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Ion–ion coincidence experiments with low extraction fields
Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
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Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Ion–ion coincidence experiments with low extraction fields R. Flammini ∗ , E. Fainelli, L. Avaldi IMIP-CNR Istituto di Metodologie Inorganiche e dei Plasmi, Via Salaria km 29.300, 00019 Monterotondo Scalo, Roma, Italy
a r t i c l e
i n f o
Article history: Received 6 November 2009 Received in revised form 6 February 2010 Accepted 21 March 2010 Available online 8 April 2010 Keywords: Ion–ion Coincidence Map Methane Simulation Concerted Synchronous Asynchronous Auger decay Dication
a b s t r a c t The fragmentation of a polyatomic molecular dication has been investigated by means of a Monte Carlo simulation which can take into account realistic experimental conditions. The simulation applied to the three body process CH4 2+ → CH2 + + H+ + H shows that the low angular acceptance, consequence of the low extraction field, does not prevent the distinction between the initial charge separation and the synchronous concerted decay mechanisms, which lead to the same final state. The comparison of the results with recent experiments [1] confirms that an initial charge separation with a following loss of a hydrogen atom describes better the experimental observations. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Experiments where two or more charged fragments are detected via time coincidence techniques represent the most suitable approach to the investigation of the fragmentation of polyatomic molecular dications. In these experiments an ion pair or an ion pair in coincidence with an electron are detected. The goal is to identify the different fragmentation patterns depending on the dication state, to measure the energy and angular distributions of the fragments and to deduce the fragmentation mechanism. The technique introduced in the eighties with laboratory photon sources [2], largely benefitted by the development of lasers and synchrotron radiation [3,4], as well as position sensitive detectors [5,6]. The core tool for these experiments is represented by an ion Time-of-Flight (TOF) spectrometer, which, via the measurement of the time T1 and T2 needed for the fragments to reach the detector from the interaction region, allows the determination of their mass and their kinetic energy. The results are usually represented by two dimensional maps with the arrival times of the fragments on the axes. Correlated ion pairs result in features with shapes strongly dependent on the fragmentation process which
∗ Corresponding author. E-mail address: roberto.fl[email protected] (R. Flammini). 0368-2048/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2010.03.015
generated them. This has been proved by a series of simulations which consider the full angular acceptance in the spectrometer [7–13]. A full angular acceptance is achieved in experiments where strong extraction fields (e.g. a few hundreds V/cm) are applied to the interaction region. However, experiments have also been performed with low extraction fields because they allow the measurement of the kinetic energy distribution of the ions with higher resolution [1,14–16]. The drawback in these latter experiments is the low angular acceptance. This might question the possibility to extract information on the fragmentation mechanisms, because only part of the features due to the correlated pair are observed in the (T1 , T2 ) maps. Here we show with a realistic simulation that also with low extraction fields the different mechanisms leading to the fragmentation of a dication can be disentangled. As a case study we will use the three body reaction CH4 2+ → CH2 + + H+ + H studied in Auger electron–ion [17], photoelectron–ion [7] as well as ion–ion coincidence experiments [1,18]. In particular the results of this simulation will be compared with the experimental data obtained in an Auger electron–ion–ion coincidence experiment. Thus in Section 2 the experimental apparatus used to collect this data is presented. In Section 3 the details of the simulation procedure are described, while the results of the simulations for the two different fragmentation mechanisms under consideration as well as the comparison with the experimental results are presented and discussed in Section 4. Finally some conclusions are collected in Section 5.
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R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
2. Experimental A detailed description of the experimental setup and procedures of the data collection have been reported elsewhere [19]. In the following only some details relevant to the present work are summarized. The vacuum chamber (base pressure ≤10−7 mbar) used for these experiments is equipped with two spectrometers: a Wiley-McLaren Time-of-Flight mass spectrometer (TOF-MS) for the detection of ions and a Cylindrical Mirror Analyzer (CMA) placed in front of the TOF-MS for the electron detection. A DC extraction field of 120 V/cm is applied to the interaction region to extract the ions. The CMA has an angular acceptance of ±7◦ around the angle = 42.7◦ . This results in an accepted geometrical solid angle of ˝ = 1.53 sterad. The electron energy resolution, E/E, is about 1.1%. This value is mainly determined by the size of the interaction zone which is about 0.1 and 2–3 mm, parallel and normal to the extraction field, respectively. With such an intrinsic energy resolution the presence of a DC field in the interaction region does not degrade the energy resolution of the Auger spectra measured by the CMA. The electron gun, has been operated at 4 keV incident energy and at a current I ≤ 1 nA during the present measurements. The Auger electron–ion coincidence electronics is based on the use of a CAMAC time-to-digital converter (TDC LeCroy 4208), operated in a multihit configuration with a common start. The pulses of the channeltron multiplier mounted at the exit slit of the CMA, after being properly amplified, discriminated (Philips Scientific 704) and delayed (Philips Scientific 794) provide the common start for the TDC and the end of the time acquisition window (10 s). The stop signals are provided by the pulses from the two Micro Channel Plates (MCP) mounted in the chevron configuration at the end of the TOF-MS. A personal computer governs the data acquisition via a CAMAC crate controller (CAEN C111), does a preliminary analysis and displays the Auger electron–ion coincidence on-line. The triple coincidence spectra are built a posteriori. The intensity of the incident electron beam and the density of the gas target (leading to ion and electron count rates of 120 kHz and 20 Hz, respectively) ensure an almost constant contribution of random coincidences over the full time spectrum investigated. In such conditions an accumulation time of about 100 h for each Auger electron–ion–ion coincidence map is needed. 3. Modeling and simulation In the simulation we have adopted the following assumptions [20]: the precursor dication has no or negligible linear momentum with respect to the kinetic fragments and its lifetime is short enough to assure that the fragmentation occurs within the interaction region; the momenta associated with the two charged fragments are well defined once the energy available in the dissociation process has been defined; conservation of the linear momentum in the first and the second step of the dissociation
holds; the directions of the fragments with respect to a fixed laboratory frame are randomly distributed (the target molecules are neither oriented nor aligned); the excitation source is unpolarized. The total TOF of each fragment ion from the center of the interaction region to the detector (Fig. 1), is the sum of three contributions associated with the three sections of the TOF spectrometer (named the extraction, the acceleration and the field free zones, labeled 1, 2 and 3, respectively): T = t1 + t2 + t3
1 t1 = a1 t2 =
2a1
1 a2
2
− x0
2a2 d −
− t3 =
s
2a1
s
− x0
2
s 2
+ v20 cos2 () − v0 cos()
+ 2a1
+ v20
s 2
− x0
+ v20 cos2 ()
cos2 ()
D−d
2a2 (s/2 − x0 ) + v20 cos2 ()
where m and q are the mass and charge of the fragment, and the accelerations in the extraction and acceleration zone, respectively, are defined as a1 =
q(Vs − Vx0 ) , m
a2 =
q(Vd − Vs ) m(s/2 − x0 )
where s, d and D are the length of the extraction, acceleration and field free regions, respectively. The angle between the direction of the ion and the axis of the spectrometer (our laboratory frame) is randomly distributed within the range 0–180◦ for the ICS (Initial Charge Separation) and 0–360◦ for the synchronous decay mechanisms. Due to the cylindrical symmetry of the setup in the simulation, there is no need to define other angles to explore all the possible orientations of the dication. Vs and Vd are the extraction and acceleration voltages, respectively. For the ion TOF spectrometer we assume the Wiley-McLaren prescriptions to achieve time focussing conditions [19,21] which link Vs and Vd once the geometrical parameters s, d and D are fixed. T is proportional to the projection of the initial momentum of the ion along the axis of the spectrometer, while the component perpendicular to the axis of the spectrometer is used to determine the probability that the ion hits the detector. In the simulations this is crucial: when the extraction field is not strong enough to bend all the trajectories towards the detector, the ions with a large component of the momentum perpendicular to the spectrometer axis are not detected. The interaction zone has been represented by a cylinder (100 m diameter and 700 m length). In the simulation the initial position, the energy and direction of the ion pairs were generated randomly. According to the assumptions made at the beginning of this section an isotropic angular distribution and a flat energy distribution of the ions have been considered. For each fragmentation mechanism fifty thousands trajectories have been computed. 4. Results
Fig. 1. Scheme of the TOF spectrometer used in the simulations. The labels 1, 2 and 3 correspond to the extraction, acceleration and field free zones, respectively. As an example, the trajectories of two ions with opposite initial momentum have been drawn (dashed line). In the simulation s = 1 cm, d = 5.4 cm, D = 55.9 cm as in Ref. [19].
Let’s consider the three body reaction CH4 2+ → CH2 + + H+ + H studied in [1]. In those experiments the dication was formed via inner shell ionization followed by Auger electron decay and the CH2 + /H+ ion pair was measured in coincidence with an Auger electron, which allows the selection of the initial dication state. To discuss in detail the mechanisms leading to the fragmentation a proper definition of the sequence of events occurring is needed. The nomenclature proposed by Maul and Gericke [22] points to the time dynamics of the process using terms like synchronous, asynchronous and sequential fragmentation, while that of Eland [23],
R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
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Fig. 2. Results of the Monte Carlo simulation of the ion–ion maps and time distributions for the CH2 + /H+ pair using the ICS model in the case of a sequential decay. Vs = 1200 and 120 V/cm, in (a) and (b), respectively. Beside each map the projections along the two axes are shown. A schematic of the dissociation process is shown in the bottom panel. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
based on the concepts of initial/deferred charge separation is more effective for the description of the mechanism of the dissociation. In the following we will make use of both these nomenclatures. The reaction CH4 2+ → CH2 + + H+ + H may proceed either via an initial charge separation (ICS) and then the loss of a H atom
where U1 and U2 are the overall energies available to the fragments in the two steps. Then, the momenta of each ion can be extracted:
CH4 2+ → CH3 ∗+ − H+
The angle ˛ takes into account that the axes of the first and second fragmentation steps may be not aligned as shown in Fig. 2, where a sketch of the reaction is reported. In Fig. 2 we show the simulation using the ICS model in the case in which the methyl ion may rotate freely around all the possible axes of the molecule, before the release of the hydrogen atom. In each figure also the time distribution relative to each ion is reported. The process has been simulated with Vs = 1200 and 120 V/cm. In this case the shape of the feature in the ion–ion map is a lozenge enlarged along the vertical axis. This corresponds to a spread in the range of values of the momentum of the CH2 + ion, because the momentum of the neutral is subtracted or added to the momentum of the methylene ion, depending on their relative orientation. When the second step of the fragmentation occurs (red arrows) all the values of ˛ are equally probable and no memory of the orientation of the first fragmentation axis (blue arrows) is retained. Considering the experimental results given in [1] where the total kinetic energy shared by H+ –CH2 + pair is about 6 ± 1 eV we used in the simulation U2 /U1 = 0.03. In the simulation U1 ranges from 6.0 to 6.06 eV and U2 from 0 to 0.2 eV. Due to the narrow energy range set for U1 and U2 both projections show a backward-forward splitting, which in turn affects the central part of the peak in the ion–ion map, reducing its intensity. Apart from the shape of the feature the most relevant quantity which characterizes the fragmentation mechanism is its slope. In 2-body reactions the momentum conservation implies the slope to be −1, while in 3-body reactions, it can assume almost
then
CH3 + → CH2 + − H
(1)
which therefore occurs in two steps, or via a synchronous concerted fragmentation CH4 2+ → CH2 + − H − H+
(2)
where the break-up in three fragments of the dication occurs simultaneously. In the first case if the release of the H atom (in the second step) occurs in a time shorter than the rotational period of the methyl ion we are in the case of an asynchronous concerted fragmentation, otherwise the process is purely sequential [22]. In the next subsections the simulation will be used to calculate the (T1 , T2 ) maps of the CH2 + /H+ pair and separately the time distributions of the two ions for all the considered mechanisms. 4.1. Fragmentation with an initial charge separation (ICS) If the reaction proceeds via an initial charge separation followed by the release of a H atom the conservation of the momenta holds in both steps and p and q, the momenta of the fragments in the first and second fragmentation steps, respectively are:
p=
2mCH3 mH mCH4
U1
and
q=
2mH mCH2 mCH3
U2
pH + = −pCH + = −p 3
and
pCH + = 2
mCH2 mCH3
p + q cos ˛
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R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
any value [23]. The slope (pCH + /pH + ) associated with this kind of 2
reaction is simply −(mCH2 /mCH3 ) because the average over 2 of cos(˛) does not alter the value of the slope even though U2 = / 0. The effect of U2 = / 0 is only the broadening of the features along the axis of the heavier fragment. In both figures beside each map the value of the slope (M) has been noted. The slope has been extracted from the data, according to the mathematical procedure suggested in [24] and is about −0.93, the value expected by the mass ratio mCH2 /mCH3 . The difference in the values of the slope for the two Vs values is of the order of 10−2 , thus the calculation of the slope seems not to be affected by the small angular acceptance. The other case to be considered for the ICS is when the axes of the two fragmentation steps are aligned. Indeed, this can happen during the charge separation in the first step because an electric field switches on along the H+ –CH3 + direction. When the second step of the dissociation occurs and a H atom departs, the stretching of the C–H bond produces a dipole moment in the methyl ion. This dipole moment in turn induces an orientation of the methyl ion along the first dissociation axis, i.e. the H3 C+ –H+ axis. This is due to the fact that the methyl ion tends to screen the charge of the proton with the C–H bond. The alignment is effective in a time shorter (5 ps) than the rotational period of the methyl ion (0.1 ns). This behavior for the methyl ion was proposed in [1] and is similar to that discussed in the literature in the case of the alignment of the XCN+ [10]. Thus in the simulation we have assigned to the angle ˛ values ranging between 0◦ and 10◦ . The process has been simulated using two different values of the extraction field Vs = 1200 and 120 V/cm, respectively, and the results of the simulation are shown in Fig. 3(a) and (b), respectively. At the bottom a scheme of the fragmentation process is also shown. Here the same U2 /U1 ratio and U1 , U2 values of the case of the sequential decay have been
used. The CH2 + radical is accelerated in both the first (blue arrow) and second (red arrow) steps of the dissociation, due to the alignment of the fragmentation axes. In Fig. 3(a), where the process has been simulated with Vs = 1200 V/cm, we see that the feature relative to the CH2 + /H+ pair in the (T1 , T2 ) map is given by a narrow lozenge with the intensity concentrated at its extremes. The value of −1.090 has been extracted for the slope. This value clearly differs from −0.93, the value predicted for a pure sequential reaction. In Fig. 3(b) the simulation of the same process has been repeated with Vs = 120 V/cm. The ion time distributions reduce to two peaks because only the ions generated within a small cone in the forward and backward directions about the axis of the spectrometer are detected. In the 3D map, only the two features at the extreme of the lozenge survive. At a first sight the size of the features in Fig. 3(b) may appear smaller than those observed at 1200 V/cm (Fig. 3(a)). This is due to the change of the scale in the T1 and T2 axes because at 120 V/cm the difference in the arrival times of ions emitted in the forward/backward direction is larger than the splitting recorded at 1200 V/cm. The slope extracted from the map using the same mathematical procedure as in the previous case is −1.092 (Fig. 3(b)). The simulation has been repeated for several values of the extraction field. The difference in the value of the slope is always of the order of 10−3 . This proves that in the case of the ICS fragmentation the use of low extraction fields does not prevent the extraction of basic information which characterizes these fragmentation processes. 4.2. Synchronous concerted fragmentation When the dication suffers a simultaneous break-up into three fragments, the momentum and energy conservation can be applied (Eq. (2)), to extract the values of the momentum of each charged
Fig. 3. Results of the Monte Carlo simulation of the ion–ion maps and time distributions for the CH2 + /H+ pair in the case of the asynchronous ICS model. Vs = 1200 and 120 V/cm, in (a) and (b), respectively. Beside each map the projections along the two axes are shown. A schematic of the dissociation process is shown in the bottom panel.
R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
fragment (Eq. (3)), as reported in [22]. A schematic of the process where the two bonds H2 C+ –H+ and the H2 C+ –H are cleaved at the same time is shown at the bottom of Fig. 4. Using the conservation of the momentum and energy, pCH + + pH + + pH = 0, 2
kin kin kin ε = ECH + + EH + + EH 2
the momenta of all the fragments can be inferred. Here we assume that the CH2 + and H are formed in their ground state and ε (the total energy available for the fragmentation) is expressed only in terms of kinetic energy: kin ECH + = 2
ε 1 + (1 + tan(˛/2))(mCH + /(4H + ,H )) 2
where H + ,H = mH + mH /(mH + + mH ) is the reduced mass of H+ and H. The expression of the momenta of the two charged fragments
43
are then pCH + = 2
2H + ,H (ε − E kin+ ) CH
2
and
pH + = −2pCH + cos 2
˛ 2
(3)
The bond angle ˛, defined as the angle formed by the momenta of H+ and H fragments at the time of the break-up, is the only parameter necessary to describe unambiguously the decay and to define the direction of the CH2 + ion. In the case of the synchronous concerted fragmentation we have performed simulations for four different cases, changing both the value of the extraction field and the range of the kinetic energy of the fragments. The results of our simulations are summarized in Fig. 4. In Fig. 4(a) we have used Vs = 1200 V/cm and ε ranging from 27 meV (kinetic energy at room temperature) to 6 eV. The feature in the 3D map is an ellipse, whose orientation and size depend on the direction of emission of the neutral fragment, i.e. on the angle ˛. This is consistent with the results obtained by Le Brun [25]. When Vs = 120 V/cm is used (Fig. 4(b)), the top-right and bottom-left part of the ellipse are cut.
Fig. 4. Results of the Monte Carlo simulation of the ion–ion maps and time distributions for the CH2 + /H+ pair in the case of synchronous concerted decay. Vs = 1200 V/cm in (a) and (c), 120 V/cm in (b) and (d); 0.027 ≤ ε ≤ 6 eV in (a) and (b), ε ∼ 6 eV in (c) and (d). A schematic of the process is shown in the bottom panel.
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R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
Fig. 5. Experimental Auger electron–ion–ion coincidence map relative to the CH2 + /H+ ion pair measured at an Auger electron of 238 eV (center). On the left (right) side, the simulation using the asynchronous ICS model (synchronous concerted decay) model are shown, respectively.
This can be understood if we consider that these parts of the map correspond to pair of ions ejected in the same half-space, either towards the detector (forward–forward) or in the opposite direction (backward–backward). The angle between the ejected CH2 + /H+ pair, is 180◦ − ˛/2, therefore it is likely that one or both ions do not hit the detector. Consistently with the case of the asynchronous fragmentation discussed in the previous section we limited ε to about 6 eV in Fig. 4(c) and (d). In the case of Vs = 1200 V/cm we still observe a feature with the contour of an ellipse, but with a reduced density in the central part. This is due to the narrow range of energy shared by the three fragments. In Fig. 4(d), where Vs = 120 V/cm is used, the effects of the narrow range of energy and the low extraction field add up, and the feature reduces to two baffles corresponding to the extreme parts of the ellipse. From the results of Fig. 4 it is clear that even with low extraction fields the shape of the feature preserves the information on the dissociation mechanism. Also in this case the features in the map are elongated along the T2 axis. This indicates a broad time distribution of the heavier fragment. However, they have a shape completely different from that of the ICS fragmentation shown in Figs. 3 and 4. 4.3. Comparison with the experiment The comparison of the simulation with the results of the Auger electron–ion–ion coincidence experiments [1] has been done for the case of the experiment performed at an Auger electron energy of 238 ± 3 eV, which corresponds to the formation of the CH4 2+ dication in the 3,1 T2 states at about 54.8 eV binding energy. In order to make a realistic comparison with the experiments the size of the interaction region, the total energy ε in the case of the synchronous concerted fragmentation or the U1 and U2 values in the case of the asynchronous fragmentation as well as the angle ˛ have been used as adjustable parameters. Moreover the results of the simulations have been binned in time intervals of 11 ns as done in the experiment. The experimental results from Ref. [1] are reported in the central panel of Fig. 5. On either sides of the experimental map, we show the results of the simulation using the two fragmentation models described in the previous sections. The two main experimental observations are the value of the slope that is −1.09 ± 0.18 and the broadening of the features along the axis of the heavier fragment. Let’s begin with the simulation according the ICS models. A reasonable representation of the data is achieved considering a target length of a few mm. This value is consistent with the overlap between the effusive gas beam and an electron beam placed at least 2 mm from the gas needle of the setup as described in [19]. As for the values of the angle ˛ and the energy U2 a more intriguing result has been obtained. Indeed, the experimental slope value of −1.09 is well reproduced by a simulation assuming an asynchronous concerted fragmentation with an angle ˛ ranging from 0◦ to 10◦ and an energy value for U2 of
less than 0.2 eV, thus in conditions of a clear alignment between the two steps of fragmentation. However, the shape of the features (not shown here) is not broadened enough along the vertical axis as in the experimental maps. The broadening is well described when 0◦ < ˛ < 180◦ is accompanied by a U2 value ranging from 0.1 to 2 eV, thus in a pure sequential scenario. The best agreement with the experiment is achieved when simulation takes into account both ICS dynamics (asynchronous and sequential), considering a distribution of angles peaked at 0◦ but ranging between 0◦ and 180◦ and U2 which ranges from 0.1 to 2 eV (Fig. 5). As for the synchronous concerted fragmentation we have considered a larger variation range of the angle ˛ (Eq. (3)) but the same uncertainty in the total available energy as in the case of the ICS. Despite this, the calculated features in the (T1 , T2 ) map are quite different from those observed in the experiment. Indeed the shape of the peaks in the case of the synchronous decay remains too narrow with respect to the case of the ICS. The results suggest that the fragmentation is stepwise and takes place via ICS. However the observation that the slope and the shape of the features in the (T1 , T2 ) maps lead to different ICS dynamics, may be explained assuming that most of the molecules undergo a very fast break-up, retaining the alignment between the two step of fragmentation (slope −1.09), while part dissociates following a slower decay process leading to a release of the neutral in any direction (shape of the features). In this regard, while our simulation allows the disentangling of the two ICS models, the present data seem to prevent a clear separation. Whether this is due to the experimental uncertainty affecting the data or this is intrinsic in the specific fragmentation process investigated is not known. In the literature a similar situation has been already reported in the case of CF2 ClBr [9]. Indeed, the measured PEPIPICO features show a “twist”: i.e. the most intense part of the feature shows a slope different from the less intense one. Eland and Treves-Brown [9] suggested that either two concurrent mechanisms or a mechanism occurring following different dynamics may be responsible of the observation. 5. Conclusion The fragmentation of a polyatomic molecular dication studied by ion–ion coincidence techniques has been investigated by Monte Carlo simulations which can take into account realistic experimental conditions. The effect of the strength of the extraction field used in the experiment has been studied. The case of three body fragmentation of the methane dication has been investigated considering both an initial charge separation or a synchronous concerted decay. The results show that the use of low extraction fields does not prevent the identification of the fragmentation mechanisms, because different mechanisms still lead to different shapes in the features observed in the (T1 , T2 ) maps. Moreover also basic quantities such as the slope of the features in the case of the initial
R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
charge separation can be extracted with sufficient accuracy from the maps obtained with a low extraction field. A comparison of the simulation with the experimental results show that the most likely process occurring for the considered dication state is ICS. Moreover, the dynamics of the fragmentation through the ICS model has been discussed: while the general shape of the experimental maps are attributed to a sequential decay process, the values of the slope of the features can only be explained with an alignment of the two fragmentation axes. Acknowledgements Work partially supported by FIRB Projects “Dinamica microscopica delle reattività chimica” and “Sorgente evoluta di radiazione coerente nei raggi X”. References [1] R. Flammini, M. Satta, E. Fainelli, G. Alberti, F. Maracci, L. Avaldi, New J. Phys. 11 (2009) 083006. [2] J.H.D. Eland, F.S. Wort, R.N. Royds, J. Electron Spectrosc. Relat. Phenom. 41 (1986) 297. [3] L.J. Frasinsky, M. Stankiewicz, K.J. Randall, P.A. Hatherly, K. Codling, J. Phys. B 19 (1986) L819. [4] M. Simon, T. LeBrun, P. Morin, M. Lavollée, J.L. Maréchal, Nucl. Instrum. Meth. B 62 (1991) 167.
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Journal of Electron Spectroscopy and Related Phenomena journal homepage: www.elsevier.com/locate/elspec
Ion–ion coincidence experiments with low extraction fields R. Flammini ∗ , E. Fainelli, L. Avaldi IMIP-CNR Istituto di Metodologie Inorganiche e dei Plasmi, Via Salaria km 29.300, 00019 Monterotondo Scalo, Roma, Italy
a r t i c l e
i n f o
Article history: Received 6 November 2009 Received in revised form 6 February 2010 Accepted 21 March 2010 Available online 8 April 2010 Keywords: Ion–ion Coincidence Map Methane Simulation Concerted Synchronous Asynchronous Auger decay Dication
a b s t r a c t The fragmentation of a polyatomic molecular dication has been investigated by means of a Monte Carlo simulation which can take into account realistic experimental conditions. The simulation applied to the three body process CH4 2+ → CH2 + + H+ + H shows that the low angular acceptance, consequence of the low extraction field, does not prevent the distinction between the initial charge separation and the synchronous concerted decay mechanisms, which lead to the same final state. The comparison of the results with recent experiments [1] confirms that an initial charge separation with a following loss of a hydrogen atom describes better the experimental observations. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Experiments where two or more charged fragments are detected via time coincidence techniques represent the most suitable approach to the investigation of the fragmentation of polyatomic molecular dications. In these experiments an ion pair or an ion pair in coincidence with an electron are detected. The goal is to identify the different fragmentation patterns depending on the dication state, to measure the energy and angular distributions of the fragments and to deduce the fragmentation mechanism. The technique introduced in the eighties with laboratory photon sources [2], largely benefitted by the development of lasers and synchrotron radiation [3,4], as well as position sensitive detectors [5,6]. The core tool for these experiments is represented by an ion Time-of-Flight (TOF) spectrometer, which, via the measurement of the time T1 and T2 needed for the fragments to reach the detector from the interaction region, allows the determination of their mass and their kinetic energy. The results are usually represented by two dimensional maps with the arrival times of the fragments on the axes. Correlated ion pairs result in features with shapes strongly dependent on the fragmentation process which
∗ Corresponding author. E-mail address: roberto.fl[email protected] (R. Flammini). 0368-2048/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2010.03.015
generated them. This has been proved by a series of simulations which consider the full angular acceptance in the spectrometer [7–13]. A full angular acceptance is achieved in experiments where strong extraction fields (e.g. a few hundreds V/cm) are applied to the interaction region. However, experiments have also been performed with low extraction fields because they allow the measurement of the kinetic energy distribution of the ions with higher resolution [1,14–16]. The drawback in these latter experiments is the low angular acceptance. This might question the possibility to extract information on the fragmentation mechanisms, because only part of the features due to the correlated pair are observed in the (T1 , T2 ) maps. Here we show with a realistic simulation that also with low extraction fields the different mechanisms leading to the fragmentation of a dication can be disentangled. As a case study we will use the three body reaction CH4 2+ → CH2 + + H+ + H studied in Auger electron–ion [17], photoelectron–ion [7] as well as ion–ion coincidence experiments [1,18]. In particular the results of this simulation will be compared with the experimental data obtained in an Auger electron–ion–ion coincidence experiment. Thus in Section 2 the experimental apparatus used to collect this data is presented. In Section 3 the details of the simulation procedure are described, while the results of the simulations for the two different fragmentation mechanisms under consideration as well as the comparison with the experimental results are presented and discussed in Section 4. Finally some conclusions are collected in Section 5.
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2. Experimental A detailed description of the experimental setup and procedures of the data collection have been reported elsewhere [19]. In the following only some details relevant to the present work are summarized. The vacuum chamber (base pressure ≤10−7 mbar) used for these experiments is equipped with two spectrometers: a Wiley-McLaren Time-of-Flight mass spectrometer (TOF-MS) for the detection of ions and a Cylindrical Mirror Analyzer (CMA) placed in front of the TOF-MS for the electron detection. A DC extraction field of 120 V/cm is applied to the interaction region to extract the ions. The CMA has an angular acceptance of ±7◦ around the angle = 42.7◦ . This results in an accepted geometrical solid angle of ˝ = 1.53 sterad. The electron energy resolution, E/E, is about 1.1%. This value is mainly determined by the size of the interaction zone which is about 0.1 and 2–3 mm, parallel and normal to the extraction field, respectively. With such an intrinsic energy resolution the presence of a DC field in the interaction region does not degrade the energy resolution of the Auger spectra measured by the CMA. The electron gun, has been operated at 4 keV incident energy and at a current I ≤ 1 nA during the present measurements. The Auger electron–ion coincidence electronics is based on the use of a CAMAC time-to-digital converter (TDC LeCroy 4208), operated in a multihit configuration with a common start. The pulses of the channeltron multiplier mounted at the exit slit of the CMA, after being properly amplified, discriminated (Philips Scientific 704) and delayed (Philips Scientific 794) provide the common start for the TDC and the end of the time acquisition window (10 s). The stop signals are provided by the pulses from the two Micro Channel Plates (MCP) mounted in the chevron configuration at the end of the TOF-MS. A personal computer governs the data acquisition via a CAMAC crate controller (CAEN C111), does a preliminary analysis and displays the Auger electron–ion coincidence on-line. The triple coincidence spectra are built a posteriori. The intensity of the incident electron beam and the density of the gas target (leading to ion and electron count rates of 120 kHz and 20 Hz, respectively) ensure an almost constant contribution of random coincidences over the full time spectrum investigated. In such conditions an accumulation time of about 100 h for each Auger electron–ion–ion coincidence map is needed. 3. Modeling and simulation In the simulation we have adopted the following assumptions [20]: the precursor dication has no or negligible linear momentum with respect to the kinetic fragments and its lifetime is short enough to assure that the fragmentation occurs within the interaction region; the momenta associated with the two charged fragments are well defined once the energy available in the dissociation process has been defined; conservation of the linear momentum in the first and the second step of the dissociation
holds; the directions of the fragments with respect to a fixed laboratory frame are randomly distributed (the target molecules are neither oriented nor aligned); the excitation source is unpolarized. The total TOF of each fragment ion from the center of the interaction region to the detector (Fig. 1), is the sum of three contributions associated with the three sections of the TOF spectrometer (named the extraction, the acceleration and the field free zones, labeled 1, 2 and 3, respectively): T = t1 + t2 + t3
1 t1 = a1 t2 =
2a1
1 a2
2
− x0
2a2 d −
− t3 =
s
2a1
s
− x0
2
s 2
+ v20 cos2 () − v0 cos()
+ 2a1
+ v20
s 2
− x0
+ v20 cos2 ()
cos2 ()
D−d
2a2 (s/2 − x0 ) + v20 cos2 ()
where m and q are the mass and charge of the fragment, and the accelerations in the extraction and acceleration zone, respectively, are defined as a1 =
q(Vs − Vx0 ) , m
a2 =
q(Vd − Vs ) m(s/2 − x0 )
where s, d and D are the length of the extraction, acceleration and field free regions, respectively. The angle between the direction of the ion and the axis of the spectrometer (our laboratory frame) is randomly distributed within the range 0–180◦ for the ICS (Initial Charge Separation) and 0–360◦ for the synchronous decay mechanisms. Due to the cylindrical symmetry of the setup in the simulation, there is no need to define other angles to explore all the possible orientations of the dication. Vs and Vd are the extraction and acceleration voltages, respectively. For the ion TOF spectrometer we assume the Wiley-McLaren prescriptions to achieve time focussing conditions [19,21] which link Vs and Vd once the geometrical parameters s, d and D are fixed. T is proportional to the projection of the initial momentum of the ion along the axis of the spectrometer, while the component perpendicular to the axis of the spectrometer is used to determine the probability that the ion hits the detector. In the simulations this is crucial: when the extraction field is not strong enough to bend all the trajectories towards the detector, the ions with a large component of the momentum perpendicular to the spectrometer axis are not detected. The interaction zone has been represented by a cylinder (100 m diameter and 700 m length). In the simulation the initial position, the energy and direction of the ion pairs were generated randomly. According to the assumptions made at the beginning of this section an isotropic angular distribution and a flat energy distribution of the ions have been considered. For each fragmentation mechanism fifty thousands trajectories have been computed. 4. Results
Fig. 1. Scheme of the TOF spectrometer used in the simulations. The labels 1, 2 and 3 correspond to the extraction, acceleration and field free zones, respectively. As an example, the trajectories of two ions with opposite initial momentum have been drawn (dashed line). In the simulation s = 1 cm, d = 5.4 cm, D = 55.9 cm as in Ref. [19].
Let’s consider the three body reaction CH4 2+ → CH2 + + H+ + H studied in [1]. In those experiments the dication was formed via inner shell ionization followed by Auger electron decay and the CH2 + /H+ ion pair was measured in coincidence with an Auger electron, which allows the selection of the initial dication state. To discuss in detail the mechanisms leading to the fragmentation a proper definition of the sequence of events occurring is needed. The nomenclature proposed by Maul and Gericke [22] points to the time dynamics of the process using terms like synchronous, asynchronous and sequential fragmentation, while that of Eland [23],
R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
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Fig. 2. Results of the Monte Carlo simulation of the ion–ion maps and time distributions for the CH2 + /H+ pair using the ICS model in the case of a sequential decay. Vs = 1200 and 120 V/cm, in (a) and (b), respectively. Beside each map the projections along the two axes are shown. A schematic of the dissociation process is shown in the bottom panel. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
based on the concepts of initial/deferred charge separation is more effective for the description of the mechanism of the dissociation. In the following we will make use of both these nomenclatures. The reaction CH4 2+ → CH2 + + H+ + H may proceed either via an initial charge separation (ICS) and then the loss of a H atom
where U1 and U2 are the overall energies available to the fragments in the two steps. Then, the momenta of each ion can be extracted:
CH4 2+ → CH3 ∗+ − H+
The angle ˛ takes into account that the axes of the first and second fragmentation steps may be not aligned as shown in Fig. 2, where a sketch of the reaction is reported. In Fig. 2 we show the simulation using the ICS model in the case in which the methyl ion may rotate freely around all the possible axes of the molecule, before the release of the hydrogen atom. In each figure also the time distribution relative to each ion is reported. The process has been simulated with Vs = 1200 and 120 V/cm. In this case the shape of the feature in the ion–ion map is a lozenge enlarged along the vertical axis. This corresponds to a spread in the range of values of the momentum of the CH2 + ion, because the momentum of the neutral is subtracted or added to the momentum of the methylene ion, depending on their relative orientation. When the second step of the fragmentation occurs (red arrows) all the values of ˛ are equally probable and no memory of the orientation of the first fragmentation axis (blue arrows) is retained. Considering the experimental results given in [1] where the total kinetic energy shared by H+ –CH2 + pair is about 6 ± 1 eV we used in the simulation U2 /U1 = 0.03. In the simulation U1 ranges from 6.0 to 6.06 eV and U2 from 0 to 0.2 eV. Due to the narrow energy range set for U1 and U2 both projections show a backward-forward splitting, which in turn affects the central part of the peak in the ion–ion map, reducing its intensity. Apart from the shape of the feature the most relevant quantity which characterizes the fragmentation mechanism is its slope. In 2-body reactions the momentum conservation implies the slope to be −1, while in 3-body reactions, it can assume almost
then
CH3 + → CH2 + − H
(1)
which therefore occurs in two steps, or via a synchronous concerted fragmentation CH4 2+ → CH2 + − H − H+
(2)
where the break-up in three fragments of the dication occurs simultaneously. In the first case if the release of the H atom (in the second step) occurs in a time shorter than the rotational period of the methyl ion we are in the case of an asynchronous concerted fragmentation, otherwise the process is purely sequential [22]. In the next subsections the simulation will be used to calculate the (T1 , T2 ) maps of the CH2 + /H+ pair and separately the time distributions of the two ions for all the considered mechanisms. 4.1. Fragmentation with an initial charge separation (ICS) If the reaction proceeds via an initial charge separation followed by the release of a H atom the conservation of the momenta holds in both steps and p and q, the momenta of the fragments in the first and second fragmentation steps, respectively are:
p=
2mCH3 mH mCH4
U1
and
q=
2mH mCH2 mCH3
U2
pH + = −pCH + = −p 3
and
pCH + = 2
mCH2 mCH3
p + q cos ˛
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R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
any value [23]. The slope (pCH + /pH + ) associated with this kind of 2
reaction is simply −(mCH2 /mCH3 ) because the average over 2 of cos(˛) does not alter the value of the slope even though U2 = / 0. The effect of U2 = / 0 is only the broadening of the features along the axis of the heavier fragment. In both figures beside each map the value of the slope (M) has been noted. The slope has been extracted from the data, according to the mathematical procedure suggested in [24] and is about −0.93, the value expected by the mass ratio mCH2 /mCH3 . The difference in the values of the slope for the two Vs values is of the order of 10−2 , thus the calculation of the slope seems not to be affected by the small angular acceptance. The other case to be considered for the ICS is when the axes of the two fragmentation steps are aligned. Indeed, this can happen during the charge separation in the first step because an electric field switches on along the H+ –CH3 + direction. When the second step of the dissociation occurs and a H atom departs, the stretching of the C–H bond produces a dipole moment in the methyl ion. This dipole moment in turn induces an orientation of the methyl ion along the first dissociation axis, i.e. the H3 C+ –H+ axis. This is due to the fact that the methyl ion tends to screen the charge of the proton with the C–H bond. The alignment is effective in a time shorter (5 ps) than the rotational period of the methyl ion (0.1 ns). This behavior for the methyl ion was proposed in [1] and is similar to that discussed in the literature in the case of the alignment of the XCN+ [10]. Thus in the simulation we have assigned to the angle ˛ values ranging between 0◦ and 10◦ . The process has been simulated using two different values of the extraction field Vs = 1200 and 120 V/cm, respectively, and the results of the simulation are shown in Fig. 3(a) and (b), respectively. At the bottom a scheme of the fragmentation process is also shown. Here the same U2 /U1 ratio and U1 , U2 values of the case of the sequential decay have been
used. The CH2 + radical is accelerated in both the first (blue arrow) and second (red arrow) steps of the dissociation, due to the alignment of the fragmentation axes. In Fig. 3(a), where the process has been simulated with Vs = 1200 V/cm, we see that the feature relative to the CH2 + /H+ pair in the (T1 , T2 ) map is given by a narrow lozenge with the intensity concentrated at its extremes. The value of −1.090 has been extracted for the slope. This value clearly differs from −0.93, the value predicted for a pure sequential reaction. In Fig. 3(b) the simulation of the same process has been repeated with Vs = 120 V/cm. The ion time distributions reduce to two peaks because only the ions generated within a small cone in the forward and backward directions about the axis of the spectrometer are detected. In the 3D map, only the two features at the extreme of the lozenge survive. At a first sight the size of the features in Fig. 3(b) may appear smaller than those observed at 1200 V/cm (Fig. 3(a)). This is due to the change of the scale in the T1 and T2 axes because at 120 V/cm the difference in the arrival times of ions emitted in the forward/backward direction is larger than the splitting recorded at 1200 V/cm. The slope extracted from the map using the same mathematical procedure as in the previous case is −1.092 (Fig. 3(b)). The simulation has been repeated for several values of the extraction field. The difference in the value of the slope is always of the order of 10−3 . This proves that in the case of the ICS fragmentation the use of low extraction fields does not prevent the extraction of basic information which characterizes these fragmentation processes. 4.2. Synchronous concerted fragmentation When the dication suffers a simultaneous break-up into three fragments, the momentum and energy conservation can be applied (Eq. (2)), to extract the values of the momentum of each charged
Fig. 3. Results of the Monte Carlo simulation of the ion–ion maps and time distributions for the CH2 + /H+ pair in the case of the asynchronous ICS model. Vs = 1200 and 120 V/cm, in (a) and (b), respectively. Beside each map the projections along the two axes are shown. A schematic of the dissociation process is shown in the bottom panel.
R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
fragment (Eq. (3)), as reported in [22]. A schematic of the process where the two bonds H2 C+ –H+ and the H2 C+ –H are cleaved at the same time is shown at the bottom of Fig. 4. Using the conservation of the momentum and energy, pCH + + pH + + pH = 0, 2
kin kin kin ε = ECH + + EH + + EH 2
the momenta of all the fragments can be inferred. Here we assume that the CH2 + and H are formed in their ground state and ε (the total energy available for the fragmentation) is expressed only in terms of kinetic energy: kin ECH + = 2
ε 1 + (1 + tan(˛/2))(mCH + /(4H + ,H )) 2
where H + ,H = mH + mH /(mH + + mH ) is the reduced mass of H+ and H. The expression of the momenta of the two charged fragments
43
are then pCH + = 2
2H + ,H (ε − E kin+ ) CH
2
and
pH + = −2pCH + cos 2
˛ 2
(3)
The bond angle ˛, defined as the angle formed by the momenta of H+ and H fragments at the time of the break-up, is the only parameter necessary to describe unambiguously the decay and to define the direction of the CH2 + ion. In the case of the synchronous concerted fragmentation we have performed simulations for four different cases, changing both the value of the extraction field and the range of the kinetic energy of the fragments. The results of our simulations are summarized in Fig. 4. In Fig. 4(a) we have used Vs = 1200 V/cm and ε ranging from 27 meV (kinetic energy at room temperature) to 6 eV. The feature in the 3D map is an ellipse, whose orientation and size depend on the direction of emission of the neutral fragment, i.e. on the angle ˛. This is consistent with the results obtained by Le Brun [25]. When Vs = 120 V/cm is used (Fig. 4(b)), the top-right and bottom-left part of the ellipse are cut.
Fig. 4. Results of the Monte Carlo simulation of the ion–ion maps and time distributions for the CH2 + /H+ pair in the case of synchronous concerted decay. Vs = 1200 V/cm in (a) and (c), 120 V/cm in (b) and (d); 0.027 ≤ ε ≤ 6 eV in (a) and (b), ε ∼ 6 eV in (c) and (d). A schematic of the process is shown in the bottom panel.
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R. Flammini et al. / Journal of Electron Spectroscopy and Related Phenomena 180 (2010) 39–45
Fig. 5. Experimental Auger electron–ion–ion coincidence map relative to the CH2 + /H+ ion pair measured at an Auger electron of 238 eV (center). On the left (right) side, the simulation using the asynchronous ICS model (synchronous concerted decay) model are shown, respectively.
This can be understood if we consider that these parts of the map correspond to pair of ions ejected in the same half-space, either towards the detector (forward–forward) or in the opposite direction (backward–backward). The angle between the ejected CH2 + /H+ pair, is 180◦ − ˛/2, therefore it is likely that one or both ions do not hit the detector. Consistently with the case of the asynchronous fragmentation discussed in the previous section we limited ε to about 6 eV in Fig. 4(c) and (d). In the case of Vs = 1200 V/cm we still observe a feature with the contour of an ellipse, but with a reduced density in the central part. This is due to the narrow range of energy shared by the three fragments. In Fig. 4(d), where Vs = 120 V/cm is used, the effects of the narrow range of energy and the low extraction field add up, and the feature reduces to two baffles corresponding to the extreme parts of the ellipse. From the results of Fig. 4 it is clear that even with low extraction fields the shape of the feature preserves the information on the dissociation mechanism. Also in this case the features in the map are elongated along the T2 axis. This indicates a broad time distribution of the heavier fragment. However, they have a shape completely different from that of the ICS fragmentation shown in Figs. 3 and 4. 4.3. Comparison with the experiment The comparison of the simulation with the results of the Auger electron–ion–ion coincidence experiments [1] has been done for the case of the experiment performed at an Auger electron energy of 238 ± 3 eV, which corresponds to the formation of the CH4 2+ dication in the 3,1 T2 states at about 54.8 eV binding energy. In order to make a realistic comparison with the experiments the size of the interaction region, the total energy ε in the case of the synchronous concerted fragmentation or the U1 and U2 values in the case of the asynchronous fragmentation as well as the angle ˛ have been used as adjustable parameters. Moreover the results of the simulations have been binned in time intervals of 11 ns as done in the experiment. The experimental results from Ref. [1] are reported in the central panel of Fig. 5. On either sides of the experimental map, we show the results of the simulation using the two fragmentation models described in the previous sections. The two main experimental observations are the value of the slope that is −1.09 ± 0.18 and the broadening of the features along the axis of the heavier fragment. Let’s begin with the simulation according the ICS models. A reasonable representation of the data is achieved considering a target length of a few mm. This value is consistent with the overlap between the effusive gas beam and an electron beam placed at least 2 mm from the gas needle of the setup as described in [19]. As for the values of the angle ˛ and the energy U2 a more intriguing result has been obtained. Indeed, the experimental slope value of −1.09 is well reproduced by a simulation assuming an asynchronous concerted fragmentation with an angle ˛ ranging from 0◦ to 10◦ and an energy value for U2 of
less than 0.2 eV, thus in conditions of a clear alignment between the two steps of fragmentation. However, the shape of the features (not shown here) is not broadened enough along the vertical axis as in the experimental maps. The broadening is well described when 0◦ < ˛ < 180◦ is accompanied by a U2 value ranging from 0.1 to 2 eV, thus in a pure sequential scenario. The best agreement with the experiment is achieved when simulation takes into account both ICS dynamics (asynchronous and sequential), considering a distribution of angles peaked at 0◦ but ranging between 0◦ and 180◦ and U2 which ranges from 0.1 to 2 eV (Fig. 5). As for the synchronous concerted fragmentation we have considered a larger variation range of the angle ˛ (Eq. (3)) but the same uncertainty in the total available energy as in the case of the ICS. Despite this, the calculated features in the (T1 , T2 ) map are quite different from those observed in the experiment. Indeed the shape of the peaks in the case of the synchronous decay remains too narrow with respect to the case of the ICS. The results suggest that the fragmentation is stepwise and takes place via ICS. However the observation that the slope and the shape of the features in the (T1 , T2 ) maps lead to different ICS dynamics, may be explained assuming that most of the molecules undergo a very fast break-up, retaining the alignment between the two step of fragmentation (slope −1.09), while part dissociates following a slower decay process leading to a release of the neutral in any direction (shape of the features). In this regard, while our simulation allows the disentangling of the two ICS models, the present data seem to prevent a clear separation. Whether this is due to the experimental uncertainty affecting the data or this is intrinsic in the specific fragmentation process investigated is not known. In the literature a similar situation has been already reported in the case of CF2 ClBr [9]. Indeed, the measured PEPIPICO features show a “twist”: i.e. the most intense part of the feature shows a slope different from the less intense one. Eland and Treves-Brown [9] suggested that either two concurrent mechanisms or a mechanism occurring following different dynamics may be responsible of the observation. 5. Conclusion The fragmentation of a polyatomic molecular dication studied by ion–ion coincidence techniques has been investigated by Monte Carlo simulations which can take into account realistic experimental conditions. The effect of the strength of the extraction field used in the experiment has been studied. The case of three body fragmentation of the methane dication has been investigated considering both an initial charge separation or a synchronous concerted decay. The results show that the use of low extraction fields does not prevent the identification of the fragmentation mechanisms, because different mechanisms still lead to different shapes in the features observed in the (T1 , T2 ) maps. Moreover also basic quantities such as the slope of the features in the case of the initial
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charge separation can be extracted with sufficient accuracy from the maps obtained with a low extraction field. A comparison of the simulation with the experimental results show that the most likely process occurring for the considered dication state is ICS. Moreover, the dynamics of the fragmentation through the ICS model has been discussed: while the general shape of the experimental maps are attributed to a sequential decay process, the values of the slope of the features can only be explained with an alignment of the two fragmentation axes. Acknowledgements Work partially supported by FIRB Projects “Dinamica microscopica delle reattività chimica” and “Sorgente evoluta di radiazione coerente nei raggi X”. References [1] R. Flammini, M. Satta, E. Fainelli, G. Alberti, F. Maracci, L. Avaldi, New J. Phys. 11 (2009) 083006. [2] J.H.D. Eland, F.S. Wort, R.N. Royds, J. Electron Spectrosc. Relat. Phenom. 41 (1986) 297. [3] L.J. Frasinsky, M. Stankiewicz, K.J. Randall, P.A. Hatherly, K. Codling, J. Phys. B 19 (1986) L819. [4] M. Simon, T. LeBrun, P. Morin, M. Lavollée, J.L. Maréchal, Nucl. Instrum. Meth. B 62 (1991) 167.
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