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Electron–electron coincidence study of double Auger processes in atoms
Journal of Electron Spectroscopy and Related Phenomena 141 (2004) 121–126
Electron–electron coincidence study of double Auger processes in atoms J. Viefhausa,∗ , A.N. Grum-Grzhimailoa,b , N.M. Kabachnika,b , U. Beckera b
a Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia
Received 20 April 2004; received in revised form 14 June 2004; accepted 14 June 2004 Available online 1 October 2004
Abstract The double Auger process after Ar 2p and Ne 1s inner-shell photoionization is investigated by means of angle resolved time-of-flight electron– electron coincidence spectroscopy. This method allows to disentangle direct double Auger from cascade Auger processes. Information about the energy sharing as well as the angular correlation of the two emitted electrons is obtained. Circular dichroism in the double Auger emission produced by circularly polarized light is discussed. © 2004 Elsevier B.V. All rights reserved. PACS: 32.80.Hd Keywords: Electron–electron coincidence; Double Auger processes; Photoionization; Energy and angular distributions; Circular dichrosim
1. Introduction Double Auger (DA) decay is one of the relaxation processes of an inner-shell vacancy in an atom or a molecule in which an outer-shell electron fills the vacancy and two other electrons are simultaneously emitted into continuum. This process is, evidently, less probable than the usual Auger relaxation with emission of one electron, nevertheless it constitutes a sizeable fraction of all decays and therefore is worth to be studied. Besides, the study of DA decay provides valuable information about correlations in atoms since the process occurs only due to electron–electron correlations. In this context it is important to point out that there are two completely different classes of multi-Auger electron emission. Apart from the direct DA decay where the two Auger electrons are emitted simultaneously there exists another class of decay which is a sequential process where the two Auger electrons are emitted one after the other in a step-by-step Auger cascade which has at least one physical intermediate state. In this paper we will concentrate on the first “direct” DA process. Since the initial and final ionic states in DA decay have definite energies, the sum of energies of two emitted electrons is determined ∗
Corresponding author. E-mail address: [email protected] (J. Viefhaus).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.06.013
by the energy conservation. However, the energy sharing between electrons is, in principle, arbitrary, therefore the electron energy distribution will be continuous in direct DA in contrast to the discrete lines of the usual Auger decay or cascade Auger decay. This in turn constitutes the main difficulty of detecting the DA process since it is difficult to separate these decay electrons from the background. Because of this in the majority of experimental studies of the multi-electron emission decay, the ion yield was measured. However, these experiments are unable to disentangle the qualitative physical difference between direct DA and cascade decay. Experimental studies of the multi-Auger electron emission process were initiated by Carlson and Krause [1] studying the decay of K-vacancies in Ne by measuring the yield of the Ne3+ ions. Evidence for the existence of direct DA transitions was soon obtained by measurements of the Auger electron energy spectrum [2]. Indications for similar two-electron emission were also found in resonant Auger processes in noble gas atoms [3–5] (for a review of early studies on DA transitions see [6]). As it was pointed out before, the yield of the multi-charged ions can be a result of a very complicated vacancy cascade and therefore it was quickly realized that coincidence measurements may help to disentangle different processes. Initiated by Krause et al. [7] the photoelectron–ion coincidence measurements [8–11] as well as Auger-electron–
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ion coincidence measurements [12] permitted to accurately determine the total yield of two Auger electron emission processes for vacancies in different shells of various atoms. The most direct way of studying the DA decay is an electron–electron coincidence experiment which can provide not only integral, but also differential in energy and angles information. Only quite recently such measurements became possible. The measurements of Hindi et al. [13] utilized the nuclear electron capture process to create a K-shell vacancy in argon. Using the electron–electron coincidence technique, they observed some characteristic features of the DA process, but they could give – due to the limited energy resolution – no quantitative information on the branching ratios of the different decay processes and the corresponding energy distributions. Recently in our group a series of measurements of DA decay induced by photoionization of K-shell in Ne and L-shell in Ar have been performed. Some of the results on Ar have already been published [14,15]. Theoretically the DA effect was first considered in the shake-off model (a sudden perturbation approximation) [16–18]. However, only total yield of the DA process was calculated. First calculations based on the many-body perturbation theory which included also energy and angular differential cross sections have been done by Amusia et al. for the Ne K-LLL process [19] and for the resonant Kr M-NNN process [20]. Similar calculations for direct DA decay in Kr have been published in [21]. A particular problem of the post-collision interaction in DA decay was considered by Sheinerman [22]. In the present paper we present some new experimental results on the energy and angular distributions of electrons from DA decay of Ne 1s−1 and Ar 2p−1 and discuss them using the theoretical analysis made recently in [23]. We discuss also a possible circular dichroism in the angular distributions of electrons from photoinduced DA decay.
2. Experiment The two main experimental prerequisites for DA studies have to be fulfilled. First, the electron spectrometer must
be able to detect a wide range of kinetic energies ranging from zero to a couple of hundreds of eV with high transmission and very low background. Second, it has to have sufficient energy resolution in order to be able to disentangle direct DA from both cascade as well as normal Auger processes. Our setup shown in Fig. 1 is based on multiple electron time-of-flight spectrometers disposed in a plane perpendicular to the incoming photon beam. This apparatus not only meets the requirements mentioned above but also has inherent coincidence timing capabilities and provides in addition angular information about the electrons ejected in DA decay. The experiments were performed both at the Hamburger Synchrotronstrahlungs-Labor (HASYLAB, storage ring DORIS III) at DESY (Ar 2p, Ne 1s) and at the Berliner Elektronenspeichering-Gesellschaft f¨ur Synchrotronstrahlung (BESSY II) (Ar 2p) using the undulator beamlines BW3-SX700 and UE56/2-PGM-1, respectively. In the DA experiments the photon energy is adjusted in such a way that an inner-shell electron is effectively ionized by the energetic photons and leaves the target atom having a kinetic energy high enough to avoid PCI effects. Ideally the kinetic energy of the photoelectron should be higher than any of the corresponding Auger electrons emitted in the subsequent Auger decay. However, in the case of deep inner shell (e.g. Ne 1s) this would require photon energies where the cross-section for photoionization as well as the photon flux would be prohibitively low. In the case of inner-shell lines having multiplets (e.g. Ar 2p) it would also be desirable to be able to resolve the fine structure allowing for studies of the differences in the corresponding Auger decays. Therefore one has to find a reasonable compromise which fits with these requirements. At the photon energies chosen (hν = 889 eV for Ne and hν = 263/270 eV for Ar) it is unavoidable that the photo line interferes with a part of the DA continuum and consequently this kinetic energy region cannot be evaluated with respect to the DA yield. The photon energies were calibrated using the available literature values for various rare gas resonances [24]. The remaining error is below 0.1 eV for all photon energies. The photon band pass was also estimated using the resonance data and was in the order of the life time
Fig. 1. Setup for the double Auger experiments using multiple time-of-flight electron–electron coincidence spectroscopy. For the Ne experiments the plane of linear polarization was horizontal.
J. Viefhaus et al. / Journal of Electron Spectroscopy and Related Phenomena 141 (2004) 121–126
width of the corresponding inner-shell hole state (0.2 eV for Ar 2p, 0.5 eV for Ne 1s). The degree of polarization was greater than 99% in all cases. The target gas (commercial purity 99.999%) was introduced effusively via a capillary (0.5 mm inner diameter) into the interaction region where it is crossed by the ionizing synchrotron radiation beam. Electrons produced in the interaction region can enter the aperture of one of the six operational time-of-flight electron spectrometers. The corresponding analyzer angles with respect to the horizontal plane were θ = −54.7◦ , 0◦ , 22.5◦ , 45◦ , 90◦ , 180◦ . The electrons are then accelerated before they enter a drift tube and are detected by a chevron stack of micro channel plates. The actual acceleration potential depends on the length of the drift tube as well as the timing structure of the storage ring producing the synchrotron radiation pulse. In all cases under study the parameters were such that electrons having kinetic energies larger than about 0.5 eV can be detected without interference with any electron coming from subsequent pulses. Because of the time-of-flight measurement the kinetic energy resolution does not have a fixed value for the entire energy range. Typical values for the resolution are ≈1–2% and ≈3–6% respectively for the long and short analyzers employed. The data acquisition is such that all time-of-flight electron spectra are recorded in parallel. Besides the non-coincident spectra, all double coincidence events are stored separately for each analyzer combination (15 in total). Typical recording times are in the order of 1000 s. Usually a set of 50–200 spectra is recorded for each case under study. All spectra are then converted from time-to-energy using Xe N-OO Auger electron spectra [25,26] which is complemented in the case of the HASYLAB measurements by a calibration set of Ne 2s/2p photoelectron spectra. This data set is also used to correct for transmission effects which depend on the kinetic energy of the electrons. For the BESSY measurements (and as a crosscheck for the HASYLAB data also) the transmission calibration is performed using a set of Ar 2p photoelectron measurements comparing the ratio of photoelectron to Auger electron intensity. In all cases the corresponding angular distributions were taken into account [27,28]. For the coincidence spectra the data processing includes a correction for random coincidences which takes into account the calculated probabilities directly determined from the corresponding singles spectra including dead-time effects. Typical total rates for the remaining physical (“true”) coincidences are in the order of 10 Hz.
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Fig. 2. Two-dimension electron–electron coincidence spectrum of Ne taken at hν = 889 eV along with two corresponding non-coincidence spectra. Structures due to normal Auger decay are marked by Ne2+ . Diagonal stripes in which the sum of the kinetic energies is constant are caused by the double Auger electrons. Two features which are due to the residual background gas (H2 O) are marked by small arrows.
information disregarding effects of the angular distribution. The most prominent features are coincidences between photoelectrons and normal Auger electrons. The underlying processes yield discrete lines in the spectra and consequently produces intensive isolated spots in the upper left and lower right corners of the coincidence map. Also in coincidence with the photoelectron we find DA intensity which extends these features towards the lowest kinetic energies detected. These processes are therefore responsible for the “cross” in the map of Fig. 2. Of main interest for the DA effect however is the “diagonal” feature which is due to electrons having a constant sum of kinetic energies. This is a direct observation of the two DA electrons in coincidence. Intense cascade-like decay would yield to discrete “spots” on this diagonal feature. As these discrete structures are absent here we can conclude already at this stage that cascade processes must be weak. Discrete structure observed in the energy region above the diagonal is due to the background gas (<1 × 10−7 hPa), most probably caused by O 1s photoelectron of H2 O in coincidence with their corresponding K-VV Auger electrons. A careful inspection of the DA continuum shows that the diagonal consists of three features which can be attributed to different final states of the triply charged ion. However, the energy resolution (especially of the shorter time-of-flight spectrometers) is unable to completely resolve these final states.
3. Results and discussion 3.1. Energy distribution of emitted electrons A compilation of coincidence spectra after Ne 1s photoionization is shown in Fig. 2 together with two noncoincident spectra. The two-dimensional coincidence map is obtained after a summation over all of the 15 coincidence combinations. It should therefore reflect the spectroscopic
Concerning the energy partitioning among the two DA electrons we see a concentration of the intensity at the edges of the diagonal feature in Fig. 2. A more quantitative picture is obtained if we select a suitable range of kinetic energies
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corresponding to different total orbital angular momentum L, total spin S and parity π of the outgoing pair of Auger electrons [23]: WπSL (θ), (1) W(θ) = πSL
Fig. 3. Measured coincident energy distribution of the Ne K-LLL double Auger taken at hν = 889 eV along with the calculated values of Ref. [19]. The gray shaded area marks the region which is omitted in the data analysis as here the double Auger intensity interferes with the Ne 1s photo line.
which covers the area of the diagonal feature in Fig. 2 completely and then plot this intensity versus the kinetic energy of one of the two electrons. The corresponding distribution is shown in Fig. 3 which includes all final states of the triply charged ion. Keeping in mind that our data are integral over all triply charged final states we have a quite satisfactory agreement with calculations by Amusia et al. [19] which are performed for the Ne 2s−2 2p−1 final states only. As a matter of fact no information on the intensity sharing of the two DA electrons can be obtained in the region where the photoelectron interferes with the DA continuum (gray area in Fig. 3). Nevertheless we see a pronounced preference for asymmetric energy sharing and no strong evidence for cascade decay. For the strongly asymmetric energy sharing the main contribution comes from the shake-off mechanism of DA decay, in which the fast electron is emitted in a normal Auger process and the slow electron is shaken off by a sudden change in the ionic potential. 3.2. Angular correlation study So far the experimental results presented have been integrated over all angular settings. With the data sets obtained it is possible however to select a certain energy sharing range of a particular final state (or a group of them) and to plot the coincidence intensity with respect to the relative angle between the two DA electrons. Before presenting the experimental results it is useful to consider the theoretical predictions for the shape of the angular correlation patterns [23] for the considered case of the Ne 1s−1 DA decay. On the theoretical side, the description of the angular correlation patterns in DA decay is based on a two-step approach, where the direct triple photoionization is negligible and the amplitude of the process is treated as a product of the holecreation and the DA decay amplitudes. Within this model, the angular correlation pattern between the two outgoing Auger electrons in the decay of the Ne 1s−1 2 Se vacancy state is presented as an incoherent sum of partial probabilities WπSL (θ)
where θ is the angle between two emission directions. The DA decay of the Ne 1s−1 2 Se state is possible to the three groups of final states in triply charged ions Ne3+ : 2s−2 2p−1 2 Po , 2s−1 2p−2 2 Se , 2 De ,2,4 Pe and 2p−3 2 Po , 2 Do . Due to the angular momentum and parity conservation, the two Auger electrons have the same L and π as the final Ne3+ states. As have been shown [23], many properties of the partial angular functions WπSL (θ) in the DA emission are similar to those of the double photoionization process, discussed in already numerous papers (for example, [29–35]). In particular, all selection rules by Maulbetsch and Briggs [30] derived from the symmetry properties of the two-electron wavefunction are fulfilled for the DA decay. Convenient parametrizations for the functions WπSL (θ) in the DA decay can be derived [23], which separate kinematical and dynamical correlation factors. For example, for the Ne3+ 2s−2 2p−1 2 Po final state, only the W1 Po (θ) and W3 Po (θ) partial angular functions of the form W1 Po (θ) = |ag0 (θ)|2 (1 + cos θ) + |au0 (θ)|2 (1 − cos θ),
(2)
W3 Po (θ) = |ag1 (θ)|2 (1 − cos θ) + |au1 (θ)|2 (1 + cos θ)
(3)
contribute into the sum (1). Here agS (θ) and auS (θ) are gerade and ungerade (with respect to the interchange of the two outgoing electrons) amplitudes, respectively. For symmetric energy sharing between the outgoing electrons, the ungerade amplitudes vanish. The dynamical correlation factors, represented by |agS (θ)|2 and |auS (θ)|2 , reflect primarily the electron–electron repulsion. In similarity with the correlation factors for the double photoionization [32,33], they are approximated by Gaussians as functions of θ with the maximum at θ = 180◦ . The products of the kinematical factors, containing all kinematical selection rules individual for each set πLS, and the dynamical factors, determine the main features of the functions WπSL (θ). Due to unresolved final ion Ne3+ states in our experiment, the sum in (1) contains terms with 10 types of symmetry: 1,3 Po ,1,3 Do ,1,3 Se ,1,3 Pe ,1,3 De . At equal energy sharing five of them, 1 Po ,1,3 Do ,3 Pe ,3 De , show the node at θ = 180◦ and a two-fold lobe around the node [23]. Experimental results for Ne K-LLL electrons are displayed in Fig. 4 for various energy sharing values. They show a similar general pattern of a two-fold lobe structure having a minimum in the back-to-back emission for the case of nearequal energy sharing. This general pattern is an indication of the above mentioned features of the functions WπSL (θ). Generally, the measured patterns resemble the case of Ar L-MMM [15] and are very similar to the angular correlation patterns of He double photoionization. However the minimum at θ = 180◦ is quite shallow in the Ne case even near
J. Viefhaus et al. / Journal of Electron Spectroscopy and Related Phenomena 141 (2004) 121–126
Fig. 4. Angular correlation patterns taken at hν = 889 eV (linearly polarized light) and summed over all Ne3+ final ionic states (total kinetic energy ΣEkin = 720 ± 40 eV). The slower electron ea is emitted in x-direction (indicated by an arrow). The numbers in brackets give the corresponding kinetic energy range of the slower electron.
equal energy sharing. This points towards a different relative weight of two-electron continuum states with respect to the Ar case. 3.3. Circular dichroism in the angular distribution Circular dichroism in the angular distribution (CDAD) in our case is the difference between the angular correlation patterns induced by the incoming radiation with right and left circular polarization. The phenomenon of CDAD in the two-electron emission from atoms has been predicted and observed for the direct and the two-step double photoionization (see [36–40] and references therein). Since the two processes, DA decay and double photoionization, are in many respects similar, it is of interest to consider the possible CDAD effect in the DA process as well. The vacancy with the nonzero angular momentum, for example the p-vacancy after the photoionization in the p-shell, may be oriented if produced by circularly polarized light. Such a polarized vacancy generally can give rise to the CDAD in the DA decay, i.e. the different angular correlation patterns between the two outgoing Auger electrons after decay of the vacancies with opposite orientations. A general theoretical treatment of the CDAD in DA emission has been done recently [23]. Here we report first experiments on the circular dichroism in the DA decay, taking the DA decay of the Ar 2p−1 vacancy state into the Ar3+ 3p3 states as an example. Contrary to the case of double photoionization, no significant evidence for CDAD in the DA decay was found in the present experiment with Ar. Fig. 5 shows the angular correlation patterns measured with left and right circularly polarized light for four different energy sharings between the two Auger electrons. Similar results are obtained for all other energy sharing conditions, however at the extreme unequal energy sharing a sizeable fraction of the intensity is due to cascade decay [15] which prevents a simple analysis in terms of direct DA only. Orientation of a p-vacancy is described by the orientation parameter A10 .
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Fig. 5. Angular correlation patterns for σ − (open symbols) and σ + (full symbols) circularly polarized photons (hν = 270 eV) for all Ar 3p−3 final ionic states (total kinetic energy ΣEkin = 163 ± 8 eV). The slower electron ea is emitted in x-direction (indicated by an arrow). The numbers in brackets give the corresponding kinetic energy range of the slower electron.
Calculations show [41,42] that this parameter for the Ar 2p−1 vacancy is rather large, |A10 | ∼ 0.5. A few reasons can explain, in principle, why despite of this the circular dichroism is not observed. In contrast to the angular correlation function for the DA decay of an isotropic vacancy (1), the circular dichroism includes the crossed terms with different L [23] and potentially different signs. The CDAD likely shows different signs also for different unresolved final terms of the Ar3+ 3p3 which could be resolved in future high resolution studies. Furthermore, only an imaginary part of the products of the gerade and ungerade amplitudes, Im(αSg αS∗ u ), enters the final result. Therefore whenever one of the amplitudes is small, this product is small too. For example, for the near equal energy sharing, when au (θ) = 0, the CDAD vanishes, as is confirmed by Fig. 5 (rightmost distribution).
4. Conclusions We have presented first coincident measurements for the case of Ne K-LLL DA electrons. The method employed allows to disentangle the simultaneous DA process with respect to cascade Auger electron emission. Similar to the situation in Ar L-MMM decay we see an even stronger dominance of the direct DA decay. This enables us to study the correlated motion of the simultaneously emitted DA electrons with respect to their angular correlation. General shape of the angular correlation patterns obtained can be qualitatively explained by the analysis of the individual contributions from the channels with different symmetries of the two-electron wavefunctions. In contrast to the case of the double photoionization of helium, we see no measurable influence of the photon polarization on the angular correlation pattern illustrated by the fact that we observe no circular dichroism in Ar L-MMM DA decay.
Acknowledgements It is a great pleasure to acknowledge the invaluable assistance of Slobodan Cvejanovi´c, Alexander V. Golovin, Sanja
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Korica, Burkhard Langer, Toralf Lischke, Georg Pr¨umper, Daniel Rolles, and Christian Wienberg during the course of the measurements as well as the support of the BESSY and HASYLAB staff, in particular, by Willy Mahler, Ralph D¨ohrmann, and Thomas M¨oller. The project is supported in part by the Bundesministerium f¨ur Bildung and Forschung (05KS1EB1/2) and the Deutsche Forschungsgemeinschaft (VI208/2-1). A.N.G. and N.M.K. are grateful to the FritzHaber-Institut der Max-Planck-Gesellschaft for hospitality and financial support. References [1] T.A. Carlson, M.O. Krause, Phys. Rev. Lett. 14 (1965) 390. [2] T.A. Carlson, M.O. Krause, Phys. Rev. Lett. 17 (1966) 1079. [3] U. Becker, T. Prescher, E. Schmidt, B. Sonntag, H.-E. Wetzel, Phys. Rev. A 33 (1986) 3891. [4] P.A. Heimann, D.W. Lindle, T.A. Ferret, S.H. Liu, L.J. Medhurst, M.N. Piancastelli, D.A. Shirley, U. Becker, H.G. Kerkhoff, B. Langer, D. Szostak, R. Wehlitz, J. Phys. B 20 (1987) 5005. [5] U. Becker, D. Szostak, M. Kupsch, H.G. Kerkhoff, B. Langer, R. Wehlitz, J. Phys. B 22 (1989) 749. ˚ [6] T. Aberg, B. Crasemann (Eds.), Atomic Inner-Shell Processes, vol. 1, Academic Press, New York, 1975, p. 353. [7] M.O. Krause, M.L. Vestal, W.H. Johnston, T.A. Carlson, Phys. Rev. 133 (1964) A385. [8] T. Hayaishi, E. Murakami, A. Yagishita, F. Koike, Y. Morioka, J.E. Hansen, J. Phys. B 21 (1988) 3203. [9] B. K¨ammerling, B. Kr¨assig, V. Schmidt, J. Phys. B 25 (1992) 3621. [10] B. Kanngießer, M. Jainz, S. Br¨unken, W. Benten, Ch. Gerth, K. Godehusen, K. Tiedtke, P. van Kampen, A. Tutay, P. Zimmermann, V.F. Demekhin, A.G. Kochur, Phys. Rev. A 62 (2000) 014702. [11] S. Br¨unken, Ch. Gerth, B. Kanngießer, T. Luhmann, M. Richter, P. Zimmermann, Phys. Rev. A 65 (2002) 042708. [12] J.C. Levin, C. Biedermann, N. Keller, L. Liljeby, C.-S. O, R.T. Short, I.A. Sellin, D.W. Lindle, Phys. Rev. Lett. 65 (1990) 988. [13] M.M. Hindi, Z. Lin, A. Recep, P.M. Miocinovi´c, R.L. Kozub, G.J. Lapeyre, Phys. Rev. A 53 (1996) R3716. [14] J. Viefhaus, in: A. Bianconi, A. Marcelli, N.L. Saini (Eds.), X-Ray and Inner-Shell Processes, AIP Conference Proceedings 652, New York, 2003, p. 307. [15] J. Viefhaus, S. Cvejanovi´c, B. Langer, T. Lischke, G. Pr¨umper, D. Rolles, A.V. Golovin, A.N. Grum-Grzhimailo, N.M. Kabachnik, U. Becker, Phys. Rev. Lett. 92 (2004) 083001.
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Electron–electron coincidence study of double Auger processes in atoms J. Viefhausa,∗ , A.N. Grum-Grzhimailoa,b , N.M. Kabachnika,b , U. Beckera b
a Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin, Germany Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia
Received 20 April 2004; received in revised form 14 June 2004; accepted 14 June 2004 Available online 1 October 2004
Abstract The double Auger process after Ar 2p and Ne 1s inner-shell photoionization is investigated by means of angle resolved time-of-flight electron– electron coincidence spectroscopy. This method allows to disentangle direct double Auger from cascade Auger processes. Information about the energy sharing as well as the angular correlation of the two emitted electrons is obtained. Circular dichroism in the double Auger emission produced by circularly polarized light is discussed. © 2004 Elsevier B.V. All rights reserved. PACS: 32.80.Hd Keywords: Electron–electron coincidence; Double Auger processes; Photoionization; Energy and angular distributions; Circular dichrosim
1. Introduction Double Auger (DA) decay is one of the relaxation processes of an inner-shell vacancy in an atom or a molecule in which an outer-shell electron fills the vacancy and two other electrons are simultaneously emitted into continuum. This process is, evidently, less probable than the usual Auger relaxation with emission of one electron, nevertheless it constitutes a sizeable fraction of all decays and therefore is worth to be studied. Besides, the study of DA decay provides valuable information about correlations in atoms since the process occurs only due to electron–electron correlations. In this context it is important to point out that there are two completely different classes of multi-Auger electron emission. Apart from the direct DA decay where the two Auger electrons are emitted simultaneously there exists another class of decay which is a sequential process where the two Auger electrons are emitted one after the other in a step-by-step Auger cascade which has at least one physical intermediate state. In this paper we will concentrate on the first “direct” DA process. Since the initial and final ionic states in DA decay have definite energies, the sum of energies of two emitted electrons is determined ∗
Corresponding author. E-mail address: [email protected] (J. Viefhaus).
0368-2048/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2004.06.013
by the energy conservation. However, the energy sharing between electrons is, in principle, arbitrary, therefore the electron energy distribution will be continuous in direct DA in contrast to the discrete lines of the usual Auger decay or cascade Auger decay. This in turn constitutes the main difficulty of detecting the DA process since it is difficult to separate these decay electrons from the background. Because of this in the majority of experimental studies of the multi-electron emission decay, the ion yield was measured. However, these experiments are unable to disentangle the qualitative physical difference between direct DA and cascade decay. Experimental studies of the multi-Auger electron emission process were initiated by Carlson and Krause [1] studying the decay of K-vacancies in Ne by measuring the yield of the Ne3+ ions. Evidence for the existence of direct DA transitions was soon obtained by measurements of the Auger electron energy spectrum [2]. Indications for similar two-electron emission were also found in resonant Auger processes in noble gas atoms [3–5] (for a review of early studies on DA transitions see [6]). As it was pointed out before, the yield of the multi-charged ions can be a result of a very complicated vacancy cascade and therefore it was quickly realized that coincidence measurements may help to disentangle different processes. Initiated by Krause et al. [7] the photoelectron–ion coincidence measurements [8–11] as well as Auger-electron–
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ion coincidence measurements [12] permitted to accurately determine the total yield of two Auger electron emission processes for vacancies in different shells of various atoms. The most direct way of studying the DA decay is an electron–electron coincidence experiment which can provide not only integral, but also differential in energy and angles information. Only quite recently such measurements became possible. The measurements of Hindi et al. [13] utilized the nuclear electron capture process to create a K-shell vacancy in argon. Using the electron–electron coincidence technique, they observed some characteristic features of the DA process, but they could give – due to the limited energy resolution – no quantitative information on the branching ratios of the different decay processes and the corresponding energy distributions. Recently in our group a series of measurements of DA decay induced by photoionization of K-shell in Ne and L-shell in Ar have been performed. Some of the results on Ar have already been published [14,15]. Theoretically the DA effect was first considered in the shake-off model (a sudden perturbation approximation) [16–18]. However, only total yield of the DA process was calculated. First calculations based on the many-body perturbation theory which included also energy and angular differential cross sections have been done by Amusia et al. for the Ne K-LLL process [19] and for the resonant Kr M-NNN process [20]. Similar calculations for direct DA decay in Kr have been published in [21]. A particular problem of the post-collision interaction in DA decay was considered by Sheinerman [22]. In the present paper we present some new experimental results on the energy and angular distributions of electrons from DA decay of Ne 1s−1 and Ar 2p−1 and discuss them using the theoretical analysis made recently in [23]. We discuss also a possible circular dichroism in the angular distributions of electrons from photoinduced DA decay.
2. Experiment The two main experimental prerequisites for DA studies have to be fulfilled. First, the electron spectrometer must
be able to detect a wide range of kinetic energies ranging from zero to a couple of hundreds of eV with high transmission and very low background. Second, it has to have sufficient energy resolution in order to be able to disentangle direct DA from both cascade as well as normal Auger processes. Our setup shown in Fig. 1 is based on multiple electron time-of-flight spectrometers disposed in a plane perpendicular to the incoming photon beam. This apparatus not only meets the requirements mentioned above but also has inherent coincidence timing capabilities and provides in addition angular information about the electrons ejected in DA decay. The experiments were performed both at the Hamburger Synchrotronstrahlungs-Labor (HASYLAB, storage ring DORIS III) at DESY (Ar 2p, Ne 1s) and at the Berliner Elektronenspeichering-Gesellschaft f¨ur Synchrotronstrahlung (BESSY II) (Ar 2p) using the undulator beamlines BW3-SX700 and UE56/2-PGM-1, respectively. In the DA experiments the photon energy is adjusted in such a way that an inner-shell electron is effectively ionized by the energetic photons and leaves the target atom having a kinetic energy high enough to avoid PCI effects. Ideally the kinetic energy of the photoelectron should be higher than any of the corresponding Auger electrons emitted in the subsequent Auger decay. However, in the case of deep inner shell (e.g. Ne 1s) this would require photon energies where the cross-section for photoionization as well as the photon flux would be prohibitively low. In the case of inner-shell lines having multiplets (e.g. Ar 2p) it would also be desirable to be able to resolve the fine structure allowing for studies of the differences in the corresponding Auger decays. Therefore one has to find a reasonable compromise which fits with these requirements. At the photon energies chosen (hν = 889 eV for Ne and hν = 263/270 eV for Ar) it is unavoidable that the photo line interferes with a part of the DA continuum and consequently this kinetic energy region cannot be evaluated with respect to the DA yield. The photon energies were calibrated using the available literature values for various rare gas resonances [24]. The remaining error is below 0.1 eV for all photon energies. The photon band pass was also estimated using the resonance data and was in the order of the life time
Fig. 1. Setup for the double Auger experiments using multiple time-of-flight electron–electron coincidence spectroscopy. For the Ne experiments the plane of linear polarization was horizontal.
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width of the corresponding inner-shell hole state (0.2 eV for Ar 2p, 0.5 eV for Ne 1s). The degree of polarization was greater than 99% in all cases. The target gas (commercial purity 99.999%) was introduced effusively via a capillary (0.5 mm inner diameter) into the interaction region where it is crossed by the ionizing synchrotron radiation beam. Electrons produced in the interaction region can enter the aperture of one of the six operational time-of-flight electron spectrometers. The corresponding analyzer angles with respect to the horizontal plane were θ = −54.7◦ , 0◦ , 22.5◦ , 45◦ , 90◦ , 180◦ . The electrons are then accelerated before they enter a drift tube and are detected by a chevron stack of micro channel plates. The actual acceleration potential depends on the length of the drift tube as well as the timing structure of the storage ring producing the synchrotron radiation pulse. In all cases under study the parameters were such that electrons having kinetic energies larger than about 0.5 eV can be detected without interference with any electron coming from subsequent pulses. Because of the time-of-flight measurement the kinetic energy resolution does not have a fixed value for the entire energy range. Typical values for the resolution are ≈1–2% and ≈3–6% respectively for the long and short analyzers employed. The data acquisition is such that all time-of-flight electron spectra are recorded in parallel. Besides the non-coincident spectra, all double coincidence events are stored separately for each analyzer combination (15 in total). Typical recording times are in the order of 1000 s. Usually a set of 50–200 spectra is recorded for each case under study. All spectra are then converted from time-to-energy using Xe N-OO Auger electron spectra [25,26] which is complemented in the case of the HASYLAB measurements by a calibration set of Ne 2s/2p photoelectron spectra. This data set is also used to correct for transmission effects which depend on the kinetic energy of the electrons. For the BESSY measurements (and as a crosscheck for the HASYLAB data also) the transmission calibration is performed using a set of Ar 2p photoelectron measurements comparing the ratio of photoelectron to Auger electron intensity. In all cases the corresponding angular distributions were taken into account [27,28]. For the coincidence spectra the data processing includes a correction for random coincidences which takes into account the calculated probabilities directly determined from the corresponding singles spectra including dead-time effects. Typical total rates for the remaining physical (“true”) coincidences are in the order of 10 Hz.
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Fig. 2. Two-dimension electron–electron coincidence spectrum of Ne taken at hν = 889 eV along with two corresponding non-coincidence spectra. Structures due to normal Auger decay are marked by Ne2+ . Diagonal stripes in which the sum of the kinetic energies is constant are caused by the double Auger electrons. Two features which are due to the residual background gas (H2 O) are marked by small arrows.
information disregarding effects of the angular distribution. The most prominent features are coincidences between photoelectrons and normal Auger electrons. The underlying processes yield discrete lines in the spectra and consequently produces intensive isolated spots in the upper left and lower right corners of the coincidence map. Also in coincidence with the photoelectron we find DA intensity which extends these features towards the lowest kinetic energies detected. These processes are therefore responsible for the “cross” in the map of Fig. 2. Of main interest for the DA effect however is the “diagonal” feature which is due to electrons having a constant sum of kinetic energies. This is a direct observation of the two DA electrons in coincidence. Intense cascade-like decay would yield to discrete “spots” on this diagonal feature. As these discrete structures are absent here we can conclude already at this stage that cascade processes must be weak. Discrete structure observed in the energy region above the diagonal is due to the background gas (<1 × 10−7 hPa), most probably caused by O 1s photoelectron of H2 O in coincidence with their corresponding K-VV Auger electrons. A careful inspection of the DA continuum shows that the diagonal consists of three features which can be attributed to different final states of the triply charged ion. However, the energy resolution (especially of the shorter time-of-flight spectrometers) is unable to completely resolve these final states.
3. Results and discussion 3.1. Energy distribution of emitted electrons A compilation of coincidence spectra after Ne 1s photoionization is shown in Fig. 2 together with two noncoincident spectra. The two-dimensional coincidence map is obtained after a summation over all of the 15 coincidence combinations. It should therefore reflect the spectroscopic
Concerning the energy partitioning among the two DA electrons we see a concentration of the intensity at the edges of the diagonal feature in Fig. 2. A more quantitative picture is obtained if we select a suitable range of kinetic energies
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corresponding to different total orbital angular momentum L, total spin S and parity π of the outgoing pair of Auger electrons [23]: WπSL (θ), (1) W(θ) = πSL
Fig. 3. Measured coincident energy distribution of the Ne K-LLL double Auger taken at hν = 889 eV along with the calculated values of Ref. [19]. The gray shaded area marks the region which is omitted in the data analysis as here the double Auger intensity interferes with the Ne 1s photo line.
which covers the area of the diagonal feature in Fig. 2 completely and then plot this intensity versus the kinetic energy of one of the two electrons. The corresponding distribution is shown in Fig. 3 which includes all final states of the triply charged ion. Keeping in mind that our data are integral over all triply charged final states we have a quite satisfactory agreement with calculations by Amusia et al. [19] which are performed for the Ne 2s−2 2p−1 final states only. As a matter of fact no information on the intensity sharing of the two DA electrons can be obtained in the region where the photoelectron interferes with the DA continuum (gray area in Fig. 3). Nevertheless we see a pronounced preference for asymmetric energy sharing and no strong evidence for cascade decay. For the strongly asymmetric energy sharing the main contribution comes from the shake-off mechanism of DA decay, in which the fast electron is emitted in a normal Auger process and the slow electron is shaken off by a sudden change in the ionic potential. 3.2. Angular correlation study So far the experimental results presented have been integrated over all angular settings. With the data sets obtained it is possible however to select a certain energy sharing range of a particular final state (or a group of them) and to plot the coincidence intensity with respect to the relative angle between the two DA electrons. Before presenting the experimental results it is useful to consider the theoretical predictions for the shape of the angular correlation patterns [23] for the considered case of the Ne 1s−1 DA decay. On the theoretical side, the description of the angular correlation patterns in DA decay is based on a two-step approach, where the direct triple photoionization is negligible and the amplitude of the process is treated as a product of the holecreation and the DA decay amplitudes. Within this model, the angular correlation pattern between the two outgoing Auger electrons in the decay of the Ne 1s−1 2 Se vacancy state is presented as an incoherent sum of partial probabilities WπSL (θ)
where θ is the angle between two emission directions. The DA decay of the Ne 1s−1 2 Se state is possible to the three groups of final states in triply charged ions Ne3+ : 2s−2 2p−1 2 Po , 2s−1 2p−2 2 Se , 2 De ,2,4 Pe and 2p−3 2 Po , 2 Do . Due to the angular momentum and parity conservation, the two Auger electrons have the same L and π as the final Ne3+ states. As have been shown [23], many properties of the partial angular functions WπSL (θ) in the DA emission are similar to those of the double photoionization process, discussed in already numerous papers (for example, [29–35]). In particular, all selection rules by Maulbetsch and Briggs [30] derived from the symmetry properties of the two-electron wavefunction are fulfilled for the DA decay. Convenient parametrizations for the functions WπSL (θ) in the DA decay can be derived [23], which separate kinematical and dynamical correlation factors. For example, for the Ne3+ 2s−2 2p−1 2 Po final state, only the W1 Po (θ) and W3 Po (θ) partial angular functions of the form W1 Po (θ) = |ag0 (θ)|2 (1 + cos θ) + |au0 (θ)|2 (1 − cos θ),
(2)
W3 Po (θ) = |ag1 (θ)|2 (1 − cos θ) + |au1 (θ)|2 (1 + cos θ)
(3)
contribute into the sum (1). Here agS (θ) and auS (θ) are gerade and ungerade (with respect to the interchange of the two outgoing electrons) amplitudes, respectively. For symmetric energy sharing between the outgoing electrons, the ungerade amplitudes vanish. The dynamical correlation factors, represented by |agS (θ)|2 and |auS (θ)|2 , reflect primarily the electron–electron repulsion. In similarity with the correlation factors for the double photoionization [32,33], they are approximated by Gaussians as functions of θ with the maximum at θ = 180◦ . The products of the kinematical factors, containing all kinematical selection rules individual for each set πLS, and the dynamical factors, determine the main features of the functions WπSL (θ). Due to unresolved final ion Ne3+ states in our experiment, the sum in (1) contains terms with 10 types of symmetry: 1,3 Po ,1,3 Do ,1,3 Se ,1,3 Pe ,1,3 De . At equal energy sharing five of them, 1 Po ,1,3 Do ,3 Pe ,3 De , show the node at θ = 180◦ and a two-fold lobe around the node [23]. Experimental results for Ne K-LLL electrons are displayed in Fig. 4 for various energy sharing values. They show a similar general pattern of a two-fold lobe structure having a minimum in the back-to-back emission for the case of nearequal energy sharing. This general pattern is an indication of the above mentioned features of the functions WπSL (θ). Generally, the measured patterns resemble the case of Ar L-MMM [15] and are very similar to the angular correlation patterns of He double photoionization. However the minimum at θ = 180◦ is quite shallow in the Ne case even near
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Fig. 4. Angular correlation patterns taken at hν = 889 eV (linearly polarized light) and summed over all Ne3+ final ionic states (total kinetic energy ΣEkin = 720 ± 40 eV). The slower electron ea is emitted in x-direction (indicated by an arrow). The numbers in brackets give the corresponding kinetic energy range of the slower electron.
equal energy sharing. This points towards a different relative weight of two-electron continuum states with respect to the Ar case. 3.3. Circular dichroism in the angular distribution Circular dichroism in the angular distribution (CDAD) in our case is the difference between the angular correlation patterns induced by the incoming radiation with right and left circular polarization. The phenomenon of CDAD in the two-electron emission from atoms has been predicted and observed for the direct and the two-step double photoionization (see [36–40] and references therein). Since the two processes, DA decay and double photoionization, are in many respects similar, it is of interest to consider the possible CDAD effect in the DA process as well. The vacancy with the nonzero angular momentum, for example the p-vacancy after the photoionization in the p-shell, may be oriented if produced by circularly polarized light. Such a polarized vacancy generally can give rise to the CDAD in the DA decay, i.e. the different angular correlation patterns between the two outgoing Auger electrons after decay of the vacancies with opposite orientations. A general theoretical treatment of the CDAD in DA emission has been done recently [23]. Here we report first experiments on the circular dichroism in the DA decay, taking the DA decay of the Ar 2p−1 vacancy state into the Ar3+ 3p3 states as an example. Contrary to the case of double photoionization, no significant evidence for CDAD in the DA decay was found in the present experiment with Ar. Fig. 5 shows the angular correlation patterns measured with left and right circularly polarized light for four different energy sharings between the two Auger electrons. Similar results are obtained for all other energy sharing conditions, however at the extreme unequal energy sharing a sizeable fraction of the intensity is due to cascade decay [15] which prevents a simple analysis in terms of direct DA only. Orientation of a p-vacancy is described by the orientation parameter A10 .
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Fig. 5. Angular correlation patterns for σ − (open symbols) and σ + (full symbols) circularly polarized photons (hν = 270 eV) for all Ar 3p−3 final ionic states (total kinetic energy ΣEkin = 163 ± 8 eV). The slower electron ea is emitted in x-direction (indicated by an arrow). The numbers in brackets give the corresponding kinetic energy range of the slower electron.
Calculations show [41,42] that this parameter for the Ar 2p−1 vacancy is rather large, |A10 | ∼ 0.5. A few reasons can explain, in principle, why despite of this the circular dichroism is not observed. In contrast to the angular correlation function for the DA decay of an isotropic vacancy (1), the circular dichroism includes the crossed terms with different L [23] and potentially different signs. The CDAD likely shows different signs also for different unresolved final terms of the Ar3+ 3p3 which could be resolved in future high resolution studies. Furthermore, only an imaginary part of the products of the gerade and ungerade amplitudes, Im(αSg αS∗ u ), enters the final result. Therefore whenever one of the amplitudes is small, this product is small too. For example, for the near equal energy sharing, when au (θ) = 0, the CDAD vanishes, as is confirmed by Fig. 5 (rightmost distribution).
4. Conclusions We have presented first coincident measurements for the case of Ne K-LLL DA electrons. The method employed allows to disentangle the simultaneous DA process with respect to cascade Auger electron emission. Similar to the situation in Ar L-MMM decay we see an even stronger dominance of the direct DA decay. This enables us to study the correlated motion of the simultaneously emitted DA electrons with respect to their angular correlation. General shape of the angular correlation patterns obtained can be qualitatively explained by the analysis of the individual contributions from the channels with different symmetries of the two-electron wavefunctions. In contrast to the case of the double photoionization of helium, we see no measurable influence of the photon polarization on the angular correlation pattern illustrated by the fact that we observe no circular dichroism in Ar L-MMM DA decay.
Acknowledgements It is a great pleasure to acknowledge the invaluable assistance of Slobodan Cvejanovi´c, Alexander V. Golovin, Sanja
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Korica, Burkhard Langer, Toralf Lischke, Georg Pr¨umper, Daniel Rolles, and Christian Wienberg during the course of the measurements as well as the support of the BESSY and HASYLAB staff, in particular, by Willy Mahler, Ralph D¨ohrmann, and Thomas M¨oller. The project is supported in part by the Bundesministerium f¨ur Bildung and Forschung (05KS1EB1/2) and the Deutsche Forschungsgemeinschaft (VI208/2-1). A.N.G. and N.M.K. are grateful to the FritzHaber-Institut der Max-Planck-Gesellschaft for hospitality and financial support. References [1] T.A. Carlson, M.O. Krause, Phys. Rev. Lett. 14 (1965) 390. [2] T.A. Carlson, M.O. Krause, Phys. Rev. Lett. 17 (1966) 1079. [3] U. Becker, T. Prescher, E. Schmidt, B. Sonntag, H.-E. Wetzel, Phys. Rev. A 33 (1986) 3891. [4] P.A. Heimann, D.W. Lindle, T.A. Ferret, S.H. Liu, L.J. Medhurst, M.N. Piancastelli, D.A. Shirley, U. Becker, H.G. Kerkhoff, B. Langer, D. Szostak, R. Wehlitz, J. Phys. B 20 (1987) 5005. [5] U. Becker, D. Szostak, M. Kupsch, H.G. Kerkhoff, B. Langer, R. Wehlitz, J. Phys. B 22 (1989) 749. ˚ [6] T. Aberg, B. Crasemann (Eds.), Atomic Inner-Shell Processes, vol. 1, Academic Press, New York, 1975, p. 353. [7] M.O. Krause, M.L. Vestal, W.H. Johnston, T.A. Carlson, Phys. Rev. 133 (1964) A385. [8] T. Hayaishi, E. Murakami, A. Yagishita, F. Koike, Y. Morioka, J.E. Hansen, J. Phys. B 21 (1988) 3203. [9] B. K¨ammerling, B. Kr¨assig, V. Schmidt, J. Phys. B 25 (1992) 3621. [10] B. Kanngießer, M. Jainz, S. Br¨unken, W. Benten, Ch. Gerth, K. Godehusen, K. Tiedtke, P. van Kampen, A. Tutay, P. Zimmermann, V.F. Demekhin, A.G. Kochur, Phys. Rev. A 62 (2000) 014702. [11] S. Br¨unken, Ch. Gerth, B. Kanngießer, T. Luhmann, M. Richter, P. Zimmermann, Phys. Rev. A 65 (2002) 042708. [12] J.C. Levin, C. Biedermann, N. Keller, L. Liljeby, C.-S. O, R.T. Short, I.A. Sellin, D.W. Lindle, Phys. Rev. Lett. 65 (1990) 988. [13] M.M. Hindi, Z. Lin, A. Recep, P.M. Miocinovi´c, R.L. Kozub, G.J. Lapeyre, Phys. Rev. A 53 (1996) R3716. [14] J. Viefhaus, in: A. Bianconi, A. Marcelli, N.L. Saini (Eds.), X-Ray and Inner-Shell Processes, AIP Conference Proceedings 652, New York, 2003, p. 307. [15] J. Viefhaus, S. Cvejanovi´c, B. Langer, T. Lischke, G. Pr¨umper, D. Rolles, A.V. Golovin, A.N. Grum-Grzhimailo, N.M. Kabachnik, U. Becker, Phys. Rev. Lett. 92 (2004) 083001.
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