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Journal of Physics B: Atomic, Molecular and Optical Physics
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 (13pp) doi:10.1088/0953-4075/47/11/115201
K-shell photoionization of B-like oxygen(O3+) ions: experiment and theory
B M McLaughlin1,2,8, J M Bizau3,4, D Cubaynes3,4, M M Al Shorman3,S Guilbaud3, I Sakho5, C Blancard6 and M F Gharaibeh7
1 Centre for Theoretical Atomic, Molecular and Optical Physics (CTAMOP), School of Mathematics andPhysics, The David Bates Building, 7 College Park, Queen’s University Belfast, Belfast BT7 1NN, UK2 Institute for Theoretical Atomic and Molecular Physics (ITAMP), Harvard Smithsonian Center forAstrophysics, MS-14, Cambridge, MA 02138, USA3 Institut des Sciences Moleculaires d’Orsay (ISMO), CNRS UMR 8214, Universite Paris-Sud, Bat. 350,F-91405 Orsay cedex, France4 Synchrotron SOLEIL - L’Orme des Merisiers, Saint-Aubin - BP 48, F-91192 Gif-sur-Yvette cedex,France5 Department of Physics, UFR of Sciences and Technologies, University Assane Seck of Ziguinchor,Ziguinchor, Senegal6 CEA-DAM-DIF, Bruyeres-le-Chatel, F-91297 Arpajon Cedex, France7 Department of Physics, Jordan University of Science and Technology, Irbid 22110, Jordan
E-mail: [email protected] and [email protected]
Received 26 February 2014, revised 18 April 2014Accepted for publication 22 April 2014Published 14 May 2014
AbstractAbsolute cross sections for the K-shell photoionization of boron-like (B-like) O3+ ions weremeasured by employing the ion–photon merged-beam technique at the SOLEILsynchrotron-radiation facility in Saint-Aubin, France. High-resolution spectroscopy with E/!E!5000 (!110 meV, full width half maximum) was achieved with photon energy from 540 upto 600 eV. Several theoretical approaches, including R-matrix, multi-configuration Dirac–Fockand screening constant by unit nuclear charge were used to identify and characterize the strong1s " 2p and the weaker 1s " 3p resonances observed in the K-shell spectra of this ion. Thetrend of the integrated oscillator strength and autoionization width (natural line width) of thestrong 1s " 2p resonances along the first few ions of the B-like sequence is discussed.
Keywords: photoionization, K-shell, oxygen ions, experiment, theory
(Some figures may appear in colour only in the online journal)
1. Introduction
Single and multiply ionization stages of C, N, O, Ne and Fehave been observed in the ionized outflow in the planetarynebulae NGC 4051, measured with the satellite XMM-Newton[1] in the soft-x-ray region. Low ionized stages of C, N and Ohave also been used in the modelling of x-ray emission fromOB super-giants [2]. Multiply ionization stages of O and Feare also seen in the XMM-Newton spectra from the Seyfertgalaxy NGC 3783, including UV imaging, x-ray and UV lightcurves, the 0.2–10 keV x-ray continuum, the iron K-emission
8 Author to whom any correspondence should be addressed.
line, and high-resolution spectroscopy in the modelling of thesoft x-ray warm absorber [3]. Detailed photoionization modelsof the brightest cluster of star formation in the blue compactdwarf galaxy Mrk 209 required abundances for ions of oxygenand nitrogen [4]. O [IV] K-lines are seen in the supernovaremnant Cassiopeia (Cas A) in the infrared spectra taken bythe Spitzer Space Telescope [5]. In Seyfert galaxies based onphotoionization models, O IV comes from higher ionizationstates and lower density regions and is an accurate indicator ofthe power of the active galactic nuclei (AGN) [6]. In the presentstudy we focus our attention on obtaining detailed spectra onthe triply ionized oxygen ion O3+ (O IV) in the vicinity of itsK-edge.
0953-4075/14/115201+13$33.00 1 © 2014 IOP Publishing Ltd Printed in the UK
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
Recent wavelength observations of K-transitions inatomic oxygen, neon and magnesium and their ions withx-ray absorption lines have been made with the high energytransmission grating (HETG) on board of the Chandra satellite[7]. Strong absorption K-shell lines of atomic oxygen, in itsvarious ionized forms, have been observed by the XMM-Newton satellite in the interstellar medium, through x-rayspectroscopy of low-mass x-ray binaries [8]. The Chandraand XMM-Newton satellite observations may be used foridentifying the absorption features present in astrophysicalsources, such as AGN and x-ray binaries and for assistance inbenchmarking theoretical calculations [9, 10].
Few experiments have been devoted to the study of K-shellphotoionization on oxygen ions. Auger spectra of singly anddoubly core-excited oxygen ions emitted in the collision of fastoxygen-ion beams with gas targets and foils were measuredby Bruch and co-workers [11]; K-shell x-ray lines from inner-shell excited and ionized ions of oxygen were observed, usingthe Lawrence Livermore National Laboratory EBIT. With amulti-ion model they were able to identify the observed K-shell transitions of oxygen ions from O2+ to O5+.
Up to now, K-shell photoionization cross-section resultshave been obtained only for O+ ions by Kawatsura et al [12].Measurements were made at Spring-8, using the merged-beamtechnique, on relative cross sections for double photoionizationspectra in the energy range of the 1s " 2p resonances,using a limited resolving power #310. K-shell single anddouble photoionization spectra of neutral oxygen have alsobeen obtained [13–15], recently revisited with high resolutionat the advanced light source (ALS) and benchmarked againstcalculations using the R-matrix with pseudo-states (RMPS)method [16, 17].
Theoretically, resonance energies and line widths forAuger transitions in B-like atomic ions have been calculatedusing a variety of methods, such as 1/Z perturbation theory[18–22], multi-configuration Dirac Fock (MCDF) [23, 24],the saddle-point-method (SPM) with R-matrix, complex-coordinate rotation methods [25–29]. Chen and Craseman[23, 24] calculated Auger and radiative decay of 1s vacancystates in the boron isoelectronic sequence using the MCDFapproach. Sun and co-workers [30] used the SPM with rotationto calculate energy levels and Auger decay widths for the1s2s22p2 and 1s2s2p3 2,4L levels in B-like carbon and foundsuitable agreement with the re-calibrated spectrum of Bruchand co-workers [31] and the combined theoretical work andhigh resolution synchrotron measurements performed at theALS [32]. In the case of O3+ ions, recent saddle-point withrotation calculations by Sun and co-workers [33] for the energylevels and Auger and radiative decay rates for the 1s2s22p2
and 1s2s2p3 2,4L levels were compared to the earlier beam-foilexperimental measurements of Bruch and co-workers [11],the MCDF work of Chen and Craseman [23, 24] and furtherextended to the higher lying 1s2p4 levels of other B-like ions[34].
State-of-the-art ab initio calculations for Auger inner-shell processes were first performed on this B-like systemby Zeng and Yuan [35] and then by Pradhan and co-workers[36] using the R-matrix method [37]. This work followed a
similar procedure to K-shell studies on Be-like B+ ions byPetrini [38]. Garcia and co-workers [39], further extendedthis work by using the R-matrix optical potential methodwithin an intermediate-coupling scheme [40]. Photoionizationfrom the ground state, along the oxygen iso-nuclear sequencewas investigated, in the photon energy region of the K-edge. In the present study we compare our results from theMCDF, RMPS approach, and the screening constant by nuclearunit charge (SCUNC) semi-empirical methods [41, 42] withmeasurements made at SOLEIL, prior EBIT measurements[43], XMM and Chandra satellite observations [3, 7, 8, 44, 45]and other theoretical results [23, 24, 35, 36, 39, 46].
In this paper we present detailed measurements of theabsolute K-shell single photoionization cross sections for B-like oxygen ions, in the 542–548 eV region and 594–599 eVphoton energy range that were explored experimentally.Theoretical predictions are made from the SCUNC, MCDFand RMPS methods to compare with the measurements. Thesecalculations enable the identification and characterizationof the very strong 1s " 2p and the weaker 1s " 3presonance peaks observed in the B-like oxygen spectra. Thepresent investigation provides absolute values (experimentaland theoretical) for photoionization cross sections for then = 2 inner-shell resonance energies, natural line widths andresonance strengths, occurring for the interaction of a photonwith the 1s22s22p 2Po ground state and 1s22s2p2 4P metastablestate of the O3+ ion. Our work would appear to be the firsttime experimental measurements that have been performed onthis prototype B-like system in the photon energy region ofthe K-edge, and complements our recent studies on K-shellphotoionization of atomic nitrogen ions [47–49] and previousinvestigations on B-like carbon, C+ [32] at the ALS, in thevicinity of the K-edge.
The layout of this paper is as follows. Section 2 brieflyoutlines the experimental procedure used. Section 3 presentsthe theoretical work. Section 4 presents a discussion of theresults obtained from both experiment and theory. In section 5we present a discussion of the variation of the integratedoscillator strengths and line widths for the first three ionsof the B-like sequence with increasing charge state. Finally insection 6 conclusions are drawn from the present investigation.
2. Experiment
2.1. Ion production
The present measurements were made using the MAIA (multi-analysis ion apparatus) set-up, permanently installed on branchA of the PLEIADES beam line [50, 51] at SOLEIL. Theset-up and the experimental procedure have been describedpreviously in detail [47]. Here we will only give a briefdescription of the set-up and procedure. A continuous oxygenion beam is produced in a permanent magnet electron cyclotronresonance ion source (ECRIS) where a micro leak (electricallydriven) is used to introduce oxygen gas at continuous rate.A 12.6 GHz radio wave is used to heat the plasma at apower of approximately 40 W. The ions are extracted from theplasma by application of a constant 4 kV bias on the source.
2
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
The ion beam is selected in mass/charge ratio by a dipolemagnet before being collimated and merged with the photonbeam in the 50 cm long-interaction region. After interaction,the charge state of the ions is analysed by a second dipolemagnet. The parent ions are collected in a Faraday cup, and thephoto-ions which have lost an electron (or increase in chargestate by one) in the interaction are counted using channelplates.
2.2. Excitation source
The photon beam is monochromatized synchrotron radiationfrom the PLEIADES beam line [50, 51]. In the photon energyrange considered here, a permanent-magnet Apple II undulatorwith 80 mm period is used. The light is monochromatizedby a plane-grating monochromator with no entrance slit. Thehigh-flux 600 lines mm$1 grating was used for this work. Highspectral purity is obtained by a combination of a quasi-periodicdesign for the undulator and the use of a varied groove depthfor the plane grating. The photon energy is determined usinga double-ionization chamber of the Samson type [52]. For thiswork, we used the 1s " 4p" transition in the O2 gas [53] and3d " 6p transitions in Xe gas [54] for calibration purposes.The photon energy is corrected for Doppler shift resultingfrom the velocity of the oxygen ions. We note that during theexperiment a misalignment in the monochromator optics didnot allow us to reach the optimum resolution and accuracy onthe photon energy.
2.3. Experimental procedure
The merged-beam set-up allows for the determination ofabsolute photoionization cross sections. At a given photonenergy, the cross section " is obtained from,
" = Se2#$q
IJ%! L
0dz
!x!yF(z)
, (1)
where S is the counting rate of photo-ions measured with thechannel-plates. A chopper, placed at the exit of the photonbeam line, allows to subtract from the photo-ions signalthe background produced by collisional-ionization processes,charge stripping on the collimator slits or autoionizing decayof metastable excited states produced in the ECRIS. In (1), q isthe charge state of the target ions, $ is the velocity of the ions inthe interaction region determined from the potentials appliedto the ECRIS and the interaction region (see below) and Iis the current produced by the photons on a AXUV100 IRDphotodiode. The efficiency # of the photodiode was calibratedat the Physikalisch-Technische Bundesanstalt beam line atBESSY in Berlin. e is the charge of the electron and J isthe current of incident ions measured in the Faraday cup. %is the efficiency of the micro-channel plates determined bycomparing the counting rate produced by a low intensity ionbeam and the current induced by the same beam in the Faradaycup. !x!yF(z) is an effective beam area (z is the propagationaxis of the two beams), where F is a two-dimensional formfactor determined using three sets of xy scanners placed at eachend and in the middle of the interaction region. The length Lof the interaction region is fixed by applying $1 kV bias on
Table 1. Typical values for the experimental parameters involved inevaluating the absolute cross section measured at a photon energy of544.8 eV.
S 70 HzNoise 300 Hz$ 4.2 105 ms$1
Photon flux 5 1011 s$1
J 70 nA% 0.48Fxy 68
a 50 cm long tube placed in the interaction region, resultingin a different velocity for the photo-ions produced inside andoutside the tube. Typical values of the parameters involved inequation (1), measured at a photon energy of 544.8 eV, aregiven in table 1.
The accuracy of the measured cross sections is determinedby statistical fluctuations on the photo-ion and backgroundcounting rates and a systematic contribution resulting fromthe measurement of the different parameters in equation (1).The latter is estimated to be 15% and is dominated by theuncertainty on the determination of the photon flux, theform factor and detector efficiency. To record the single-photoionization spectra, the field in the second dipole magnet isadjusted to detect with the channel plates the photo-ions whichhave gained one charge while the photon energy is scanned.Two acquisition modes have been used. One with no voltageapplied on the interaction tube, allowing better statistics sincethe whole interaction length of the photon and ion beams isused. In this mode, only relative cross sections are obtained.In the second mode, the voltage is applied to the tube to definethe interaction length L, allowing the determination of crosssections in absolute value.
3. Theory
3.1. SCUNC: B-like oxygen
The starting point of the screening constant by unit nuclearcharge formalism is the total energy of the (N&n&%;2S+1 L' )
excited states of two electron systems given by (in Rydbergunits),
E"N&n&%;2S+1 L'
#= $Z2
$1
N2
+ 1n2
[1 $ ((N&n&%;2S+1 L' ; Z)]2%. (2)
In this equation, the principal quantum numbers N and n arerespectively for the inner and the outer electron of the He-likeiso-electronic series. The (-parameters are screening constantsby unit nuclear charge expanded in inverse powers of Z andare given by the expression,
((N&n&%;2S+1 L' ) =&
k=1
fk
'1Z
(k
(3)
where fk(N&n&%;2S+1 L' ) are parameters that are evaluatedempirically from existing experimental measurements onresonance energies. In the same way one may get the Auger
3
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
widths ) in Rydbergs (1 Rydberg = 13.605 69 eV) from theformula
)(Ry) = Z2
)
1 $&
q
fq
'1Z
(q*2
. (4)
For the B-like O3+ ion the total energies of the 1sNsxnpy 2S+1Lstates are given by
E(1sNsxnpy;2S+1 L' ) = $Z2
)
1 + xN2
'1 $
&
k=1
fk
&'
1Z
(k(2*
$ Z2
+
, yn2
-
1 $&
k=1
f %k
'1Z
(k.2
/
0 . (5)
Here x and y are the number of electrons in the s and porbitals respectively. As the &-orbital quantum number is equalto zero in the Nsx orbital, we neglect the dependence of the(-parameters on &. This approximation permits one to simplifyequation (3) for each of the 1sNsxnpy 2S+1L' resonances whereonly one parameter (here f1) is to be evaluated empirically andsimilarly f2 for the Auger widths.
The ALS experimental measurements of Schlachter andco-workers on K-shell photoionization of B-like carbonions [32] were used to determine the appropriate empiricalparameters fk and fq for the resonance energy and Augerwidths. The ALS experimental data of Schlachter and co-workers on C+ (Z = 6)[32] for the 1s2s22p2 2D, 1s2s22p2 2P,and 1s2s22p2 2S levels are located at 287.93 ± 0.03, 288.40±0.03 and 289.90 ± 0.03, respectively, where the valuesare given in eV. Using the ground state energy of C+,$1018.8467 eV [55] we obtain f1(
2D) = 1.7903 ± 0.0003,f1(
2P) = 1.7944 ± 0.0003 and f1(2S) = 1.8075 ± 0.0003 for
use in equation (2). The ALS experimental values for the Augerwidths (given in meV) on C+ for these same resonances, arerespectively 105 ± 15, 59 ± 6, and 112 ± 25 and we find thatf2(
2D) = 5.9121 ± 0.0060, f2(2P) = 5.9341 ± 0.0033 and
f2(2S) = 5.9093 ± 0.0096 which are used in equation (4). The
SCUNC estimates for the resonance energies and Auger widthsfor O3+ and N2+ using these values are given in tables 2–5.
3.2. MCDF: B-like oxygen
MCDF calculations were performed based on a fullintermediate coupling regime in a j j-basis using the codedeveloped by Bruneau [56]. Photoexcitation cross sectionshave been carried out for B-like atomic oxygen ions in theregion of the K-edge. Only electric dipole transitions have beencomputed using length and velocity forms. In the present study,oscillator strengths calculated using the two gauges differ byless than 8%. Photoexcitation from the two levels (2P'
1/2,3/2)of the ground configuration 1s22s22p and from metastablelevels (4P1/2,3/2,5/2) of the configuration 1s22s2p2 have beencalculated separately. In both cases, multiple orbitals with thesame quantum number have been used in order to describe thecorrelation and relaxation effects. Wavefunctions have beencalculated minimizing the Slater transition state. Each electricdipole transition has been dressed by a Lorentzian profile witha full width half maximum (FWHM) equal to 10 meV.
Calculations of the 2P'1/2,3/2 photoexcitation cross sections
have been performed using the following set of configurations.The initial configurations used were: 1s22s2np (with n = 2,..., 5), 1s22s2pns (with n = 3, ..., 5). The final configurationswere: 1s2s22p2, 1s2s22pnp (with n = 3, ..., 5). Such notationmeans that the radial functions 1s1/2 and 2p1/2,3/2 are not thesame for initial and final configurations. Similarly for the4P1/2,3/2,5/2 levels, photoexcitation cross sections have beenperformed using the following set of configurations: initialconfigurations: 1s22s2pnp (with n = 2, ..., 4), 1s22s3&2 (& =0, 1, 2), 1s22s4&2 (& = 0, 1, 2), 1s22s3p4p, final configurations:1s2snpn%pn%%p (with n, n% and n%% = 2, ..., 4).
The wavefunctions have been calculated minimizing thefollowing energy functional,
E =1
*(2J* + 1)E*
21
*(2J* + 1)+
1( (2J( + 1)E(
21
( (2J( + 1)(6)
where * and ( run over all the initial and final states,respectively.
3.3. R-matrix: B-like oxygen
The R-matrix method [40], with an efficient parallelimplementation of the codes [57–59] was used to determine allthe cross sections presented here, for both the initial 2Po groundstate and the 4P metastable states. Cross section calculationswere carried out in LS-coupling with 390-levels retained inthe close-coupling expansion. The Hartree–Fock 1s, 2s and2p tabulated orbitals of Clementi and Roetti [60] were usedwith n = 3 physical and n = 4 pseudo orbitals of the O3+
ion determined by energy optimization on the appropriatephysical and hole–shell states [61], using the atomic structurecode CIV3 [62]. The n = 4 pseudo-orbitals are includedto account for core relaxation and additional correlationeffects in the multi-configuration interaction wavefunctions.All the O4+ residual ion states were then represented by usingmulti-reference-configuration-interaction wave functions. Thenon-relativistic R-matrix approach was used to calculate theenergies of the O3+ bound states and the subsequent PI crosssections. PI cross sections out of the 1s22s22p 2Po ground stateand the 1s22s2p2 4P metastable state were then obtained for alltotal angular momentum scattering symmetries that contribute.
The RMPS method was used to determine all the crosssections (in LS-coupling) with 390 levels of the O4+ residualion included in the close-coupling calculations. Due to thepresence of metastable states in the beam, PI cross-sectioncalculations were performed for both the 1s22s22p 2Po groundstate and the 1s22s2p2 4P metastable state of the O3+ ion.
The scattering wavefunctions were generated by allowingthree-electron promotions out of selected base configurationsof O3+ into the orbital set employed. Scattering calculationswere performed with twenty continuum functions and aboundary radius of 9.4 Bohr radii. For both the 2Po groundstate and the 4P metastable states the outer region electron-ion collision problem was solved (in the resonance regionbelow and between all the thresholds) using a suitably chosenfine energy mesh of 2&10$7 Rydbergs (!2.72 µeV) to fullyresolve all the resonance structure in the PI cross sections.Radiation and Auger damping were also included in the crosssection calculations.
4
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
Table 2. B-like atomic oxygen ions, quartet core-excited states. Comparison of the present experimental and theoretical results for theresonance energies E (res)
ph (in eV), natural line widths ) (in meV) and resonance strengths " PI (in Mb eV), for the dominant corephoto-excited n = 2 states of the O3+ ion, in the photon energy region 541–548 eV with previous investigations. The experimental error inthe calibrated photon energy is estimated to be ±70 meV.
Resonance SOLEIL R-matrix MCDF/others(label) (experimenta) (theory) (theory)
1s2s[3S]2p3[2D'] 4D' E (res)ph 542.330 ± 0.082a 542.351b 542.058c
± 0.013d
1( 542.933 ± 0.12e 542.719f 543.686g
542.552h
542.909i
) 24 ± 14a 73b
80f 38g
96h
74i
" PI 2.49± 0.90a 2.59b 2.54c
1s2s[1S]2p3[4S'] 4S' E (res)ph 542.532 ± 0.080a 542.628b 542.506c
± 0.011d
2( 543.203f 542.557g
542.209h
543.028i
) 23 ± 14a 20b
19f 13g
30h
20i
" PI 2.61 ± 0.99a 2.57b 3.07c
1s2s[3S]2p3[2P'] 4P' E (res)ph 545.730 ± 0.079a 545.808b 545.773c
± 0.010d
3( 546.131f 547.006g
545.764h
546.692i
) 70 ± 23a 59b
60f 29g
76h
55i
" PI 1.44± 1.10a 1.67b 1.82c
a SOLEIL, experimental work.b R-matrix, RMPS present work.c MCDF, present work.d Uncertainty relative to resonance line 5.e EBIT, experimental work [43].f R-matrix, [35].g MCDF, Chen and co-workers [23, 24].h SCUNC, present work.i Saddle point + complex rotation, [33].
4. Results and discussion
Figure 1 displays the photoionization cross sections measuredat SOLEIL in the region of the 1s " 2p resonances. Inthe upper panel, the continuous line shows the cross sectionmeasured in the relative mode with 170 ± 4 meV band-width(BW), and the open points are the ones obtained with a largerstep in the absolute mode. The error bars give the total accuracyof the cross sections. The lower panel shows the cross sectionsrecorded in the relative mode with improved resolution,150 ± 25 meV BW for the region 542–543 eV, and110 ± 13 meV for the region 543.3–545.3 eV. The relativemeasurements have been placed on an absolute scale bynormalization to the absolute cross section by means ofthe area under the lines, which is independent of the
experimental BW. The error bars on the relative measurementsgive the statistical uncertainty.
K-shell photoionization contributes to the ionizationbalance in a more complicated way than outer-shellphotoionization. In fact K-shell photoionization whenfollowed by Auger decay couples three or more ionizationstages instead of two in the usual equations of ionizationequilibrium [63]. Promotion of a K-shell electron in O3+ ionsto an outer np-valence shell (1s " np transition) from theground state produces states that can autoionize, forming anO4+ ion and an outgoing free electron.
The 1s " 2p photo-excitation process on the 1s22s22p 2Po
ground-state of B-like oxygen ion is,h$ + O3+(1s22s22p 2Po)
" O3+(1s2s22p2[3P, 1D, 1S]2S, 2P, 2D)
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J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
Table 3. B-like atomic oxygen ions, doublet core-excited states arising from the configuration 1s2s22p2. Comparison of the presentexperimental and theoretical results for the resonance energies E (res)
ph (in eV), natural line widths ) (in meV) and resonance strengths " PI (inMb eV), for the dominant core photo-excited n = 2 states of the O3+ ion, in the photon energy region 541–547 eV with previousinvestigations. The experimental error in the calibrated photon energy is estimated to be ±70 meV.
Resonance SOLEIL R-matrix MCDF/others(label) (experimenta) (theory) (theory)
1s2s22p2 [1D]2D E (res)ph 543.801 ± 0.073a 543.757b 543.691c
± 0.004d 544.021e 545.539f
4( 544.614 ± 1.00g 545.465h 543.809i
544.003j 544.334k
) 144 ± 8a 131b
140e 64f
27h 151i
76j 155k
" PI 12.41 ± 2.59a 11.85b 15.32c
1s2s22p2 [3P]2P E (res)ph 544.794 ± 0.071a 544.869b 544.731c
± 0.000d
5( 545.201 ± 0.096l 545.299e 545.068f
544.340 ± 0.40m 546.909h 544.501i
544.330 ± 0.40m 545.066j 544.945n
545.225 ± 0.40o 544.985p
544.946 ± 0.40o 545.379k
545.409 ± 1.00g
) 35 ± 4a 75b
67e 28f
14h 78i
76j 92k
" PI 19.68±2.59a 17.45b 27.90c
1s2s22p2 [1S]2S E (res)ph 546.908 ± 0.085a 546.954b 548.783c
± 0.016d
6( 547.914 ± 1.00g 547.276e 547.066f
552.022h 546.711i
547.791j 547.624k
) 26 ± 22a 130b
125e 58f
22h 162i
127j 91k
" PI 3.73 ± 1.67a 1.87b 3.05c
a SOLEIL, experimental work.b R-matrix, RMPS present work.c MCDF, present work.d Uncertainty relative to resonance line 5.e R-matrix, [35].f Chen and co-workers [23, 24].g BEAM-FOIL, experimental work, assignments are from Sun andco-workers [33].h R-matrix, [36].i SCUNC, present work.j R-matrix, optical potential [39].k Saddle-point + complex rotation, [33].l EBIT, experimental work [43].m XMM, [3, 8] andn Flexible Atomic Code (FAC), [46].o Chandra observations, [44, 45].p HFR, Garcia and co-workers, [39].
which can decay via autoionization mainly toO4+(1s22s21S) + e$(k2
&1), or O4+(1s22snp1P
') + e$"
k2&2
#,
where k2&i
(i = 1, 2) represent the energies of the outgoingAuger electrons from the two different decay processes,respectively.
Three Auger lines are expected in the spectrum,corresponding to the 1s2s2 2p2 2S, 2P and 2D resonances, due
to 1s " 2p core-excited states from the ground state of theparent ion. In the present experimental investigations, O3+
ions are extracted from a high temperature plasma inside theECRIS, where the ions are produced in all the excited states,and in particular the 1s22s2p2 4P metastable state has a lifetimelong enough to travel to the interaction region and contributeto the photoionization signal.
6
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
Table 4. B-like atomic oxygen ions, doublet core-excited states arising from the configuration 1s2s22p3p. Comparison of the presentexperimental and theoretical results for the resonance energies E (res)
ph (in eV), natural line widths ) (in meV) for these photo-excited states ofthe O3+ ion, in the photon energy region 594–599 eV with previous investigations. The experimental error in the calibrated photon energy isestimated to be ±110 meV.
Resonance SOLEIL R-matrix MCDF/others(label) (experimenta) (theory) (theory)
1s2s22p3p 2D E (res)ph 595.671 ± 0.134a 595.534b 595.749c
595.806d 595.977e
7() – 90b
66d 91e
1s2s22p3p 2P E (res)ph 597.348 ± 0.123a 597.352b 597.419c
597.616d 597.629e
8() 133 ± 71a 122b
75d 37e
1s2s22p3p 2S E (res)ph 598.362 ± 0.175a 598.347b 598.382c
598.585d 598.309e
9() – 98b
87d 100e
a SOLEIL, experimental work.b R-matrix, RMPS present work.c MCDF, present work.d R-matrix, optical potential [39].e SCUNC, present work.
For the 1s22s2p2 4P metastable state, autoionizationprocesses occurring by the 1s " 2p photo-excitation processare;
h$ + O3+(1s22s2p2 4P)
)O3+[1s2s[1,3S]2p3(4So, 2Do, 2Po)]4So, 4Po, 4Do
)O4+(1s22snp 3Po) + e$"
k2&3
#,
giving rise to three additional lines, which are observed in thespectra as illustrated in figures 1 and 2, where k2
&3represent the
energy of the outgoing Auger electron.Figure 2 compares the experimental cross sections
obtained with a 170 meV BW (continuous line on the toppanel of figure 1) with our theoretical MCDF and R-matrixresults for the photon energy range of 541–548 eV. TheR-matrix optical potential calculations (dashed line) areincluded for completeness. The error bars on the experimentaldata give the statistical uncertainty. Since the relativepopulation of 4P metastable term of the O3+ ion presentin the parent experimental beam cannot be determinedexperimentally, theory may be used to estimate its content.From our theoretical R-matrix studies on this system we findthat an admixture of 80% ground states and 20% metastablestates in the parent ion beam appears to give the closestagreement between theory and experiment. The same relativepopulations have been found in previous experimental studieson B-like ions: C+ [32] and N2+ [49], performed with the sametype of ion source.
The peaks found in the theoretical photoionization crosssections spectrum were fitted to Fano profiles for overlapping
resonances [64–66] as opposed to the energy derivative of theeigenphase sum method [67–69]. The theoretical values forthe natural line widths ) determined from this procedure arepresented in tables 2 and 3 for the strong peaks in the photonregion 540– 549 eV and compared with results obtained fromthe high-resolution SOLEIL synchrotron measurements andwith other methods. Note, in table 3 we have included thebeam-foil values quoted by Sun et al [33] who reinterpretedthe measurements of Bruch and co-workers [11].
We note the good agreement obtained by both theoreticalresults for the position and intensity of the lines. The R-matrixcalculations include Auger and radiation damping, missingfrom the MCDF calculations and give lines positions andintensities in closer agreement with experiment. Tables 2and 3 summarizes our experimental, R-matrix and MCDFvalues for the position, width and strength of the observedlines, as well as the results of our SCUNC calculations withpreviously published experimental [11, 43] and theoretical data[35, 36, 39]. Our experimental values, including experimentalBWs, were obtained by fitting the data with Voigt profiles tothe spectra shown on figure 1.
Concerning the excitation energy of the lines, the EBITmeasurements [43] give values significantly lower (by 0.5 eV)than our values. We note that, in the EBIT work, only the linesdue to the ions in the ground states were observed, with aninsufficient resolving power (#1100) to separate the individuallines. A comparison of the various theoretical predictionsshows that our RMPS calculations give the best overallagreement with experiment, almost all energies lying withinthe experimental uncertainties. Our semi-empirical SCUNCcalculations give satisfactory agreement with experiment,with a maximum discrepancy of 0.3 eV. Considering the
7
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
Table 5. B-like ions, doublet core-excited states arising from theconfiguration 1s2s22p2. Comparison of the present experimental andtheoretical results for the integrated oscillator strengths f and thenatural line widths ) (in meV) for the dominant core photo-excitedn = 2 states of the first three B-like ions with previousinvestigations.
Resonance SOLEIL/ALS R-matrix Others(label) (experiment) (theory) (theory)
1s2s22p2 [1D]2DC+ f 0.05 ± 0.015a 0.069b
) 105 ± 15a 102b
103c
N2+ f 0.115 ± 0.02d 0.119b
) 122 ± 19d 122b 123e
109f
O3+ f 0.142 ± 0.03d 0.135b 0.135g
0.137h 0.174i
) 144 ± 8d 131b 151e
140h 155j
76f
1s2s22p2 [3P]2PC+ f 0.10 ± 0.03a 0.135b
) 59 ± 6a 56b
62c
N2+ f 0.191 ± 0.03d 0.220b
) 58 ± 7d 62b 66e
43f
O3+ f 0.224 ± 0.03d 0.200b 0.243g
0.253h 0.318i
) 35 ± 4d 75b 78e
67h 92j
76e
1s2s22p2 [1S]2SC+ f 0.008 ± 0.002a 0.014b
) 112 ± 25a 105b
93c
N2+ f 0.014 ± 0.005d 0.017b
) 120 ± 60d 106b 132e
94f
O3+ f 0.043± 0.02d 0.029b 0.035g
0.027h 0.030i
) 26 ± 22d 130b 162e
125h 91j
127f
a ALS, experimental work [32].b R-matrix, RMPS, 390 levels present work.c R-matrix, RMPS, 135 levels [32].d SOLEIL, experimental work.e SCUNC, present work.f R-matrix, optical potential [39].g CIV3. structure calculations, [35].h R-matrix, [35].i MCDF, present work. jSaddle-point + complex rotation, [33].
work of Garcia et al [39], we remark that better agreementis achieved from simple SUPERSTRUCTURE calculations(approximation AS1 in paper [39]) rather than by their moresophisticated R-matrix calculations.
As in the case for neutral oxygen [10, 16, 17] there is adiscrepancy in the position of the strongest 1s " 2p transitionin the K-shell spectrum of O3+ (O IV) compared with veryrecent Chandra HETG observations [7] (where the K* linesfrom two elements are observed at 22.6969 A, 546.260 eVand 22.6965 A, 546.270 eV). In contrast to this the present
high resolution measurements made at SOLEIL (22.758 A,544.794 eV), shows excellent agreement with previous XMMobservations (22.7769 ± 0.02 A, 544.340 eV and 22.75 ± 0.02A, 544.985 eV) [3, 8], Chandra observations (22.74 ± 0.02A, 545.225 eV and 22.7509 ± 0.02 A, 544.946 eV) [44, 45]and EBIT measurements (22.741 ± 0.005 A, 545.201 eV)[43] including the current RMPS predictions (22.7586 A,544.869 eV).
Our measured widths are in agreement with theoreticalpredictions for the 4So, 2D and 4Po lines, but are systematicallylower compared to theory for the 2P and 2S lines. All thetheoretical strengths in tables 2 and 3 have been weighted bythe 80% and 20% population of the ground and metastablestates, respectively.
Figure 3 illustrates the cross sections for the photonenergy range 593–599 eV, in the vicinity of the 1s " 3ptransitions, which occurs from the ground state of the O3+
ion. The measurements in this energy region were takenin the relative mode with a spectral resolution of 190 ±20 meV. They are compared to the results of our R-matrixRMPS, MCDF and the R-matrix optical [39] calculations. Therelative measurements have been normalized on the area ofresonance line 8 calculated with the R-matrix parallel suite ofcodes. As previously, to compare directly with experiment allthe theoretical calculations were convoluted with a Gaussianfunction of 190 meV FWHM and weighted 80% for theground-state population and 20% for the metastable state. Inthis energy region it is seen that the metastable contributionis negligible. Our experimental and theoretical excitationenergies, widths and strengths are given in table 4. Due tolimited statistics, the natural width could only be obtainedexperimentally for the most intense 1s " 3p transitions,where the strongest peak observed in this photon energy regionis due to the 1s22s22p 2Po " 1s2s22p3p 2P transition. Wefind an experimental value for the energy of this resonanceto be located at 597.348 ± 0.123 eV. Theoretical predictionsfrom the RMPS give a value of 597.345 eV for the energy ofthis resonance and the MCDF value is 597.419 eV. For this1s " 3p resonance the SOLEIL experimental measurementsyield a value 133 ± 71 meV for the Auger width compared tothe RMPS method of 122 meV. SCUNC estimates give for this1s " 3p resonance peak an energy position of 597.629 eVand an Auger width of 37 meV. The RMPS calculations giveexcitation energies in excellent agreement with measurements,while the predictions for this same 1s " 3p resonance linefrom the MCDF and SCUNC methods indicate the energy isat a higher energy, respectively 0.06 eV and 0.3 eV.
In tables 2 and 3 we have used the Heisenberg uncertaintyprinciple (!E!t = !/2, i.e. ) = 658.211 89/2+ , where thenatural line width ) is in meV and + the lifetime, is in femto-seconds) to convert the MCDF and saddle point Auger rates[23, 24, 33] for the 1s " 2p resonance transitions to widths(in meV) for comparison purposes.
5. Auger widths and f -values for B-like ions; C+,N2+ and O3+ ions
To gain some physical insight into how a photon interactswith ions along the B-like sequence, we draw comparison
8
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
541 542 543 544 545 546 547 548
0
25
50
75
100
125
541 542 543 544 545 546 547 548
Photon energy (eV)
0
25
50
75
100
125
(a)
(b)
O3+E=170 meV
E=150 meV
Cro
ss S
ect
ion (
Mb)
4
23
1
5
6
E=110 meV
Figure 1. SOLEIL experimental K-shell photoionization cross section of O3+ ions in the 541–548 eV photon energy range. Upper panel (a):measured with 170 meV band-width. Solid points: the error bars give the total uncertainty; blue line: normalized relative measurements.Lower panel (b): lines 1 and 2 measured with 150 meV band-width, only lines 4–5 are measured with the 110 meV band-width. The errorbars represent the statistical uncertainty.
541 542 543 544 545 546 547 548
Photon energy (eV)
0
50
100
150
Cro
ss S
ect
ion
(M
b)
MCDFOPTICAL POTENTIAL4P (20%)2Po (80%)EXPT (SOLEIL)
O3+
1s2
s2p
34D
o
E=170 meV
1s2
s2p
34S
o
1s2
s2p
34P
o
1s2
s22p
22D
1s2
s22p
22P
1s2
s22p
22S
1 23
4
5
6
Figure 2. Photoionization cross sections for O3+ ions measured with a 170 meV band pass in the region of 1s " 2p photo-excitations. Solidpoints (magentta), experimental cross sections. The error bars give the statistical uncertainty of the experimental data. The R-matrix (RMPS,solid red line, ground state, 80% 2Po, metastable, blue line 20% 4P). Dotted line with solid green circles are the present MCDF calculations(80% 2Po and 20% 4P). The optical potential R-matrix results (dashed black line 80% 2Po) are from the results of Garcia and co-workers [39].Theoretical work shown was convoluted with a Gaussian profile of 170 meV FWHM and a weighting of the ground and metastable states(see text for details) to simulate the measurements. Tables 2 and 3 give the designation of the resonances 1(– 6( in this photon energy region.
9
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
593 594 595 596 597 598 599
Photon energy (eV)
-10
0
10
20
Cro
ss S
ect
ion (
Mb)
2Po (80%)4P (20%)OPTICAL POTENTIALMCDFEXPT (SOLEIL)
O3+
E=190 meV1s2
s22p3p 2
D
1s2
s22p3p 2
P
1s2
s22p3p 2
S
8
7 9
Figure 3. Photoionization cross sections for O3+ ions measured with a 190 meV band pass in the region of the 1s " 3p. Solid circles:experimental cross section measured in the relative mode, normalized on the R-matrix results (see text). The error bars give the statisticaluncertainty of the experimental data. R-matrix (RMPS, red line 80% 2Po, blue line 20% 4P). MCDF calculations (dotted black line withgreen circles 80% 2Po). The optical potential (dashed black line 80% 2Po) R-matrix results of Garcia and co-workers [39]. Theoretical workshown was convoluted with a Gaussian profile of 190 meV FWHM and a weighting of the ground and metastable states (see text for details)to simulate the measurements. Table 4 gives the designation of the resonances 7(– 9( in this photon energy region.
with previous and more recent experimental and theoreticalwork on the B-like ions; C+ [32], N2+ [49], O3+ [33] and thecurrent investigation on O3+ in the K-shell region. Results forthe cross sections and resonance parameters from the RMPSapproximation provide accurate results which are used herefor comparison purposes across all three ions. In order to havea consistent comparison with the earlier ALS experimentaldata made on B-like carbon ion, C+ [32], RMPS calculationswere performed on the C+ B-like ion using the same 390-level approximation presently used for O3+ and previouslyfor N2+ [49] ions. Resonance parameters were extracted anda consistent comparison made between the experimental andtheoretical work for all three ions of the B-like sequence, notavailable currently with other theoretical approaches.
The indirect photoionization cross section for eachresonance can be derived from the calculated oscillatorstrengths, where the integrated oscillator strengths f of thespectra, may be calculated using,
" (E ) = 2'2*a20R*
d fdE
= 1.097 618 & 10$16 d fdE
eVcm2 (7)
where * is the fine structure constant, a0 is the Bohr radius, R*is the Rydberg constant and d f /dE is the differential oscillatorstrength per unit energy [64, 70]. Rearranging and integratingwe have the expression for the oscillator strength f namely,
f = 9.11 & 10$32 E2
E1
" (E ) dE (8)
where " (E ) is the photoionization cross section in Mb(1 Mb = 1.0 & 10$18 cm2), E is the photon energy in eV,and E1 and E2 are the appropriate energy limits of the rangefor which the photoionization cross section is to be calculated.
Experimental and theoretical f -values were determinedfor the strong 1s " 2p core-excited resonances, resultingfrom 100% of the parent ion in the ground states for thefirst three members of the B-like sequence. The integratedoscillator strengths f (equation (8)) are presented in figure 4and numerical values in table 5 compared with other theoreticalmethods. We see from figure 4 and table 5 that the areaunder the peaks of the resonances for the RMPS 390-levelapproximation are in suitable agreement with the availableexperimental studies for all three ions. Similarly in figure 5,(for all three parent ions) and table 5 we present experimentaland theoretical values (determined using a variety of methods)for the resonant Auger widths ) (meV) of these same states.While there is satisfactory agreement between the R-matrixtheoretical results and experiment for the integrated oscillatorstrength f along the isoelectronic sequence (as illustratedin figure 4) from figure 5, we see differences for the O3+
parent ion between theory and experiment for the resonanceAuger widths of both the 1s2s22p2 2P and 1s2s22p2 2S core-excited states. The RMPS and saddle point calculations predicta monotonically increasing of the width for the three core-excited states, whereas in the case of the O3+ ion the presentSOLEIL experiment show strong decreasing for the both the 2Pand 2S resonance Auger states. Furthermore, from table 5 thisbehaviour is not supported by other theoretical methods for the
10
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
0 1 2 3 4Charge Q
0.00
0.05
0.10
0.15
0.20
0.25
Osc
illa
tor
Str
en
gth
, f
1s2s22p2 2P
1s2s22p2 2D
1s2s22p2 2S
1s2s22p2 2S RMPS
1s2s22p2 2D RMPS
1s2s22p2 2P RMPS
B-like
Figure 4. Oscillator strengths f for the 1s2s22p2 2P, 2D, 2S Auger states of the first three ions in the B-like sequence versus increasingcharge Q. The Auger states, 1s2s22p2 2S (green solid triangles), 1s2s22p2 2D (blue solid circles), 1s2s22p2 2P (red solid squares), are fromexperimental studies on C+[32], N2+ [49] and the present O3+ investigation. Theoretical results, R-matrix with pseudo-states (RMPS, opentriangles 1s2s22p2 2S, open squares 1s2s22p2 2P, open circles 1s2s22p2 2D), see table 5 for numerical values.
0 1 2 3 4Charge Q
0
50
100
150
200
Auger
wid
th
(m
eV
)
1s2s22p2 2P
1s2s22p2 2D
1s2s22p2 2S
1s2s22p2 2S RMPS
1s2s22p2 2D RMPS
1s2s22p2 2P RMPS
B-like
Figure 5. Autoionization resonance widths ) (meV) for the 1s2s22p22P, 2D, 2S Auger states of the first three ions in the B-like sequenceversus increasing charge Q. The Auger states, 1s2s22p2 2S (green solid triangles), 1s2s22p2 2D (blue solid circles), 1s2s22p2 2P (red solidsquares), are from experimental studies on C+[32], N2+ [49] and the present O3+ investigation. Theoretical results, R-matrix withpseudo-states (RMPS, open triangles 1s2s22p2 2S, open squares 1s2s22p2 2P, open circles 1s2s22p2 2D), see table 5 for numerical values.
same resonance widths of these Auger states, as consistencybetween the different state-of-the art theoretical approaches(where electron correlation is satisfactory included) is found.The difference between theory and experiment for thesetwo resonance is as yet unexplained so further independentinvestigations would be desirable to resolve this issue.
6. Conclusions
K-shell photoionization cross sections for B-like oxygen ions,O3+, have been determined using state-of-the-art experimentaland theoretical methods. High-resolution spectroscopy wasable to be achieved with E/!E = 5000, covering the energy
11
J. Phys. B: At. Mol. Opt. Phys. 47 (2014) 115201 B M McLaughlin et al
range 540–630 eV. Several strong resonance peaks are foundin the cross sections in the energy region 542–548 eV and593–599 eV. These resonance peaks are identified as the 1s "2p and 1s " 3p transitions in the O3+ K-shell spectrum andassigned spectroscopically with their resonance parameterstabulated in tables 2–4. For the observed resonance peaks,suitable agreement is found between the present theoreticaland experimental results both on the photon-energy scale andon the absolute cross-section scale for this prototype B-likesystem. A comparison between theory and experiment forthe integrated oscillator strengths f and Auger autoionizationwidths ), for the strong 1s " 2p resonances of the firstfew members of the B-like isoelectronic sequence highlightdifferences, particularly in the present experimental studieson the O3+ ion for the Auger widths of the 1s2s22p2 2Pand 1s2s22p2 2S core-excited states. These differences areas yet unexplained and would require further independentinvestigations.
The strength of the present study is the high resolutionof the spectra along with theoretical predictions made usingthe state-of-the-art multi-configuration Dirac–Fock, R-matrixwith pseudo-states methods and predictions from a semi-empirical approach. Cross section results from earlier R-matrixinvestigations (Garcia and co-workers [39], Pradhan and co-workers [36]) were restricted to the ground-state of this ion.The present results have been compared with high resolutionexperimental measurements made at the SOLEIL synchrotronradiation facility and with other theoretical methods so wouldbe suitable to be incorporated into astrophysical modellingcodes like CLOUDY [71, 72], XSTAR [73] and AtomDB[74] used to numerically simulate the thermal and ionizationstructure of ionized astrophysical nebulae.
Acknowledgment
The experimental measurements were performed on thePLEIADES beam line, at the SOLEIL Synchrotron radiationfacility in Saint-Aubin, France. The authors would like tothank the SOLEIL staff and, in particular C Miron the localcontact of the PLEIADES beam line during the experimentfor their helpful assistance. MFG acknowledges fundingfrom the Scientific Research Support Fund, Jordan, forsupporting a research visit to SOLEIL, under contract numberBas/2/02/2010. BMM acknowledges support from the USNational Science Foundation through a grant to ITAMP atthe Harvard-Smithsonian Center for Astrophysics, the RTRAnetwork Triangle de la Physique and a visiting researchfellowship from Queen’s University Belfast. We thank JohnC Raymond and Randall K Smith at the Harvard-SmithsonianCenter for Astrophysics for discussions on the astrophysicalapplications. The computational work was carried out at theNational Energy Research Scientific Computing Center inOakland, CA, USA, the Kraken XT5 facility at the NationalInstitute for Computational Science (NICS) in Knoxville, TN,USA and at the High Performance Computing Center Stuttgart(HLRS) of the University of Stuttgart, Stuttgart, Germany.Stefan Andersson from Cray Research is acknowledged forhis advice and assistance with the implementation of the
parallel R-matrix codes on the Cray-XE6 at HLRS. TheKraken XT5 facility is a resource of the Extreme Scienceand Engineering Discovery Environment (XSEDE), which issupported by National Science Foundation grant number OCI-1053575. This research also used resources of the Oak RidgeLeadership Computing Facility at the Oak Ridge NationalLaboratory, which is supported by the Office of Science ofthe US Department of Energy under Contract No. DE-AC05-00OR22725.
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