. In atomic structure calculations an accurate theoreticaltreatment of electron correlations in many-electron systems is still a challenge. Furthermore,the double photoionization process provides insight in fundamental aspects of atomic physicsas Breit interaction, quantum electrodynamics (QED) and relativity eﬀects.The double K-shell ionization of a neutral target leads to a so-called hollow atom, i.e. anatom with an innermost shell empty and outer shells occupied. Since the probability for creat-ing double 1s vacancies by photon impact is quite low (∼ 10−2–10−6), experimental data arescarce. With the advent of intense and energy tunable x-ray synchrotron sources hollow atomshave drawn renewed interest on both the experimental and theoretical side. In particular, theinvestigation of the photon energy dependence of the double 1s vacancy production becameaccessible. A compilation of the available experimental data for the double-to-single photoion-ization probability PKK as a function of the atomic number, including the present work, isshown in Fig. 2. For elements in the range 10 < Z < 20, to the best of our knowledge, the prob-ability for double 1s vacancy production PKK as a function of the incident photon beam energyhas not been determined beforehand. For low-Z atoms the only measurement, performed bymeans of high-resolution Auger electron spectroscopy, was reported for Ne at a photon energyof 5 keV [2].a e-mail: joanna.hoszowska@unifr.ch24 The European Physical Journal Special TopicsRadiative decay of the 1s double vacancy states yields K x-ray hypersatellite spectra. Infact, Briand et al. [3], in the pioneering work on the K x-ray spectrum of doubly ionizedGa atoms, has identiﬁed these shifted in energy x-ray transitions resulting from the decay ofdoubly ionized states in the same shell and called them hypersatellites. In the present work,the double-to-single photoionization cross-section ratios PKK for Mg, Al, and Si were deducedfrom the relative intensities of the resolved hypersatellite (1s−2 → 1s−12p−1) to the diagram(1s−1 → 2p−1) x-ray transitions by employing the high-resolution x-ray emission spectroscopytechnique. We have raised the question as to the role of outer shell electrons in the double K-shellphotoionization of low-Z atoms. Through a comparison of the photon energy dependence of theK-shell double photoionization cross-sections for hollow atom production to the correspondingDPI cross sections for He-like highly charged counterparts, the inﬂuence of outer shell electronson the electron-electron interactions in the double photoionization process was examined. Thedouble photoionization cross-sections for He-like ions Mg10+, Al11+ and Si12+ were calculatedwithin the framework of the convergent close-coupling formalism [4,5].2 ExperimentThe experiments were carried out at two undulator beam lines, ID21 and ID26, at the EuropeanSynchrotron Radiation Facility (ESRF), Grenoble, France, by means of high-resolution x-rayspectroscopy employing the Fribourg von Hamos Bragg-type curved crystal spectrometer [6].The x-ray emission spectra of Mg were measured using a TlAP(001) crystal (2d = 25.772 A˚)in second order and those of Al and Si with an ADP(101) (2d = 10.642 A˚) crystal in ﬁrstorder. The diﬀracted x-rays were recorded with a 26.8mm long and 8mm high position-sensitive back-illuminated CCD (charged coupled device) camera consisting of 1340 columns and400 rows with a pixel size of 20×20µm2. The CCD detector was cooled down thermo-electricallyto −50◦C. Self-supported 3.3µm and 50µm thick metallic foils of Mg, 1µm thick foil of Al anda 1mm thick c-Si sample were used. The energy calibration and the instrumental response ofthe crystal spectrometer were determined from the measurements of the Kα x-ray lines of Mg,Al and Si, and the Lβ1 lines of Se and Ag with reference energy values from [7] and natural linewidths from [8]. The instrumental response function of the spectrometer was found to be wellreproduced by a Lorentzian proﬁle with a width (FWHM) of 0.54(1) eV at the energy of theMg K-hypersatellite line and a Gaussian proﬁle width (FWHM) of 0.32(1) eV and 0.40(1) eVfor the Al and Si K-hypersatellite line, respectively. At the ID21 beam line monochromaticphoton beams with a 10 eV bandpass were obtained using two 20 A˚ Ni(B4C) multilayers andresidual upper harmonics were suppressed with a Ni mirror. The beam size was deﬁned bymeans of a 1mm in diameter pinhole. A slit width of 0.2mm was used as the best compromisebetween an acceptable energy resolution and the detection eﬃciency. At the ID26 beam line thedouble-crystal Si(111) monochromator was employed and the Si coated and Cr coated doublemirrors were used for harmonic rejection. The beam was focused horizontally to ∼ 250µm atthe sample thereby permitting to operate the spectrometer in the so-called slit-less geometryleading to a higher overall detection eﬃciency. The incident photon ﬂux was ∼1–3× 1012 ph/son both beam lines.The high-resolution K-hypersatellite x-ray emission spectra of Mg and Si at are shown inFig. 1. For light elements only the Kαh2 hypersatellite (1P1 → 1S0) is observed, the spin-ﬂipKαh1 transition (3P1 → 1S0) being forbidden by the E1 selection rule in the L-S coupling schemethat prevails for low-Z elements. The K-hypersatellite x-ray emission line is accompanied byL-satellites resulting from the presence of the 2p and 2s vacancies during the x-ray transition.In addition, on the low energy side of the Kαh2 x-ray spectra the KβL2(K−1L−2 → L−2M−1)and the KβL1(K−1L−1 → L−1M−1) satellite transitions can be seen for Mg and Si, respec-tively. To deduce the intensities of the K-hypersatellite lines the measured spectra of Mg wereﬁtted with Lorentzian proﬁles and those of Al and Si with Voigt functions. The obtained x-rayline intensities were corrected for the sample self-absorption and absorption of the incidentx-rays, the photon ﬂux, the spectrometer solid angle, as well as for the CCD detector quantumeﬃciency.Advances in X-Ray and Inner Shell Processes 250501001502001352 1357 1362 1367 1372 1377 1382Energy (eV)Counts/7255 sEbeam=2.996 keVK 2hK L2K 2hL1Mga)130001700021000250001855 1860 1865 1870 1875 1880 1885Energy (eV)Counts/3206 s Si Ebeam=5.5 keVK L1 K 2hK 2hL1b)Fig. 1. High-resolution K-hypersatellite x-ray emission spectra of Mg (a) and Si (b) measured atphoton energies close to the maximum of the DPI cross sections. Kαh2 hypersatellite transition energiesof 1367.86(6) eV for Mg and 1874.87(4) eV for Si were found.3 Results and discussionFollowing the single photon absorption, the double ionization proceeds via electron-electroninteraction. Two dominant mechanisms, namely the shakeoﬀ (SO) and the electron inelasticscattering (so-called knock-out KO or two-step-one TS1) contibute to the double K-shell pho-toionization. In the shake process the primary electron is ejected rapidly and due to a suddenchange of the atomic potential a subsequent removal of the remaining electron to the continuumor to a bound state takes place. The double K-shell phoionization via shake is a consequenceof the change in the self-consistent ﬁeld and electron-electron correlations. In the case of TS1,the outgoing photoelectron knocks out the second one in an (e,2e) like electron impact half-collision. The initial-state correlations are important in shakeoﬀ, while the ﬁnal-state electroninteractions are essential for the electron scattering TS1.The photon energy dependence of the TS1 and the SO processes diﬀer. Shake prevails at highphoton energies, while TS1 dominates at low and intermediate excitation energies to becomenegligible in the photoabsorption asymptotic regime where the double-to-single photoionizationratio approaches a constant value. To probe the evolution of the double ionization probabilitywith the photon energy, the Kαh x-ray transitions were measured at diﬀerent incident beamenergies from 2.746 keV to 8.000 keV for Mg, from 3.122 keV to 7.000 keV for Al, and from3.600 keV to 10.000 keV for Si. The ratios of the double-to-single K-shell ionization by photoab-sorption PKK and the DPI cross-sections σ2+ were determined from the relative intensities Iof the measured Kαh2 and Kα x-ray emission lines employing the expressions: PKK =ωKIKαhωKKIKαand PKK =σ2+σ+, where ωK and ωKK are the ﬂuorescence yields for the single- and double-hole state [9], respectively, and σ+ stands for the single K-shell photoionization cross sectionfrom [10]. The double to single K-shell photoionization ratios in the peak region of the photonenergy evolution PmaxKK were determined to be 2.02(11) × 10−3 for Mg, 1.78(12) × 10−3 for Aland 1.43(8)×10−3 for Si. The experimental results are represented in Fig. 2 along with the datafor other elements, the power law ﬁt from [11] and the Z-scaling laws for He-like ions. In fact, toplot the trend of the PKK in the peak region as a function of Z was ﬁrst suggested by Kanteret al. [12]. A signiﬁcantly larger electron scattering contribution in heavy atoms compared tolow-Z elements was evinced and a weaker 1/Z1.6-dependence than the 1/Z2 fall-oﬀ for shake-oﬀof the double photoionization probability PmaxKK was established [11]. Our results for the double-to-single photoionization cross section ratios of Mg, Al, and Si are in good agreement with the1/Z1.6-dependence of the PmaxKK for neutral atoms. However, compared to the calculated PmaxKKvalues for two-electron targets of 1.23× 10−3 for Mg10+, 1.10× 10−3 for Al11+ and 9.37× 10−4for Si12+, they lie systematically higher. The same holds for the values of the DPI cross sectionsσ2+ as illustrated in Fig. 3. For the helium isoelectronic sequence the shake-oﬀ (SO) ratio in thehigh-energy limit can be calculated quite accurately provided that electron correlation whenone electron is close to the nucleus is accounted for in the initial state wave function [13–15].The double-to-single ratio in the asymptotic limit can be also deduced from the double K-shellionization following nuclear electron capture (EC). As shown in Fig. 2, both the theoretical pre-dictions for SO and the EC radioactive source measurements are in good agreement. In a recent26 The European Physical Journal Special Topics1.0E-051.0E-041.0E-031.0E-021.0E-011 10 100Atomic number ZPKKMaximumPower law fit  Kanter et al. 0.12/Z1.61He-like Kheifets & Bray 0.14/Z1.9AsymptoticPower law fitForrey et al. 0.0698/Z1.92ECFig. 2. The ratio of double to single K-shell photoionization versus the atomic number. • Presentresults, ∗ [22], ◦ [25,26],  [23],  [11], × [18,24], and EC (electron capture) [27]. For He-like ions thePmaxKK are from Kheifets and Bray [4] and this work (thick solid line). The photoabsorption asymptoticlimits of Forrey et al. (dashed line) [15] are also shown.0510152025302000 4000 6000 8000 10000 12000 14000 16000E(eV)2+(b)Fig. 3. The double K-shell photoionization cross sections σ2+ as a function of the photon energy forMg ◦ experimental results, and Mg10+ • present CCC calculations in the velocity gauge.work [16] on correlated wave functions for the K-shell electrons of neutral atoms and helium-like atoms it was found that the inﬂuence of passive outer shell electrons on electron-electroncorrelation is very small. The outer shell electrons aﬀect the electron-nucleus interaction butnot the electron-electron interaction. Thus, it is plausible to assume that the photoabsorptionasymptotic shake-oﬀ values for the He-like ions and neutral atoms are almost the same. Sincethe TS1 term predominates in the broad maximum of the PKK because of the diﬀerent photonenergy dependence of the TS1 and the SO processes, the observed higher values of PmaxKK forneutral atoms indicate that the electron scattering contribution to DPI is more important thanfor He-like ions. This ﬁnding is related to the proportionality of electron-impact ionization ofa hydrogen-like ion to the TS1 term of the double photoionization of the same He-like atom[17–21].In conclusion, the comparison of our results with other experimental data and theory con-ﬁrms the importance of the ﬁnal-state electron-electron interaction term TS1 to the double1s photoionization probability for Mg, Al and Si. The eﬀect of outer shell electrons on thedouble K-shell photoionization in neutral low-Z atoms is primarily reﬂected in the electronscattering contribution due to the change of the eﬀective nuclear charge. Calculations of thedouble photoionization cross sections for neutral atoms would certainly shed new light on theelectron-electron interactions.Advances in X-Ray and Inner Shell Processes 27The financial support of the Swiss National Science Foundation is acknowledged. The authors wouldlike to thank the ESRF for support, in particular Dr. D. Reichert and Dr. R. Tucoulou from the ID21beam line and Dr. Tsu Chien Weng from the ID26 beam line.References1. J.H. McGuire, Electron Correlation and Dynamics in Atomic Collisions (Cambridge UniversityPress, Cambridge, UK, 1997)2. S.H. Southworth, et al., Phys. Rev. A 67, 062712 (2003)3. J.P. Briand, et al., Phys. Rev. Lett. 27, 777 (1971)4. A.S. Kheifets, I. Bray, Phys. Rev. A 58, 4501 (1998)5. A.S. Kheifets, I. Bray, Phys. Rev. A 75, 042703 (2007)6. J. Hoszowska, et al., Nucl. Instrum. Meth. Phys. Res. A 376, 129 (1996)7. R.D. Deslattes, et al., Rev. Mod. Phys. 75, 35 (2003)8. J.L. Campbell, T. Papp, At. Data Nucl. Data Tables 77, 1 (2001)9. M.H. Chen, Phys. Rev. A 44, 239 (1991)10. http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html11. E.P. Kanter, et al., Phys. Rev. A 73, 022708 (2006)12. E.P. Kanter, et al., Phys. Rev. Lett. 83, 508 (1999)13. T. Pattard, et al., J. Phys. B: At. Mol. Opt. Phys. 36, L189 (2003)14. M.A. Kornberg, J.E. Miraglia, Phys. Rev. A 49, 5120 (1994)15. R.C. Forrey, et al., Phys. Rev. A 51, 2112 (1995)16. D.M. Mitnik, J.E. Miraglia, J. Phys. B: At. Mol. Opt. Phys. 38, 3325 (2005)17. J.A.R. Samson, et al., Phys. Rev. Lett. 65, 2861 (1990)18. J.A.R. Samson, et al., Phys. Rev. A 57, 1906 (1998)19. A.S. Kheifets, J. Phys. B: At. Mol. Opt. Phys. 34, L247 (2001)20. T. Schneider, J.-M. Rost, Phys. Rev. A 67, 062704 (2003)21. T. Pattard, J. Burgdo¨rfer, Phys. Rev. A 64, 042720 (2001)22. M. Oura, et al., J. Phys. B: At. Mol. Opt. Phys. 35, 3847 (2002)23. J. Ahopelto, Phys. Scr. 20, 71 (1979)24. L. Spielberger, et al., Phys. Rev. Lett. 74, 4615 (1995)25. R. Diamant, et al., Phys. Rev. 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Double K-shell photoionization of low-Z atoms and He-like ions

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Double K-shell photoionization of low-Z atoms and He-like ions

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