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Experimental (e, 2e) study of exchange interferences in the resonant Auger decay of Ar induced by electron impact
Journal of Electron Spectroscopy and Related Phenomena 189 (2013) 65–70
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Experimental (e, 2e) study of exchange interferences in the resonant Auger decay of Ar induced by electron impact Béla Paripás a,∗ , Béla Palásthy a , Matjaz Zˇ itnik b a b
Department of Physics, University of Miskolc, H-3515 Miskolc-Egyetemváros, Hungary J. Stefan Institute, Jamova 39, P.O. Box 3000, SI 1000 Ljubljana, Slovenia
a r t i c l e
a b s t r a c t
i n f o
Article history: Received 2 April 2013 Received in revised form 15 July 2013 Accepted 15 July 2013 Available online 24 July 2013 Keywords: Exchange interference Argon Constant-ionic-state (e, 2e) experiment (CIS)
Any two autoionizing resonances with a common final ionic state can be made to interfere by an appropriate selection of electron impact energy. To reveal the exchange interference effects a selective detection of electron pairs related to the selected final state is desired. We have performed a constant ionic state (e, 2e) experiment (CIS) isolating the final state by keeping the sum of transmission energies of two independent electron spectrometers constant. In the focus of this work are the exchange interference effects of 2p−1 4p and 2p−1 4p resonances in argon decaying to the 3p−2 (1 D)4p2 P, 2 D final ionic state with energy 3/2 1/2 EF = 37.3 ± 0.2 eV. We have developed a method to experimentally verify for the exchange interference effect. It is based on a comparison of the CIS spectrum recorded at the critical primary electron energy that activates the interferences, and the constructed, interference-free CIS spectrum that is build up from the CIS spectrum measured at primary electron energy away from the critical value. The results possibly indicate small exchange interference effects that may have been considerably smeared out at present experimental energy resolution. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Interference usually refers to the superposition of waves that are correlated or coherent with each other, because, for example, they originate from the same source and reach the interaction region by two different geometrical pathways. In quantum mechanics, however, the two different pathways correspond to two different indistinguishable ways of forming the same final state from a common initial quantum state. In a well-known case the F(EF ) final ionic state with energy EF is formed from the G(0) initial (ground) atomic state either directly (1a) or via an intermediate R(ER ) resonance (1b): − − − G(0) + epr (Epr ) → F(EF ) + esc (Esc ) + eej (Eej )
(1a)
− − − − (Epr ) → R(ER ) + esc (Esc ) → F(EF ) + esc (Esc ) + eej (Eej ) G(0) + epr
(1b)
− In both processes the primary electron epr is inelastically scat− − tered (esc ) and another electron (eej ) is ejected. In case (1b) of the resonant two-step pathway the energy of each electron in the final state is determined, so that two peaks appear in the single electron spectrum at Esc = Epr − ER and Eej = ER − EF . The direct process (1a)
∗ Corresponding author. Tel.: +36 46 565156. E-mail address: fi[email protected] (B. Paripás). 0368-2048/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.elspec.2013.07.005
leads to the two electrons in the final state that share the excess energy Epr − EF in a continuous manner. The asymmetric energy sharing is favoured but there are no sharp peaks in the electron spectrum. A bound-continuum quantum interference that occurs between the resonant and the direct process is a well-known Fano interference which causes an asymmetric distortion of spectral lines in the electron spectrum. In the coincidence experiments, however, both the scattered and the ejected electrons are detected. Selecting the scattered electron detection energy Esc , the energy of the ejected electron Eej = Epr − EF − Esc is determined and a peak appears at the corresponding energies (Esc , Eej ) in the coincidence spectrum. This is true for any electron energy sharing of the excess energy Epr − EF , but only at the specific energy sharing the coincidence peak of the direct process (1a) overlaps with the coincidence peak due to the resonant process (1b) so that an interference may occur. Such type of interference effects could be present in our recently published work concerning resonant Auger spectra [1] emitted upon electron impact excitation of argon. Among others the Ar 2p−1 4p resonant 3/2 Auger spectrum is reported: the measured (e, 2e) spectrum contains relatively high intensity (more than 50% of the peak signal) of the “background” signal from the direct process which results in the same final state Ar+∗ 3p−2 (1 D)4p. The contribution of the direct process was measured by a separate out-of-resonance experiment with detuned electron energy sharing that excludes the signal of the resonant process. We found that the spectrum obtained by
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taking the difference of the spectrum taken under resonant conditions and the nonresonant spectrum differs substantially from the calculated resonant Auger spectrum, mostly by emphasizing the shake-up contribution [2]. On the other hand, the agreement of the calculated spectrum without the interference effects with the corresponding experimental photoinduced resonant Auger spectra is rather good. Since in photoexcited spectra the relative amplitude of the direct process is practically negligible, the result of our electron impact experiment may be considered as an indirect proof of the interference between the one-step and the two-step process (1). There is another, bound–bound type of interference that can modify the coincidence spectrum and involves two nonoverlapping resonances R and R that are excited by an electron impact on the atomic ground state G and decay to the common final state by electron emission: − − − − G(0) + epr (Epr ) → R (ER ) + esc (Esc ) → F(EF ) + esc (Esc ) + e (Eej ) ej
(2a)
− − − − G(0) + epr (Epr ) → R (ER ) + esc (Esc ) → F(EF ) + esc (Esc ) + e (Eej ) ej
(2b) Electron pairs are observed in coincidence by two electron spectrometers, and the interference condition requires that the energy (and spin) of the scattered electron from one reaction path equals the energy (and spin) of the Auger electron released along the − − other reaction path: in such case the electron pairs (esc , e ) ej
− − and (esc , e ) are indistinguishable. The so-called interchannel ej
exchange interference therefore occurs only at unique value of electron impact energy: Epr = ER + ER − EF . The interchannel exchange interference effects were firstly observed in the non-coincidence (energy-loss) experiments in the energy region of helium autoionizing resonances [3]. Later on these effects were studied mostly by inner shell photoionization, looking at small changes of the Auger spectral line shape [4] or the angular distribution [5] when the photon impact energy was tuned across the critical photon energy. Detection of both, the photoelectron and the corresponding Auger electron in (, 2e) experiments, or the scattered and the Auger electron in (e, 2e) experiments, offers an opportunity to improve the interference contrast by restricting the detected electron angular range (Ref. [6], and refs. therein). It is clear that most suitable pairs of the inner core-hole excited states (resonances) decaying into the same final states are those that differ only by the total angular momentum of the core-hole. Auger lines are often sorted out by recognizing similar spectral patterns that are shifted in energy exactly by the spin–orbit splitting of the intermediate core-hole states [7]. For Ar the 2p−1 4p and 2p−1 4p excited 3/2 1/2 atomic states can be regarded as the R and R resonances of Eqs. (2a) and (2b). Out of the final states populated by the Auger decay the most intense are chosen for this study: Ar+∗ 3p−2 (1 D2 )4p2 P, 2 D final state doublet with EF = 37.3 ± 0.2 eV energy. The corresponding resonance energies are ER = 246.0 eV and ER = 248.2 eV [8] and the corresponding interchannel exchange interference is expected to occur at Epr = 456.9 eV involving two electrons with energies 208.7 eV and 210.9 eV in the final state. − − Ar1 S0 (0) + epr (456.9) → Ar∗ 2p−1 4p(246.0) + esc (210.9) 3/2 − − → Ar+∗ 3p−2 (1 D)4p2 P(37.3) + esc (210.9) + eAu (208.7)
To ease the understanding these energy levels and transitions are shown in a bar diagram of Fig. 1. We notice that energy of the 3p−2 (1 D)3d2 P, 2 D valence satellite states with EF = 37.3 ± 0.2 eV [9] practically coincides with energy of the selected odd parity final state 3p−2 (1 D)4p. Similar to above, the even parity doublet may be populated by the Auger decay of 2p−1 3d and 2p−1 3d resonances and, as the corresponding reso3/2 1/2 nance energies are ER = 247.0 eV and ER = 249.2 eV [8], so that the exchange interference occurs at a closely electron impact energy of 458.9 eV. Moreover, at Epr = 457.5 eV there may be interchannel exchange interference for the same even parity final state that involves neighboring 2p−1 3d and the 2p−1 4d resonances that are 3/2 3/2
separated for 0.8 eV only. Besides, for each resonance R there is the so-called intra-channel exchange interference that modifies the coincidence spectra when the scattered and emitted electron are indistinguishable (have the same energy and spin projection). Such kind of interference occurs for every final state of a given resonance at a specific critical electron impact energy Epr = 2ER − EF . The critical electron impact energies for the above mentioned resonances 2p−1 4p, 2p−1 3d, 2p−1 4d, 2p−1 3d and 2p−1 4p are 454.7 eV, 3/2 3/2 3/2 1/2 1/2 456.7 eV, 458.3 eV, 459.1 eV, and 461.1 eV, respectively. When dealing with electron impact excitation, atomic resonances with different values of the total angular momentum J may be excited, as presented in Ref. [2]. For example, in the frame of the Distorted Wave Born Approximation it was calculated that at 350 eV electron impact excitation the quasi degenerate 2p−1 4p resonan3/2 ces with J = 0, 1, 2, 3 are populated in the ratio 1:0.18:0.28:0.15 that applies approximately also for the present experimental configuration. Since an accurate theoretical description of the electron impact excitation and the following resonant Auger decay that involves several pairs of interfering resonances and a strong underlying amplitude of the direct process is much more demanding than description of the photoionization with the Auger decay, for which the relevant expressions were derived [6,10,11], it is important to approach the problem from the experimental point of view. In this paper we report the first experimental results about the exchange interference effects in the resonant Auger decay of the core-hole resonances created by an electron impact. As described below, the net effect of the exchange interference for the selected final state is accessed by comparison of the constant ionic state coincidence spectra measured at the critical electron impact energy and away from it.
(3a)
2. Measurement of the constant ionic state spectrum in electron scattering experiment
(3b)
Our experimental setup was described previously [12], so here we only give a brief description. The instrument consists of two electrostatic spectrometers, both of the so-called “box” type distorted field cylindrical mirror analysers (CMA) [13]. The Auger
− − Ar1 S0 (0) + epr (456.9) → Ar∗ 2p−1 4p(248.2) + esc (208.7) 1/2 − − (208.7) + eAu (210.9) → Ar+∗ 3p−2 (1 D)4p2 P(37.3) + esc
Fig. 1. The bar diagram of the energy levels and transitions of the considered interchannel exchange interference.
B. Paripás et al. / Journal of Electron Spectroscopy and Related Phenomena 189 (2013) 65–70
electron energy spectrum Eej was measured by a double pass cylindrical “box” type analyzer (EB ), while the scattered electrons having a given energy Esc were detected by the single pass spectrometer (EA ) (from this point rather the EB , EA symbols are used to stress the indistinguishability of scattered and ejected electrons). The gas target beam was perpendicular to the common axis of the two spectrometers and also to the projectile electron beam. A relative energy resolution measured by the full-width-at-half-maximum (FWHM) of the single and double pass spectrometers are 0.9% and 0.5%, respectively. Consequently the width of the final state “window” is about 2.1 eV. In the first experiments the two spectrometers were set to measure the coincidence rate in an energy range 205.0 eV ≤EA , EB ≤ 214.0 eV with a 0.5 eV energy step to identify the main spectral features. The electron energy scales were calibrated (and monitored) against the known energies of the Ar LMM Auger transitions. The position of the coincidence peak pertaining to the ionization of the Ar 3s electron with binding energy of 29.2 eV served to monitor the electron impact energy Epr [8]. A series of (e, 2e) spectra was recorded by scanning the transmission energy of the spectrometer B. The count rate of the spectrometer A served to monitor the stability of the electron beam and the target gas pressure. The spectra taken at different EA values were internormalized by comparison to the (e, 2e) spectrum acquired in the reversed scan mode (EA scanning, EB fixed). A full series of the acquired (e, 2e) spectra served to build the (EA , EB ) spectral plane. Such a spectral map measured at electron impact energy 457.5 eV is presented in Fig. 2a. For two identical electron spectrometers observing the same part of the solid angle, symmetric with respect to the electron beam direction, the spectral map should be symmetric with respect to the diagonal, but the instrumental effects (different spectrometer resolutions, etc.) broke this symmetry. The strongest coincidence signal found at about 205.5–206 eV is attributed to the normal Auger electrons from L2 − M23 M23 (1 D) and L3 − M23 M23 (3 P) transitions detected in coincidence with inelastically scattered electrons while the “third” slow ejected electron, that undergoes a strong post–collision interaction (PCI) with the Auger electron, remains unobserved. The signal of the direct processes is distributed along the lines perpendicular to the diagonal since at the fixed electron impact energy the sum of energies of the two (scattered and ejected) electrons must be a constant for a given final state. The energies of the 3p−2 nl excited final ionic states are in the 36–40 eV energy range and the corresponding wide stripe of electron energies would be located around the dashed line in Fig. 2 which marks the position of the above mentioned final states with 37.3 eV energy. The coincidence signal drop along this stripe shows relatively small contribution of the direct process compared to the resonant one at this primary electron energy. The localized signal “spot” at the top-right corner of the map in Fig. 2a corresponds to the 3s−1 ionic state, formed by the direct knock-out process: − − − Ar1 S0 (0) + epr (457.5) → Ar+ 3s−1 (29.2) + esc (214.0) + eej (214.3)
(4)
At a given primary energy the resonant Auger process occurs at a specific scattered electron energy where the energy loss equals the resonance energy. As the Auger electron energy is also fixed, the corresponding coincidence yield is localized on the spectral map. Fig. 2b gives the expected map positions of the coincidence signal of the two step process for a number of excited Ar 2p coreholes. For example, the dotted line in Fig. 2 denotes the region where the coincidence signal associated with the final state energy EF = Epr − EA − EB ≈ 37.3 eV is expected (the direct process), and the coincidence “spots” lying along this line at positions (208.7 eV, 210.9 eV) and (210.9 eV, 208.7 eV) correspond to the (3a), and (3b)
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Fig. 2. (a) The (EA , EB ) spectral map of the argon 2p core-hole region interpolated from the series of (e, 2e) spectra, recorded at Epr = 457.5 eV primary electron energy. The darkest coloured cell corresponds to 1700 coincidence events, and the full range is split linearly into a 16 grade grayscale. (b) Expected positions of resonant Auger (circles) and normal Auger signal (strips) at Epr = 457.3 eV. The corresponding intermediate states 2px nl are denoted by nlx and represented by the horizontal and vertical lines. The circle radius is proportional to the relative intensities of resonant Auger lines in the photoexcitation experiment [14]. The dashed line denotes the Ar+ final ionic states 3p−2 (1 D)4p2 P and 3p−2 (1 D)3d2 P, 2 D at 37.3 eV.
processes mediated by the 2p−1 4p resonances. Consequently, 3/2,1/2 the information about the selected final state is concentrated along the line perpendicular to the diagonal of the spectral map. To study the exchange interference effects for a given final state most efficiently, the diagonal scan (according to the dashed line) must be performed at selected primary energy. The coincidence yield is measured by scanning the transmission energy of both spectrometers at the same time and in the opposite directions, so as to keep EA + EB fixed. Such a measurement is called a constant ionic state (CIS) coincidence spectroscopy, in analogy with the noncoincidence photoionization studies where the detection energy of the photoelectron or the resonant Auger electron is scanned in step with the incoming photon energy. The CIS spectrum which nearly corresponds to the dashed straight line in Fig. 2 is shown in Fig. 3. An essential advantage of diagonal scan in that case is that the direct process by itself produces only a straight background and never a peak-like structure in the coincidence spectrum. The observed peak structure in Fig. 3 is therefore due to the resonant processes. It corresponds to the resonant peaks that are dominant in the spectral map of Fig. 2. As our measurement was made 0.8 eV
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Fig. 3. The result of a line scan (CIS spectrum) at 457.7 eV primary energy with Epr − EF ≈ EA + EB = 420 eV. The energy spectrum measured by the single (EA , full squares, upper energy scale) and by the double pass (EB , open circles, lower energy scale) spectrometer is shown. The random coincidences (≈ 30 %) subtracted from the coincidence signals, the error bars contain the statistical error of this background removal, too (in every figure).
above the “critical” primary electron impact energy of 456.9 eV, the peaks appear at 209.5 eV and 211.7 eV, slightly higher with respect to (3a) and (3b), and the peak structure is broadened out. As mentioned above, the asymmetry of the peak structure is caused by instrumental effects. The interchannel exchange interference involving the other intense pair of 2p3/2,1/2 3d−1 resonances and Ar +∗ 3p−2 (1 D)3d2 P, 2 D final states that are practically overlapping with Ar +∗ 3p−2 (1 D)4p2 P is expected to appear at Epr = 458.9 eV. Here the interfering processes are: − − (458.9) → Ar∗ 2p−1 3d(247.0) + esc (211.9) Ar1 S0 (0) + epr 3/2 − − → Ar+∗ 3p−2 (1 D)3d2 P(37.3) + esc (211.9) + eAu (209.7)
(5b)
− − Ar1 S0 (0) + epr (458.9) → Ar∗ 2p−1 4p(246.0) + esc (212.9) 3/2
(6a)
− − (458.9) → Ar∗ 2p−1 4p(248.2) + esc (210.7) Ar1 S0 (0) + epr 1/2 − − (210.7) + eAu (210.8). → Ar +∗ 3p−2 (1 D)4p2 P(37.3) + esc
We remark that in Fig. 4 the primary energy was 0.2 eV higher than the critical value, but that does not essentially modify the above conclusions since the uncertainty of the detected electron energy is substantially larger. On the basis of Fig. 3 and Fig. 4 it is obvious – at least for our experimental conditions – that the lines pertaining to the 2p−1 4p and 2p−1 4p excitations dominate the coincidence 3/2 1/2 line spectrum at the selected final ionic state energy, concealing much the signal of all the other transitions. Observing behaviour of these peaks for the selected final state energy with respect to the primary electron energy therefore offers a possibility to verify for the exchange interference effects. 3. Dependence of CIS spectrum on primary electron energy
The CIS spectrum measured close to the “critical” primary electron energy Epr = 458.9 eV is shown in Fig. 4. Although they may be some contribution of (5a) and (5b) in the spectrum, the peaks expected at 209.7 eV and 211.9 eV are not discernible. However, the triple peak structure at that electron impact energy may be well explained by the Auger decay of 2p−1 4p resonances: 3/2,1/2
− − → Ar+∗ 3p−2 (1 D)4p2 P(37.3) + esc (212.9) + eAu (208.7)
of the 2p−1 4p channel (the intra-channel exchange interference). 1/2
(5a)
− − (458.9) → Ar∗ 2p−1 3d(249.2) + esc (209.7) Ar1 S0 (0) + epr 1/2 − − → Ar+∗ 3p−2 (1 D)3d2 P(37.3) + esc (209.7) + eAu (211.9)
Fig. 4. The same as in Fig. 3 but measured at 459.1 eV primary energy and Epr − EF ≈ EA + EB = 421.8 eV. The expected positions of the scattered (sc) and Auger (Au) electron peaks according to Eqs. (6a) and (6b) equations are also shown on both energy scales, the corresponding intermediate states 2px nl are denoted by nlx as in Fig. 2b.
(6b)
While the 2p−1 3d mediated signal is expected to contribute the signal in the two spectral “valleys” in Fig. 4, the (6b) case contributes intensity to the middle peak in the spectrum. These three contributions may be affected by the exchange interference: the 2p−1 3d signal due to indistinguishability of the coincidence electron pairs (the interchannel exchange interference), and (6b) due to indistinguishability of two electrons within the coincidence pair
It is seen in Fig. 4 that the left coincidence peak has shifted on the energy scale of the single pass spectrometer by the difference of primary energies, i.e. by another 1.4 eV compared to Fig. 3 (from to 211.7 eV to 213.1 eV) and, at the same time the right peak remained at the same energy (208.7 eV). If the energy scale of the double pass spectrometer is considered, vice-versa is true: the left peak is fixed and the right one is moving. Whenever the coincidence peaks are well separated one can tell for a given spectrometer which one is moving and which one is still – the first situation corresponds to the click of the scattered electron and the second to the click of the resonant Auger electron. The CIS spectrum is therefore a combination of “moving” and “standing” peaks, depending on which spectrometer energy scale the spectrum is presented. The introduction of a new invariant energy scale can simplify the coincident spectra and can support their comprehension to a certain extent. The zero point of this electron energy scale for every electron impact energy is set to the cross section of the diagonal in the coincidence plane (EA = EB ) and the perpendicular diagonal scan defined by EA + EB = Epr − EF . The new energy coordinate is therefore the difference between the electron energy detected by the double pass spectrometer and (Epr − EF )/2. Meanwhile the energy of electrons detected by the single pass spectrometer according to the invariant scale is the same in magnitude but opposite in sign. The corresponding scattered and Auger electron peaks are therefore situated symmetrically with respect to the new zero energy point. Changing the primary electron energy all the peaks will move on the invariant energy scale as shown in Fig. 5.
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Fig. 5. The two CIS spectra (EF ≈ 37.3 eV) that are shown in Figs. 3 and 4 but the invariant energy scale is applied (see in the text). The notations of peaks correspond to the double spectrometer.
By further increasing the primary energy we can achieve that the scattered and resonant Auger electron peaks – overlapping in the critical primary energy region – are completely separated. The CIS spectrum of the final state with energy 37.3 eV as measured at 465.7 eV primary energy is shown in Fig. 6. At this primary energy the coincidence peaks originating from the 2p−1 4p and 2p−1 4p 1/2 3/2 resonances are shifted to 217.5 eV and 219.7 eV energy of the scattered electron, corresponding to 3.3 eV and 5.5 eV on the new energy scale. The corresponding resonant Auger lines at 208.7 eV and 210.9 eV appear at −3.3 eV and −5.5 eV on the new energy scale (for the electrons detected by the single pass spectrometer the sign of energies are exchanged). The peaks are separated by 2.2 eV (spin–orbit splitting of 2p3/2,1/2 core-hole) and the intensity ratio is not far from 2:1 as expected from the statistics. This also supports an assumption that the final state “window” at 37.3 eV is filled in mostly from 2p−1 4p resonances. 3/2,1/2 In the middle of the spectrum – at zero invariant electron energy – where there is no signal above the background, corresponding to the direct processes, the spectrum can be cut in half. The
Fig. 6. CIS spectra (EF ≈ 37.3 eV) when the scattered and resonant Auger peaks are completely separated, measured at 465.7 eV (empty squares), 464.3 eV (full circles), and 462.9 eV (full squares) primary energies. The notation of spectrum components and electron peaks as in Fig. 5.
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Fig. 7. CIS spectrum measured at 459.1 eV primary energy as in Fig. 4 (full squares) compared to the constructed spectrum (open squares). The notation of electron peaks according to Eqs. (6a) and (6b) as in Fig. 4.
negative energy half corresponds to the Auger electron detected by the double pass spectrometer in coincidence with the scattered electron detected by the single pass spectrometer. For the positive half, however, the role of the two spectrometers is exchanged. 4. Experimental testing of the exchange interference effects Decreasing the primary electron energy from 465.7 eV the two “half-spectra” are effectively shifted on top of each other and the intensities overlapped. Without the exchange interference effects the recombination amounts to a simple summation. The spectra in Fig. 6 can be thus employed to construct the interference-free spectra for the same final state at different primary electron energies by shifting the two “half-spectra” and performing the summation. For example, to obtain the interference-free spectral shape at Epr = 459.1 eV (Fig. 4) the two “half-spectra” have to be shifted for 6.6 eV towards one another and summed up. The energy shift can cause a systematic error due to the energy dependence of transmission functions of spectrometers. This is taken into account by an additional 5% signal error in the constructed spectrum. If the constructed spectrum does not significantly differs from the measured one, the net exchange interference effects must be small. The comparison in Fig. 7 does indeed support this idea: the match of the two spectra is rather good suggesting that interference effects in the spectrum are small. Although the statistics is rather low, we can state with more than 90% probability that there are only random differences between the constructed and directly measured spectrum. To decrease the statistical error all the “separated” spectra given in Fig. 6 were used in the construction procedure. We note that Fano type interference between the direct and the resonant process are present also in the separated spectra and that interference-free term implies the absence of interference within the same or between several different resonant paths. Further on we have measured CIS spectrum at the “critical” primary energy Epr = 456.9 eV for reaction (1) and compared it with the constructed spectrum. From the result in Fig. 8 one can see that the two spectra have quite similar shape, meaning that the interference effects are not very significant. In this case the statistical analysis gives more than 80% probability that the differences between the two spectra are just random. We cannot claim the existence of interference effect although the statistics of the measurement is doubled in comparison with Fig. 7. The differences
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Fig. 8. CIS spectrum measured at the critical primary energy Epr = 456.9 eV (full squares) compared to the constructed spectrum (open squares). The electron peaks are according to Eqs. (3a) and (3b), their notations are as in Fig. 4.
between the two spectra, however, are a bit larger and more systematic than in Fig. 7. The right peak of the measured spectrum is lower compared to the constructed one, the missing intensity partly moved into the “valley” between the two peaks. For that part of the spectrum (from −0.3 to 1.5 eV) the difference of the two spectra is locally significant, since the probability that these differences are just random is less than 30%. The flatter “valley” can hint a weak inter-channel exchange interference of the processes leading to the Ar +∗ 3p−2 (1 D2 )4p(2 P, 2 D) final state. In any case, if they exist, the interference effects are weak. One of the main reasons could be that due to the relatively large electron energy detection uncertainty with respect to the 2p core-hole natural line width (120 meV) the interferences are pretty much averaged out in this difficult experiment [6,10,11]. Because of these reasons the energy resolution should be increased in the future experiments. 5. Conclusions In this work we made an effort to experimentally address a possible existence of exchange interference effects due to different paths in electron impact induced resonant Auger decay of argon leading to the same final ionic state. We found that in the coincidence spectral map of the excited 2p core-hole states recorded at the primary electron energy in the so-called “critical” energy region (the scattered electron energy approximately equals the 4p resonances decaying into Auger electron energy) the 2p−1 3/2,1/2
3p−2 (1 D)4p2 P, 2 D final state with 37.3 eV energy give rise to the dominant spectral features in the resonant Auger spectra. Our experimental approach to check for the possible exchange interference effects in this specific case is based on a comparison of CIS spectra for the selected final state recorded in the coincidence mode by scanning simultaneously the transmission energy of each spectrometer in the opposite direction so as to keep the sum of transmission energies constant. The experimental verification of the interference is based on the idea that at increased (decreased) primary energy the coincidence electron peaks – which are
overlapping at the “critical” primary energy – are completely separated and the type of each of the detected particles by any of two spectrometers is unambiguous (scattered or Auger electron). The slip of the separated “half-spectra” towards each other in accordance with the primary energy difference results in the interference-free spectrum at the “critical” electron impact energy. The comparison of the constructed CIS spectrum with the CIS spectrum measured at the critical energy informs us about the relative strength of the exchange interference effects. According to our results the method of shifting both halves of the separated spectrum towards each other works reasonably well, and the interference-free spectra in the overlap region can be constructed relatively easy. Although we found a small systematic difference between the measured and the constructed spectra at the critical energy, the difference is still not significant enough to state unambiguously the existence of strong interference effects. This is in agreement with conclusions of the recent photoionization study dealing with Kr 3d5/2,3/2 and Xe 4d5/2,5/2 [6] according to which the effects of the exchange interference are substantially reduced by angular integration and when the experimental energy resolution largely surpasses the natural line width of the intermediate states. The same method applied with one order tighter experimental energy resolution might reveal larger contrast between the two data sets but the realisation would require to substantially improve the efficiency of the present (e, 2e) experiment. Additional complication arises from the fact that there are several different pairs of core-hole states excited that have different total angular momenta J and interfere independently. To address in details the problem of exchange interferences in the Ar 2p core-hole region the experimental control over the energy conservation in the electron impact induced resonant Auger decay should be very tight – a few tens of meV which is of the order of the multiplet splitting [2]. Acknowledgments This research was (partially) carried out in the framework of the Center of Excellence of Mechatronics and Logistics at the University of Miskolc. References ˝ [1] B. Paripás, B. Palásthy, M. Zˇ itnik, K. Tokési, Nucl. Instrm. Meth. Res. B 279 (2012) 66–72. ˇ ˇ [2] B. Paripás, B. Palásthy, M. Stuhec, M. Zitnik, Phys. Rev. A 82 (2010) 0325081–032508-1066. [3] J.P.V. den Brink, G. Nienhuis, J. van Eck, H.M. Heideman, J. Phys. B 22 (1989) 3501. [4] J.A. de Gouw, J. van Eck, A.C. Peters, J. van der Weg, H.G.M. Heideman, Phys. Rev. Lett. 71 (1993) 2875. [5] S. Fritzsche, J. Nikkinen, S.-M. Huttula, H. Aksela, M. Huttula, S. Aksela, Phys. Rev. A 75 (2007) 012501. [6] M. Zˇ itnik, K. Buˇcar, A. Miheliˇc, P. Lablanquie, F. Penent, J. Paladoux, L. Andriˇc, P. Bolognesi, L. Avaldi, Phys. Rev. A 87 (2013) 013436. [7] L.O. Werme, T. Bergmark, K. Siegbahn, Phys. Scr. 6 (1972) 141. [8] G.C. King, M. Tronc, F.H. Read, R. Bradford, J. Phys. B 10 (1977) 2479. [9] R. Camilloni, M. Zˇ itnik, C. Comicioli, K.C. Prince, M. Zacchigna, C. Crotti, C. Ottaviani, C. Quaresima, P. Perfetti, G. Stefani, Phys. Rev. Lett. 77 (1996) 2646. [10] L. Végh, J.H. Macek, Phys. Rev. A 50 (1994) 4031. [11] L. Végh, Phys. Rev. A 50 (1994) 4036. [12] B. Paripás, B. Palásthy, Radiat. Phys. Chem. 76 (2007) 565–569. ˝ [13] A. Kövér, D. Varga, I. Csernyi, E. Szmola, G. Mórik, L. Gulyás, K. Tokési, Nucl. Instrm. Meth. Res. A 373 (1996) 51. [14] J.A. de Gouw, J. van Eck, A.C. Peters, J. van der Weg, H.G.M. Heideman, J. Phys. B 28 (1995) 2127.
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Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Experimental (e, 2e) study of exchange interferences in the resonant Auger decay of Ar induced by electron impact Béla Paripás a,∗ , Béla Palásthy a , Matjaz Zˇ itnik b a b
Department of Physics, University of Miskolc, H-3515 Miskolc-Egyetemváros, Hungary J. Stefan Institute, Jamova 39, P.O. Box 3000, SI 1000 Ljubljana, Slovenia
a r t i c l e
a b s t r a c t
i n f o
Article history: Received 2 April 2013 Received in revised form 15 July 2013 Accepted 15 July 2013 Available online 24 July 2013 Keywords: Exchange interference Argon Constant-ionic-state (e, 2e) experiment (CIS)
Any two autoionizing resonances with a common final ionic state can be made to interfere by an appropriate selection of electron impact energy. To reveal the exchange interference effects a selective detection of electron pairs related to the selected final state is desired. We have performed a constant ionic state (e, 2e) experiment (CIS) isolating the final state by keeping the sum of transmission energies of two independent electron spectrometers constant. In the focus of this work are the exchange interference effects of 2p−1 4p and 2p−1 4p resonances in argon decaying to the 3p−2 (1 D)4p2 P, 2 D final ionic state with energy 3/2 1/2 EF = 37.3 ± 0.2 eV. We have developed a method to experimentally verify for the exchange interference effect. It is based on a comparison of the CIS spectrum recorded at the critical primary electron energy that activates the interferences, and the constructed, interference-free CIS spectrum that is build up from the CIS spectrum measured at primary electron energy away from the critical value. The results possibly indicate small exchange interference effects that may have been considerably smeared out at present experimental energy resolution. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Interference usually refers to the superposition of waves that are correlated or coherent with each other, because, for example, they originate from the same source and reach the interaction region by two different geometrical pathways. In quantum mechanics, however, the two different pathways correspond to two different indistinguishable ways of forming the same final state from a common initial quantum state. In a well-known case the F(EF ) final ionic state with energy EF is formed from the G(0) initial (ground) atomic state either directly (1a) or via an intermediate R(ER ) resonance (1b): − − − G(0) + epr (Epr ) → F(EF ) + esc (Esc ) + eej (Eej )
(1a)
− − − − (Epr ) → R(ER ) + esc (Esc ) → F(EF ) + esc (Esc ) + eej (Eej ) G(0) + epr
(1b)
− In both processes the primary electron epr is inelastically scat− − tered (esc ) and another electron (eej ) is ejected. In case (1b) of the resonant two-step pathway the energy of each electron in the final state is determined, so that two peaks appear in the single electron spectrum at Esc = Epr − ER and Eej = ER − EF . The direct process (1a)
∗ Corresponding author. Tel.: +36 46 565156. E-mail address: fi[email protected] (B. Paripás). 0368-2048/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.elspec.2013.07.005
leads to the two electrons in the final state that share the excess energy Epr − EF in a continuous manner. The asymmetric energy sharing is favoured but there are no sharp peaks in the electron spectrum. A bound-continuum quantum interference that occurs between the resonant and the direct process is a well-known Fano interference which causes an asymmetric distortion of spectral lines in the electron spectrum. In the coincidence experiments, however, both the scattered and the ejected electrons are detected. Selecting the scattered electron detection energy Esc , the energy of the ejected electron Eej = Epr − EF − Esc is determined and a peak appears at the corresponding energies (Esc , Eej ) in the coincidence spectrum. This is true for any electron energy sharing of the excess energy Epr − EF , but only at the specific energy sharing the coincidence peak of the direct process (1a) overlaps with the coincidence peak due to the resonant process (1b) so that an interference may occur. Such type of interference effects could be present in our recently published work concerning resonant Auger spectra [1] emitted upon electron impact excitation of argon. Among others the Ar 2p−1 4p resonant 3/2 Auger spectrum is reported: the measured (e, 2e) spectrum contains relatively high intensity (more than 50% of the peak signal) of the “background” signal from the direct process which results in the same final state Ar+∗ 3p−2 (1 D)4p. The contribution of the direct process was measured by a separate out-of-resonance experiment with detuned electron energy sharing that excludes the signal of the resonant process. We found that the spectrum obtained by
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taking the difference of the spectrum taken under resonant conditions and the nonresonant spectrum differs substantially from the calculated resonant Auger spectrum, mostly by emphasizing the shake-up contribution [2]. On the other hand, the agreement of the calculated spectrum without the interference effects with the corresponding experimental photoinduced resonant Auger spectra is rather good. Since in photoexcited spectra the relative amplitude of the direct process is practically negligible, the result of our electron impact experiment may be considered as an indirect proof of the interference between the one-step and the two-step process (1). There is another, bound–bound type of interference that can modify the coincidence spectrum and involves two nonoverlapping resonances R and R that are excited by an electron impact on the atomic ground state G and decay to the common final state by electron emission: − − − − G(0) + epr (Epr ) → R (ER ) + esc (Esc ) → F(EF ) + esc (Esc ) + e (Eej ) ej
(2a)
− − − − G(0) + epr (Epr ) → R (ER ) + esc (Esc ) → F(EF ) + esc (Esc ) + e (Eej ) ej
(2b) Electron pairs are observed in coincidence by two electron spectrometers, and the interference condition requires that the energy (and spin) of the scattered electron from one reaction path equals the energy (and spin) of the Auger electron released along the − − other reaction path: in such case the electron pairs (esc , e ) ej
− − and (esc , e ) are indistinguishable. The so-called interchannel ej
exchange interference therefore occurs only at unique value of electron impact energy: Epr = ER + ER − EF . The interchannel exchange interference effects were firstly observed in the non-coincidence (energy-loss) experiments in the energy region of helium autoionizing resonances [3]. Later on these effects were studied mostly by inner shell photoionization, looking at small changes of the Auger spectral line shape [4] or the angular distribution [5] when the photon impact energy was tuned across the critical photon energy. Detection of both, the photoelectron and the corresponding Auger electron in (, 2e) experiments, or the scattered and the Auger electron in (e, 2e) experiments, offers an opportunity to improve the interference contrast by restricting the detected electron angular range (Ref. [6], and refs. therein). It is clear that most suitable pairs of the inner core-hole excited states (resonances) decaying into the same final states are those that differ only by the total angular momentum of the core-hole. Auger lines are often sorted out by recognizing similar spectral patterns that are shifted in energy exactly by the spin–orbit splitting of the intermediate core-hole states [7]. For Ar the 2p−1 4p and 2p−1 4p excited 3/2 1/2 atomic states can be regarded as the R and R resonances of Eqs. (2a) and (2b). Out of the final states populated by the Auger decay the most intense are chosen for this study: Ar+∗ 3p−2 (1 D2 )4p2 P, 2 D final state doublet with EF = 37.3 ± 0.2 eV energy. The corresponding resonance energies are ER = 246.0 eV and ER = 248.2 eV [8] and the corresponding interchannel exchange interference is expected to occur at Epr = 456.9 eV involving two electrons with energies 208.7 eV and 210.9 eV in the final state. − − Ar1 S0 (0) + epr (456.9) → Ar∗ 2p−1 4p(246.0) + esc (210.9) 3/2 − − → Ar+∗ 3p−2 (1 D)4p2 P(37.3) + esc (210.9) + eAu (208.7)
To ease the understanding these energy levels and transitions are shown in a bar diagram of Fig. 1. We notice that energy of the 3p−2 (1 D)3d2 P, 2 D valence satellite states with EF = 37.3 ± 0.2 eV [9] practically coincides with energy of the selected odd parity final state 3p−2 (1 D)4p. Similar to above, the even parity doublet may be populated by the Auger decay of 2p−1 3d and 2p−1 3d resonances and, as the corresponding reso3/2 1/2 nance energies are ER = 247.0 eV and ER = 249.2 eV [8], so that the exchange interference occurs at a closely electron impact energy of 458.9 eV. Moreover, at Epr = 457.5 eV there may be interchannel exchange interference for the same even parity final state that involves neighboring 2p−1 3d and the 2p−1 4d resonances that are 3/2 3/2
separated for 0.8 eV only. Besides, for each resonance R there is the so-called intra-channel exchange interference that modifies the coincidence spectra when the scattered and emitted electron are indistinguishable (have the same energy and spin projection). Such kind of interference occurs for every final state of a given resonance at a specific critical electron impact energy Epr = 2ER − EF . The critical electron impact energies for the above mentioned resonances 2p−1 4p, 2p−1 3d, 2p−1 4d, 2p−1 3d and 2p−1 4p are 454.7 eV, 3/2 3/2 3/2 1/2 1/2 456.7 eV, 458.3 eV, 459.1 eV, and 461.1 eV, respectively. When dealing with electron impact excitation, atomic resonances with different values of the total angular momentum J may be excited, as presented in Ref. [2]. For example, in the frame of the Distorted Wave Born Approximation it was calculated that at 350 eV electron impact excitation the quasi degenerate 2p−1 4p resonan3/2 ces with J = 0, 1, 2, 3 are populated in the ratio 1:0.18:0.28:0.15 that applies approximately also for the present experimental configuration. Since an accurate theoretical description of the electron impact excitation and the following resonant Auger decay that involves several pairs of interfering resonances and a strong underlying amplitude of the direct process is much more demanding than description of the photoionization with the Auger decay, for which the relevant expressions were derived [6,10,11], it is important to approach the problem from the experimental point of view. In this paper we report the first experimental results about the exchange interference effects in the resonant Auger decay of the core-hole resonances created by an electron impact. As described below, the net effect of the exchange interference for the selected final state is accessed by comparison of the constant ionic state coincidence spectra measured at the critical electron impact energy and away from it.
(3a)
2. Measurement of the constant ionic state spectrum in electron scattering experiment
(3b)
Our experimental setup was described previously [12], so here we only give a brief description. The instrument consists of two electrostatic spectrometers, both of the so-called “box” type distorted field cylindrical mirror analysers (CMA) [13]. The Auger
− − Ar1 S0 (0) + epr (456.9) → Ar∗ 2p−1 4p(248.2) + esc (208.7) 1/2 − − (208.7) + eAu (210.9) → Ar+∗ 3p−2 (1 D)4p2 P(37.3) + esc
Fig. 1. The bar diagram of the energy levels and transitions of the considered interchannel exchange interference.
B. Paripás et al. / Journal of Electron Spectroscopy and Related Phenomena 189 (2013) 65–70
electron energy spectrum Eej was measured by a double pass cylindrical “box” type analyzer (EB ), while the scattered electrons having a given energy Esc were detected by the single pass spectrometer (EA ) (from this point rather the EB , EA symbols are used to stress the indistinguishability of scattered and ejected electrons). The gas target beam was perpendicular to the common axis of the two spectrometers and also to the projectile electron beam. A relative energy resolution measured by the full-width-at-half-maximum (FWHM) of the single and double pass spectrometers are 0.9% and 0.5%, respectively. Consequently the width of the final state “window” is about 2.1 eV. In the first experiments the two spectrometers were set to measure the coincidence rate in an energy range 205.0 eV ≤EA , EB ≤ 214.0 eV with a 0.5 eV energy step to identify the main spectral features. The electron energy scales were calibrated (and monitored) against the known energies of the Ar LMM Auger transitions. The position of the coincidence peak pertaining to the ionization of the Ar 3s electron with binding energy of 29.2 eV served to monitor the electron impact energy Epr [8]. A series of (e, 2e) spectra was recorded by scanning the transmission energy of the spectrometer B. The count rate of the spectrometer A served to monitor the stability of the electron beam and the target gas pressure. The spectra taken at different EA values were internormalized by comparison to the (e, 2e) spectrum acquired in the reversed scan mode (EA scanning, EB fixed). A full series of the acquired (e, 2e) spectra served to build the (EA , EB ) spectral plane. Such a spectral map measured at electron impact energy 457.5 eV is presented in Fig. 2a. For two identical electron spectrometers observing the same part of the solid angle, symmetric with respect to the electron beam direction, the spectral map should be symmetric with respect to the diagonal, but the instrumental effects (different spectrometer resolutions, etc.) broke this symmetry. The strongest coincidence signal found at about 205.5–206 eV is attributed to the normal Auger electrons from L2 − M23 M23 (1 D) and L3 − M23 M23 (3 P) transitions detected in coincidence with inelastically scattered electrons while the “third” slow ejected electron, that undergoes a strong post–collision interaction (PCI) with the Auger electron, remains unobserved. The signal of the direct processes is distributed along the lines perpendicular to the diagonal since at the fixed electron impact energy the sum of energies of the two (scattered and ejected) electrons must be a constant for a given final state. The energies of the 3p−2 nl excited final ionic states are in the 36–40 eV energy range and the corresponding wide stripe of electron energies would be located around the dashed line in Fig. 2 which marks the position of the above mentioned final states with 37.3 eV energy. The coincidence signal drop along this stripe shows relatively small contribution of the direct process compared to the resonant one at this primary electron energy. The localized signal “spot” at the top-right corner of the map in Fig. 2a corresponds to the 3s−1 ionic state, formed by the direct knock-out process: − − − Ar1 S0 (0) + epr (457.5) → Ar+ 3s−1 (29.2) + esc (214.0) + eej (214.3)
(4)
At a given primary energy the resonant Auger process occurs at a specific scattered electron energy where the energy loss equals the resonance energy. As the Auger electron energy is also fixed, the corresponding coincidence yield is localized on the spectral map. Fig. 2b gives the expected map positions of the coincidence signal of the two step process for a number of excited Ar 2p coreholes. For example, the dotted line in Fig. 2 denotes the region where the coincidence signal associated with the final state energy EF = Epr − EA − EB ≈ 37.3 eV is expected (the direct process), and the coincidence “spots” lying along this line at positions (208.7 eV, 210.9 eV) and (210.9 eV, 208.7 eV) correspond to the (3a), and (3b)
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Fig. 2. (a) The (EA , EB ) spectral map of the argon 2p core-hole region interpolated from the series of (e, 2e) spectra, recorded at Epr = 457.5 eV primary electron energy. The darkest coloured cell corresponds to 1700 coincidence events, and the full range is split linearly into a 16 grade grayscale. (b) Expected positions of resonant Auger (circles) and normal Auger signal (strips) at Epr = 457.3 eV. The corresponding intermediate states 2px nl are denoted by nlx and represented by the horizontal and vertical lines. The circle radius is proportional to the relative intensities of resonant Auger lines in the photoexcitation experiment [14]. The dashed line denotes the Ar+ final ionic states 3p−2 (1 D)4p2 P and 3p−2 (1 D)3d2 P, 2 D at 37.3 eV.
processes mediated by the 2p−1 4p resonances. Consequently, 3/2,1/2 the information about the selected final state is concentrated along the line perpendicular to the diagonal of the spectral map. To study the exchange interference effects for a given final state most efficiently, the diagonal scan (according to the dashed line) must be performed at selected primary energy. The coincidence yield is measured by scanning the transmission energy of both spectrometers at the same time and in the opposite directions, so as to keep EA + EB fixed. Such a measurement is called a constant ionic state (CIS) coincidence spectroscopy, in analogy with the noncoincidence photoionization studies where the detection energy of the photoelectron or the resonant Auger electron is scanned in step with the incoming photon energy. The CIS spectrum which nearly corresponds to the dashed straight line in Fig. 2 is shown in Fig. 3. An essential advantage of diagonal scan in that case is that the direct process by itself produces only a straight background and never a peak-like structure in the coincidence spectrum. The observed peak structure in Fig. 3 is therefore due to the resonant processes. It corresponds to the resonant peaks that are dominant in the spectral map of Fig. 2. As our measurement was made 0.8 eV
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Fig. 3. The result of a line scan (CIS spectrum) at 457.7 eV primary energy with Epr − EF ≈ EA + EB = 420 eV. The energy spectrum measured by the single (EA , full squares, upper energy scale) and by the double pass (EB , open circles, lower energy scale) spectrometer is shown. The random coincidences (≈ 30 %) subtracted from the coincidence signals, the error bars contain the statistical error of this background removal, too (in every figure).
above the “critical” primary electron impact energy of 456.9 eV, the peaks appear at 209.5 eV and 211.7 eV, slightly higher with respect to (3a) and (3b), and the peak structure is broadened out. As mentioned above, the asymmetry of the peak structure is caused by instrumental effects. The interchannel exchange interference involving the other intense pair of 2p3/2,1/2 3d−1 resonances and Ar +∗ 3p−2 (1 D)3d2 P, 2 D final states that are practically overlapping with Ar +∗ 3p−2 (1 D)4p2 P is expected to appear at Epr = 458.9 eV. Here the interfering processes are: − − (458.9) → Ar∗ 2p−1 3d(247.0) + esc (211.9) Ar1 S0 (0) + epr 3/2 − − → Ar+∗ 3p−2 (1 D)3d2 P(37.3) + esc (211.9) + eAu (209.7)
(5b)
− − Ar1 S0 (0) + epr (458.9) → Ar∗ 2p−1 4p(246.0) + esc (212.9) 3/2
(6a)
− − (458.9) → Ar∗ 2p−1 4p(248.2) + esc (210.7) Ar1 S0 (0) + epr 1/2 − − (210.7) + eAu (210.8). → Ar +∗ 3p−2 (1 D)4p2 P(37.3) + esc
We remark that in Fig. 4 the primary energy was 0.2 eV higher than the critical value, but that does not essentially modify the above conclusions since the uncertainty of the detected electron energy is substantially larger. On the basis of Fig. 3 and Fig. 4 it is obvious – at least for our experimental conditions – that the lines pertaining to the 2p−1 4p and 2p−1 4p excitations dominate the coincidence 3/2 1/2 line spectrum at the selected final ionic state energy, concealing much the signal of all the other transitions. Observing behaviour of these peaks for the selected final state energy with respect to the primary electron energy therefore offers a possibility to verify for the exchange interference effects. 3. Dependence of CIS spectrum on primary electron energy
The CIS spectrum measured close to the “critical” primary electron energy Epr = 458.9 eV is shown in Fig. 4. Although they may be some contribution of (5a) and (5b) in the spectrum, the peaks expected at 209.7 eV and 211.9 eV are not discernible. However, the triple peak structure at that electron impact energy may be well explained by the Auger decay of 2p−1 4p resonances: 3/2,1/2
− − → Ar+∗ 3p−2 (1 D)4p2 P(37.3) + esc (212.9) + eAu (208.7)
of the 2p−1 4p channel (the intra-channel exchange interference). 1/2
(5a)
− − (458.9) → Ar∗ 2p−1 3d(249.2) + esc (209.7) Ar1 S0 (0) + epr 1/2 − − → Ar+∗ 3p−2 (1 D)3d2 P(37.3) + esc (209.7) + eAu (211.9)
Fig. 4. The same as in Fig. 3 but measured at 459.1 eV primary energy and Epr − EF ≈ EA + EB = 421.8 eV. The expected positions of the scattered (sc) and Auger (Au) electron peaks according to Eqs. (6a) and (6b) equations are also shown on both energy scales, the corresponding intermediate states 2px nl are denoted by nlx as in Fig. 2b.
(6b)
While the 2p−1 3d mediated signal is expected to contribute the signal in the two spectral “valleys” in Fig. 4, the (6b) case contributes intensity to the middle peak in the spectrum. These three contributions may be affected by the exchange interference: the 2p−1 3d signal due to indistinguishability of the coincidence electron pairs (the interchannel exchange interference), and (6b) due to indistinguishability of two electrons within the coincidence pair
It is seen in Fig. 4 that the left coincidence peak has shifted on the energy scale of the single pass spectrometer by the difference of primary energies, i.e. by another 1.4 eV compared to Fig. 3 (from to 211.7 eV to 213.1 eV) and, at the same time the right peak remained at the same energy (208.7 eV). If the energy scale of the double pass spectrometer is considered, vice-versa is true: the left peak is fixed and the right one is moving. Whenever the coincidence peaks are well separated one can tell for a given spectrometer which one is moving and which one is still – the first situation corresponds to the click of the scattered electron and the second to the click of the resonant Auger electron. The CIS spectrum is therefore a combination of “moving” and “standing” peaks, depending on which spectrometer energy scale the spectrum is presented. The introduction of a new invariant energy scale can simplify the coincident spectra and can support their comprehension to a certain extent. The zero point of this electron energy scale for every electron impact energy is set to the cross section of the diagonal in the coincidence plane (EA = EB ) and the perpendicular diagonal scan defined by EA + EB = Epr − EF . The new energy coordinate is therefore the difference between the electron energy detected by the double pass spectrometer and (Epr − EF )/2. Meanwhile the energy of electrons detected by the single pass spectrometer according to the invariant scale is the same in magnitude but opposite in sign. The corresponding scattered and Auger electron peaks are therefore situated symmetrically with respect to the new zero energy point. Changing the primary electron energy all the peaks will move on the invariant energy scale as shown in Fig. 5.
B. Paripás et al. / Journal of Electron Spectroscopy and Related Phenomena 189 (2013) 65–70
Fig. 5. The two CIS spectra (EF ≈ 37.3 eV) that are shown in Figs. 3 and 4 but the invariant energy scale is applied (see in the text). The notations of peaks correspond to the double spectrometer.
By further increasing the primary energy we can achieve that the scattered and resonant Auger electron peaks – overlapping in the critical primary energy region – are completely separated. The CIS spectrum of the final state with energy 37.3 eV as measured at 465.7 eV primary energy is shown in Fig. 6. At this primary energy the coincidence peaks originating from the 2p−1 4p and 2p−1 4p 1/2 3/2 resonances are shifted to 217.5 eV and 219.7 eV energy of the scattered electron, corresponding to 3.3 eV and 5.5 eV on the new energy scale. The corresponding resonant Auger lines at 208.7 eV and 210.9 eV appear at −3.3 eV and −5.5 eV on the new energy scale (for the electrons detected by the single pass spectrometer the sign of energies are exchanged). The peaks are separated by 2.2 eV (spin–orbit splitting of 2p3/2,1/2 core-hole) and the intensity ratio is not far from 2:1 as expected from the statistics. This also supports an assumption that the final state “window” at 37.3 eV is filled in mostly from 2p−1 4p resonances. 3/2,1/2 In the middle of the spectrum – at zero invariant electron energy – where there is no signal above the background, corresponding to the direct processes, the spectrum can be cut in half. The
Fig. 6. CIS spectra (EF ≈ 37.3 eV) when the scattered and resonant Auger peaks are completely separated, measured at 465.7 eV (empty squares), 464.3 eV (full circles), and 462.9 eV (full squares) primary energies. The notation of spectrum components and electron peaks as in Fig. 5.
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Fig. 7. CIS spectrum measured at 459.1 eV primary energy as in Fig. 4 (full squares) compared to the constructed spectrum (open squares). The notation of electron peaks according to Eqs. (6a) and (6b) as in Fig. 4.
negative energy half corresponds to the Auger electron detected by the double pass spectrometer in coincidence with the scattered electron detected by the single pass spectrometer. For the positive half, however, the role of the two spectrometers is exchanged. 4. Experimental testing of the exchange interference effects Decreasing the primary electron energy from 465.7 eV the two “half-spectra” are effectively shifted on top of each other and the intensities overlapped. Without the exchange interference effects the recombination amounts to a simple summation. The spectra in Fig. 6 can be thus employed to construct the interference-free spectra for the same final state at different primary electron energies by shifting the two “half-spectra” and performing the summation. For example, to obtain the interference-free spectral shape at Epr = 459.1 eV (Fig. 4) the two “half-spectra” have to be shifted for 6.6 eV towards one another and summed up. The energy shift can cause a systematic error due to the energy dependence of transmission functions of spectrometers. This is taken into account by an additional 5% signal error in the constructed spectrum. If the constructed spectrum does not significantly differs from the measured one, the net exchange interference effects must be small. The comparison in Fig. 7 does indeed support this idea: the match of the two spectra is rather good suggesting that interference effects in the spectrum are small. Although the statistics is rather low, we can state with more than 90% probability that there are only random differences between the constructed and directly measured spectrum. To decrease the statistical error all the “separated” spectra given in Fig. 6 were used in the construction procedure. We note that Fano type interference between the direct and the resonant process are present also in the separated spectra and that interference-free term implies the absence of interference within the same or between several different resonant paths. Further on we have measured CIS spectrum at the “critical” primary energy Epr = 456.9 eV for reaction (1) and compared it with the constructed spectrum. From the result in Fig. 8 one can see that the two spectra have quite similar shape, meaning that the interference effects are not very significant. In this case the statistical analysis gives more than 80% probability that the differences between the two spectra are just random. We cannot claim the existence of interference effect although the statistics of the measurement is doubled in comparison with Fig. 7. The differences
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Fig. 8. CIS spectrum measured at the critical primary energy Epr = 456.9 eV (full squares) compared to the constructed spectrum (open squares). The electron peaks are according to Eqs. (3a) and (3b), their notations are as in Fig. 4.
between the two spectra, however, are a bit larger and more systematic than in Fig. 7. The right peak of the measured spectrum is lower compared to the constructed one, the missing intensity partly moved into the “valley” between the two peaks. For that part of the spectrum (from −0.3 to 1.5 eV) the difference of the two spectra is locally significant, since the probability that these differences are just random is less than 30%. The flatter “valley” can hint a weak inter-channel exchange interference of the processes leading to the Ar +∗ 3p−2 (1 D2 )4p(2 P, 2 D) final state. In any case, if they exist, the interference effects are weak. One of the main reasons could be that due to the relatively large electron energy detection uncertainty with respect to the 2p core-hole natural line width (120 meV) the interferences are pretty much averaged out in this difficult experiment [6,10,11]. Because of these reasons the energy resolution should be increased in the future experiments. 5. Conclusions In this work we made an effort to experimentally address a possible existence of exchange interference effects due to different paths in electron impact induced resonant Auger decay of argon leading to the same final ionic state. We found that in the coincidence spectral map of the excited 2p core-hole states recorded at the primary electron energy in the so-called “critical” energy region (the scattered electron energy approximately equals the 4p resonances decaying into Auger electron energy) the 2p−1 3/2,1/2
3p−2 (1 D)4p2 P, 2 D final state with 37.3 eV energy give rise to the dominant spectral features in the resonant Auger spectra. Our experimental approach to check for the possible exchange interference effects in this specific case is based on a comparison of CIS spectra for the selected final state recorded in the coincidence mode by scanning simultaneously the transmission energy of each spectrometer in the opposite direction so as to keep the sum of transmission energies constant. The experimental verification of the interference is based on the idea that at increased (decreased) primary energy the coincidence electron peaks – which are
overlapping at the “critical” primary energy – are completely separated and the type of each of the detected particles by any of two spectrometers is unambiguous (scattered or Auger electron). The slip of the separated “half-spectra” towards each other in accordance with the primary energy difference results in the interference-free spectrum at the “critical” electron impact energy. The comparison of the constructed CIS spectrum with the CIS spectrum measured at the critical energy informs us about the relative strength of the exchange interference effects. According to our results the method of shifting both halves of the separated spectrum towards each other works reasonably well, and the interference-free spectra in the overlap region can be constructed relatively easy. Although we found a small systematic difference between the measured and the constructed spectra at the critical energy, the difference is still not significant enough to state unambiguously the existence of strong interference effects. This is in agreement with conclusions of the recent photoionization study dealing with Kr 3d5/2,3/2 and Xe 4d5/2,5/2 [6] according to which the effects of the exchange interference are substantially reduced by angular integration and when the experimental energy resolution largely surpasses the natural line width of the intermediate states. The same method applied with one order tighter experimental energy resolution might reveal larger contrast between the two data sets but the realisation would require to substantially improve the efficiency of the present (e, 2e) experiment. Additional complication arises from the fact that there are several different pairs of core-hole states excited that have different total angular momenta J and interfere independently. To address in details the problem of exchange interferences in the Ar 2p core-hole region the experimental control over the energy conservation in the electron impact induced resonant Auger decay should be very tight – a few tens of meV which is of the order of the multiplet splitting [2]. Acknowledgments This research was (partially) carried out in the framework of the Center of Excellence of Mechatronics and Logistics at the University of Miskolc. References ˝ [1] B. Paripás, B. Palásthy, M. Zˇ itnik, K. Tokési, Nucl. Instrm. Meth. Res. B 279 (2012) 66–72. ˇ ˇ [2] B. Paripás, B. Palásthy, M. Stuhec, M. Zitnik, Phys. Rev. A 82 (2010) 0325081–032508-1066. [3] J.P.V. den Brink, G. Nienhuis, J. van Eck, H.M. Heideman, J. Phys. B 22 (1989) 3501. [4] J.A. de Gouw, J. van Eck, A.C. Peters, J. van der Weg, H.G.M. Heideman, Phys. Rev. Lett. 71 (1993) 2875. [5] S. Fritzsche, J. Nikkinen, S.-M. Huttula, H. Aksela, M. Huttula, S. Aksela, Phys. Rev. A 75 (2007) 012501. [6] M. Zˇ itnik, K. Buˇcar, A. Miheliˇc, P. Lablanquie, F. Penent, J. Paladoux, L. Andriˇc, P. Bolognesi, L. Avaldi, Phys. Rev. A 87 (2013) 013436. [7] L.O. Werme, T. Bergmark, K. Siegbahn, Phys. Scr. 6 (1972) 141. [8] G.C. King, M. Tronc, F.H. Read, R. Bradford, J. Phys. B 10 (1977) 2479. [9] R. Camilloni, M. Zˇ itnik, C. Comicioli, K.C. Prince, M. Zacchigna, C. Crotti, C. Ottaviani, C. Quaresima, P. Perfetti, G. Stefani, Phys. Rev. Lett. 77 (1996) 2646. [10] L. Végh, J.H. Macek, Phys. Rev. A 50 (1994) 4031. [11] L. Végh, Phys. Rev. A 50 (1994) 4036. [12] B. Paripás, B. Palásthy, Radiat. Phys. Chem. 76 (2007) 565–569. ˝ [13] A. Kövér, D. Varga, I. Csernyi, E. Szmola, G. Mórik, L. Gulyás, K. Tokési, Nucl. Instrm. Meth. Res. A 373 (1996) 51. [14] J.A. de Gouw, J. van Eck, A.C. Peters, J. van der Weg, H.G.M. Heideman, J. Phys. B 28 (1995) 2127.