- Email: [email protected]
Collisions of electrons with highly-charged ions
Nuclear Instruments and Methods in Physics Research B 98 (199.5) 107-113
Beam Interactions with Materials&Atoms
ELSEVIER
Collisions of electrons with highly-charged G.H. Dunn a3*, N. DjuriC ‘, Y-S Chung a, M. Bannister
ions
b, A.C.H. Smith ’
a JILA of the National Institure of Standards and Technology and the lJnit,ersity of Colorado, Boulder, CO 80309-0440, ’ Oak Ridge National LaboraIm): Oak Ridge, TN 37831, USA ’ UtGersity College, Londott WCIE6BT, United Kingdom
USA
Abstract This progress report, in addition to describing recent work in the authors’ laboratory, highlights the general character and importance of electron collisions with highly-charged ions (HCI) and describes major advances in the field since the previous conference on the subject. Thus, while the authors’ principle efforts are currently directed toward investigation of excitation of HCI, there have been very notable advances by others in the areas of ionization and recombination and an attempt is made to put these into context of the field in general. Also, for the first time, significant progress is now being made by others in experimental investigation of elastic scattering of electrons from HCI.
1. Introduction Infinite numbers of infinite series of resonances enrich the study of collisions between electrons and highlycharged ions (HCI), which then takes on the mantle of being both intensely interesting and vitally important. Resonances can and do alter cross sections enough that their presence substantially modifies the behavior of plasmas such as those in hot astrophysical environments, controlled fusion devices, and X-ray lasers, i.e. the environments where HCI are major species. Thus, the modelling of these environments is crucially dependent upon electron-HCI collision data including resonance effects. Further enriching this scene is the fact that under some circumstances the resonances in electron-HCI collisions can be varied (controlled) by the presence of external fields or collisions - a feature which is sometimes very dramatic for dielectronic recombination. As noted, there are many motivations for the study of such collisions, and one currently stimulating our own work is the need to obtain experimental benchmarks so that theory can be confidently used to obtain the data necessary to model the edge plasma [I] of controlled fusion reactors. The edge plasma plays an important role in the heating and stability of fusion plasmas. The plasma near the walls of a fusion device is typically characterized by low temperatures in the region T = 2-200 eV and particle densities in the range 10”-10’5 cm-a. Character-
* Corresponding author, tel. + 1 303 492 7824, fax + 1 303 492 5235, E-mail: [email protected].
istic of the low temperatures and proximity to the vessel walls, particle constituents are atoms, molecules and ions of hydrogen, helium, carbon, oxygen, and a host of metal and other impurities of low fractional content coming from walls, limiters and divertors. Ions are typically in charge states up to about 10. Supposing charge neutrality and comparable electron and ion temperatures, electron collisions dominate over those between heavy particles such as atoms or ions, since the collision frequencies are greater than those between heavy particles by the ratio of velocities, N (1836 A)‘/’ where A is the atomic mass. Only highly-resonant heavyparticle collisions, such as resonant charge transfer, will have cross sections large enough to offset the velocity factor and give a rate comparable to that for electron collisions. In a preponderance of cases, resonances in electron-ion collisions may be thought of as starting with a “dielectronic capture”. Consider an electron incident on an ion with just E less energy than E,,, the energy needed to excite a core electron from the initial state i to an excited state j. In the attractive Coulomb field, the incident electron gains kinetic energy, so that in close proximity to the ion there is more than enough energy to excite the core electron. Supposing that it does so, however, the incident electron is left bound with energy E - there has been a capture of one electron associated with the excitation of another. Obviously, due to quantization of energy, this can occur only if E corresponds to a bound level - i.e. the process is “resonant”. The resulting doubly excited state is referred to by various terms: resonance, compound state, complex, etc. Stabilization of the compound state can occur along a variety of paths: (1) If the two electrons
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00084-4
3.1. COLLISIONS WITH ELECTRONS
108
G.H. Dunn et al. /Nucl. Instr. and Meth. in Phys. Res. B 98 (199.5)107-113
share their energy, the incident electron may go out again with energy, Ei, - E, and a resonance feature will appear in the cross section for elastic scattering. (2) If one of the excited electrons radiates some energy, the system stabilizes and dielectronic recombination has occurred. (3) If the core electron which became excited was an inner-shell electron, there may be enough energy in the compound state that the electron can share its energy both with the incident electron and another outer shell electron(s), leading to double (multiple) autoionization, and resonant-excitation-double-autoionization (REDA) has occurred. (4) The excited core electron may share its energy with the incident electron thus ejecting it, but if, in the process, it moves into state k rather than returning to state i as in (1) above, then resonant excitation to state k will have occurred - now appearing as a resonance feature in the excitation cross section. In each of these cases the cross section to obtain the stabilized product can approximately be expressed as a multi-step process, so that
As Aan +A, + . . +A,
.
(1)
I
Here a,” is the dielectronic capture cross section with the incident electron’s being captured into level n. It is proportional ( 5 >, through detailed balance, to the autoionization rate A,” of the doubly excited state. The branching ratio to the final state considered B, is equal to the ratio shown in brackets involving decay rates via various channels including the rate A, to the final state considered, and the sum is over all n. When A, is a radiative rate (A,), as in the case of dielectronic recombination (DR), the sum in Eq. (1) becomes sensitive to the relative size of A, and the autoionization rate A, , and it has been shown [2,3] and observed [4] that elect& fields can dramatically affect the number of terms contributing in a significant way to the sum. Thus, for dielectronic recombination one can “tune” the value of the cross section with external fields. However, this tuning effect is not likely to be present to any great extent for the other stabilization routes, and such an effect has been neither seen nor predicted.
2. Ionization, recombination
and elastic scattering
This progress report primarily focuses on work in the authors’ laboratory in the area of electron-ion excitation. However, in this volume there are no other reviews or progress reports on electron-ion processes. Given that there have been very significant recent strides in observing ionization, recombination, and elastic scattering, we here take the opportunity to briefly summarize some of the major advances in those other areas which have occurred since the Sixth Conference on the Physics of Highly
Charged Ions. In so doing, we call attention in some instances to other papers in this volume. Before discussing individual processes, it is important to emphasize a major advance in the technology of electron coolers at ion storage rings, since this has been the venue for most of the recombination work in recent years, and - as noted below - is now becoming important for ionization work as well. The critical stride [5] was the improvement of the efficiency of electron cooling by adiabatically expanding the electron beam in a decreasing magnetic field, thereby lowering the transverse electron temperature. This, of course, has resulted in vastly improved electron-energy distributions in electron-ion studies. The improvement has been implemented at Stockholm, where it was invented, at Heidelberg, and at Aarhus. 2.1. ionization The experimental study of electron-impact ionization of ions has been pursued successfully and with great expertise over some years [6] and the techniques and understanding are relatively mature. Nevertheless, there have been some very notable advances recently, and two stand out in particular. First, ion-storage-ring technology has now been applied to ionization by taking the rather obvious step of installing a detector in the appropriate location inside the ring after the cooler (this, as opposed to outside the ring for recombination studies). Taken together with the implementation of the improved perpendicular cooling mentioned above, extraordinary results have been obtained on Li-like C114+ and Si”’ [7], and on Na-like Fe”+ [8]. Observation of the clear REDA peaks is especially gratifying for the latter case, since it was for Fet5+ that the process was first hypothesized [9]. The exciting detailed experimental data will now provide a standard against which the theory can be judged. Comparisons at this point indicate that it is not routine to obtain agreement, and theoretical development and experimental exploration still are necessary. The second breakthrough which we call attention to is the measurement of ionization cross sections for very-high Z hydrogen like ions at high energies [lo] in Super EBIT. This testing of ionization theory under highly relativistic conditions suggests through the early data that the theory is missing something - agreement between theory and experiment is not good. 2.2. Recombination As already mentioned, the study of electron recombination with ions is now almost exclusively performed using ion-storage rings. An excellent overview of the field covering work over the past decade can be found in the NATO monograph [ll] on the subject. Again, the field has become relatively mature, but there are a number of outstand-
G.H. Dunn et al. /Nacl. Instr. and Meth. in Phys. Res. B 98 (1995) 107-113 ing questions and issues, and there have been recent advances in the field which will be mentioned. Because the process in its entirety involves resonances, there are already dramatic results [7,12,13], and the field will continue to benefit greatly from the recent perpendicular cooling innovation mentioned above in terms of obtaining much more highly-resolved resonance structures. Indeed, resolution is good enough that precision spectroscopy and QED tests are being seriously considered [14] using dielectronic recombination resonances. Measurements on radiative recombination “at zero” relative energy of electrons and ions continue to produce anomalously large cross section values [13,15]. This anomaly, which has been reported a number of times reaching as far back as four years, remains to be explained. Three-body processes and interference of radiative and dielectronic recombination have been variously invoked in unsuccessful attempts to resolve this. Finally, in this brief discussion of recombination advances and outstanding issues, it should be mentioned that there is only one clear-cut experiment [4] which tests the theory of field enhancement of DR. This important phenomenon has suffered benign neglect since the nearly sole means for studying DR has come to reside at storage rings. An important exception to this is a recent experiment [16] on C3’ using a crossed beams method and detecting photons and product ions in coincidence [17]. Just as in earlier experiments at Oak Ridge where anomalously large field enhancements of DR cross sections were found for Li-like ions, (summarized in Ref. [ll]) so also is it the case in the recent Harvard experiment. Contrary to the Oak Ridge experiments, however, the ambient electric field in which the collisions take place is well-defined and known. The statistical uncertainty in the measurement is, however, large enough that the disagreement between experiment and theory is inconclusive; i.e. the disagreement is only suggestive. The interesting physics involved in this enhancement and the potential importance of it in plasma environments invites further investigation. One would hope for a means to achieve this at storage rings. 2.3. Elastic scattering
It seems paradoxical that complex processes such as already discussed have been studied over a period of many years and that it is only in the past few years that seemingly-more-simple elastic scattering of electrons from ions has been measured. These studies were ushered in by Huber et al. [l&19] who measured relative differential elastic cross sections for electron scattering from Xe6+ and from Ba2+ using a colliding beams technique. Recently, another method has been introduced [20] which leads to measurements of integrated elastic backscattering. Both methods give results with significant deviations from Rutherford scattering, but the limited results so far seem in all cases to agree with more complete theory. As dis-
cussed, the field is new and no dielectronic have as yet been observed.
3. Excitation
109 resonances
- methods
Electron-impact excitation of HCI has been studied by numerous techniques over a period of about twenty five years; yet despite this, there remains a serious need for experiments which will adequately test theoretical calculations, especially when resonances play a role. The topic has recently been reviewed by Phaneuf [21], and a complete discussion of techniques and listing of cases studied can be found in the thesis by Bell [22]. Here, we merely list the different techniques and give only brief comments on most of them. The reader is referred to the references above for more detail and for further references. 3.1. CBFR The crossed beams with forced radiation method was used early to measure excitation of the 2s state of hydrogen-like ions. The method yielded relative cross sections, and results were normalized to Born approximation calculations at high energy. 3.2. CB The crossed beams with fluorescence detection has been used for a great fraction of the absolute total cross section measurements for ion excitation. Absolute accuracies and precisions are good, but with detection sensitivities in the neighborhood of 10e4, the method is tedious and difficult, requiring absolute radiometry and detection of low signal levels in the presence of high backgrounds. 3.3. PL‘AS The plasma rate method was used in the late 1960’s and early 1970’s. Observations of fluorescence in a plasma along with electron density and temperature and ion density, coupled with modelling of the plasma with various assumptions allows extraction of the excitation rate coefficient. There are substantial uncertainties in the method, and it seems the method is no longer being pursued. 3.4. EA When an inner-shell electron is excited, autoionization may result. Thus, the observation of structural “features” in the ionization cross section at electron energies where there are inner shell excitation thresholds can often lead to information about the inner-shell excitation cross section. This EA method has the advantage that one generally collects 100% of the ionized products of the collision. It has the disadvantage that the branching ratios for autoion-
3.1. COLLISIONS WITH ELECTRONS
110
G.H. Dunn et al. /Nucl. lnstr. and Meth. in Phys. Rex El 98 (1995) 107-113
ization must be assumed or calculated, and the (uncertain) background of underlying ionization must be subtracted.
In the crossed beams energy loss method electrons which have lost an amount of energy equal to the excitation energy are detected at what may typically be a variable angle. Thus, it is used to measure differential cross sections, supplying valuable information for testing theory which isn’t available in total cross section measurements. The angular range through which data can be collected is generally limited, and the results are relative cross sections which must then be normalized - typically to elastic cross sections. Progress with this method is reported in this volume [23]. A variant of the CBEL method in which electrons are collected over a broad angular range has recently been introduced for study of singly charged ions [24] and it is intended that it will be used for study of HCI as well. 3.6. EBIT/S The electron-beam ion trap (EBIT) and electron-beam ion source (EBIS) are used successfully to study a number of electron-ion collisions, including excitation. The Xradiation from the device is observed as a function of electron energy (which is momentarily changed from the equilibrium value). Cross section values are obtained by normalizing the signal to another signal for which the cross section is thought to be known - for example, radiative recombination in the case of EBIT. This method allows excitation measurements on very-highly-charged ions; and though the results are relative and normalized, it is generally felt that the normalization is quite secure. The electron energy resolution is quite bad - several tens of eV - but for processes being measured with thresholds at several keV, this probably isn’t as serious a deficiency as it sounds. 3.7. MEIBEL The merged-electron-ion beams energy loss method is currently being used in our laboratory for electron excitation of HCI. Progress using this technique will occupy the remainder of the discussion here, aside from summary remarks With this method, absolute total cross sections are measured near threshold, and gross features of differential cross sections are extracted. The technique features near total collection of collision products, resulting in a detection efficiency of about 70%, and an electron-energy resolution of about 0.2 eV. It has been used in our laboratory for measurements on C+ [25], Si3+ [26], Ar’+ [27], 0” [28], and Krbf [29]. A similar approach has been used by Chutjian et al. [30] for singly-charged ions, and implemen-
Fig. 1. Schematic view of the MEIBEL apparatus. The uniform magnetic field is in the z direction, the electric field in the y direction and E X B is in the Y direction.
tation of changes to enable measurements on HCI are in progress. The MEIBEL technique utilizes crossed electric and magnetic fields, E = Ej and B = Bk, and the properties of the trochoidal paths of charged particles in such fields. For these trajectories, we have, x = p/w, [ w, t - sin( w, t)], y = p/w, [l - COS(W,t)l, 2 = i,t, i = p [l - COS(W,t)], j = p sin( w, t), and i = i,, where p = E/B is the drift velocity in the x direction. It can be seen that after an integral number n of cyclotron periods, nT, = 2nn/w,, the particle velocity is equal to its initial velocity, its y coordinate has its initial value, and its x and z coordinates are advanced by pnT, and i,nT, respectively. Fig. 1, which is a schematic of the MEIBEL apparatus, illustrates how these properties are implemented in our laboratory. The apparatus is immersed in a uniform solenoidal magnetic field parallel to the incident ion beam. Electrons from an electron gun are focused into a region (the merger) having a transverse electric field of about 10 V/mm. Referring to the discussion above, for our case n is always 2; and after two periods, the electron velocity is again along the z axis, but the trajectory has been displaced from its initial x position by 2pT,. Multiply-charged ions from the Oak Ridge National Laboratory Electron Cyclotron Resonance Ion Source are merged with the electrons at the merger exit. Ions and electrons then travel together in an electric-field-free region (about 63.5 mm long) where the collisions take place. At the end of this collision region, the primary electrons and forward-travelling inelastically scattered electrons are separated by the action of a second pair of parallel plates (the demerger) with an electric field of about 2.5 V/mm. As in the case of the merger, the demerger plates are biased positive and negative with respect to the median plane. The demerger acts as an electron velocity-dispersion device, where the net velocity in the z direction and the drift velocity p in the x direction determine a position in a plane parallel to the y-z plane and at an x distance d from the beam axis. Unscattered electrons, deflected by the demerger through a
G.H. Dunn et al. /Nucl.
111
Instr. and Meth. in Phys. Rex B 98 (1995) 107-113
relatively small angle, are collected by a Faraday cup and their current is measured. Scattered electrons, deflected through much larger angles in the demerger, strike a position-sensitive detector (PSD) and are counted. Ions are deflected and collected in a Faraday cup and their current is measured. The operating pressure is approximately 1.5 X 10-s Pa. The measurement of the extent of electron and ion beam overlap (form factor) along the merge path is accomplished using a movable beam probe [31] employing fluorescent screen and digitized video techniques. Electrons scattered elastically at large angles by ions in the merge path could in principle also reach the detector, but are blocked from entering the demerger by a series of apertures. The signal on the PSD is accompanied by large background countrates due to electron and ion scattering on gas and surfaces. Because of the low signal-to-noise ratio (less than lo-* 1, both beams are chopped at 2 kHz in a phased four-way chopping scheme [28], and the detector output is accumulated in four histogramming memories according to position and temporal block. The four temporally distinguished memories correspond to different combinations of the beams’ being on and off so that (after correction for detection-system dead times) the memory contents can be appropriately added and subtracted to obtain the signal as a function of position. The excitation cross section is determined from the expression
where R is the observed signal countrate from detection of inelastically scattered electrons by the PSD, E the measured PSD detection efficiency, F the form factor, and lze, ~1~.I,, and Ii are the velocities and currents of the electrons and ions of charge e and qe, respectively. All quantities in the equation are absolutely determined so that the resultant measured cross sections are absolute.
LLiiiii Electron Energy IeVl Fig. 2. Absolute cross section versus electron energy for emission of 2p-2s radiation (15.5 nm) by electron impact on ground state C3+ ions. Points are from Ref. [32], theory (dashed curve. 2 state close coupling with exchange) is from Ref. [36] and is convoluted with the experimental energy distribution (solidcurve).
latter it is from a 7-state close coupling R-Matrix calculation [37]. Given the quality of agreement, there appears to be no good reason to pursue further experiments with this class of transition - theory appears to have the situation well in hand. However, some equivocation must be made in that in none of the experiments noted above were strong resonances encountered. In the cases of Si3+ [26] and Ar7+ [27] the experiments were limited to energies below the positions of predicted resonances. In the Ar7+ case there is a hint in the experimental rest&s of a resonance at 19 eV - below the 19.7 eV energy at which the first resonance is predicted, but the evidence is not clear.
2
4. Excitation
- results
Using the CB method, we have in the past measured excitation cross sections for the resonance lines of Li-like C3+ [32] and N4+ [33] and for Na-like Al’+ [34] and for a host of singly-ionized ions [35]. As already noted, with the MEIBEL technique we have measured excitation cross sections for resonance transitions for Li-like 05+ and Na-like Si3+ and Ar7+. In all these cases for resonance excitations, the agreement between experiment and theory is quite satisfactory and within combined uncertainties. Typical examples of results showing both experiment and theory are shown for the fluorescence measurements on C3+ [32] and the energy loss experiments on Ar’+ 1271 in Figs. 2 and 3 respectively. In the former case, the theory is two-state-close coupling with exchange [36], while in the
E ”
‘:
‘0 1 0 -
4: J-
.:
2-
Electron
Energy
(eV)
Fig. 3. Measured (Ref. 12711 total absolute cross sections for electron-impact excitation of Ar ” (3s --) 3~) using the MEIBEL technique. The solid curve represents a seven-state close coupling R-matrix calculation (Ref. [37]) after convolution with an electron energy distribution of 0.2 eV FWHM.
3.1. COLLISIONS
WITH ELECTRONS
112
C.H. Dunn et al./Nucl.
Kr@+(4s* 'S) -
6 +
Krw(4s4p
Instr. and Meth. in Phys. Rex B 98 (1995) 107-113
'P) .
I
L.~.~.~.~.J
84.0
14.5
IS.0
Electron
lS.5
16.0
Energy
163
17.0
17.5
(eV)
Fig. 4. Absolute total cross sections for electron-impact excitation of the 4s’ ‘S + 4s4p 3P transition in Kr6+ as a function of the collision energy using the MEIBEL technique (Ref. [29]).
The MEIBEL technique is not carried to higher energies because at a defined scattered electron energy defined by the ion velocity, backscattered electrons in the center of mass (CM) frame will also be backscattered in the laboratory frame and then be lost from the detector. Indeed, we have made use of this effect to deduce gross features of differential excitation cross sections for Ar7+ [27] and 05+ [28]. We showed that near threshold the inelastic scattering is predominantly in the backward quadrants. This was an unexpected result which has since been confirmed by theoretical calculations [38]. When resonances are measured in excitation, there is evidence that much more theoretical effort is needed to obtain agreement. Fig. 4 shows results [29] using the MEIBEL technique for the intercombination excitation 4sz1S + 4s4p 3P in Kr6+. No theoretical results are shown in the figure, since the results are just now in press [39]. Agreement between theory and experiment was obtained only after much effort with the theory. Originally, ten state close coupling (1OCC) calculations in L-S coupling gave a set of results predicting the two major resonances as observed in the experiment. Twenty CC gave results that also predicted two major resonances, but agreement with experiment was significantly worse. Full Breit-Pauli 14state close coupling calculations give reasonable agreement after careful treatment of perturber resonances. It is now known that the two major resonances are associated with n = 9 and 10. These resonances are strongly perturbed by 4d and 4f resonances and the final results are extremely sensitive to the exact location and size of these perturbers [39]. Griffin et al. [40] have recently emphasized that there may be much greater sensitivity to interactions between resonances when the interaction is direct, as in excitation, as opposed to when the interaction is through a continuum, as in DR. The Kr”+ case seems to be a paradigm of such sensitivity.
5. Summary remarks There seem to be strong reasons to experimentally pursue more cases where resonances play a strong role in the excitation process in order to give further guidance to theoretical developments in the excitation of HCI. There is less incentive to experimentally investigate strong transitions unless there is good reason to believe that resonances will be affecting the cross sections, since theory seems able to make adequate calculations of such excitations. Differential cross sections for ion excitation are proving to be interesting, and may be quite meaningful in guiding theory in further development.
Acknowledgements We are grateful for support from the Office of Fusion Energy of the US Department of Energy, Contract no. DE-A105-86ER532237 with the National Insitute of Standards and Technology and Contract no. DE-ACOS840R21400 with Martin Marietta Energy Systems.
References [l] G. Dunn, At. Plasma-Material Int. Data for Fusion 2, (19921 25, Suppl. .I. Nucl. Fusion. [2] K. LaGattuta, I. Nasser and Y. Hahn, Phys. Rev. A 33 (19861 2782. [3] C. Bottcher, D.C. Griffin and MS. Pindzola, Phys. Rev. A 34 (1986) 860. [4] A. Miiller, D.S. BeliC, B.D. DePaola, N. DjuriC, G.H. Dunn, D.W. Mueller and C. Timmer, Phys. Rev. A 36 (1987) 599. [5] H. Danared, G. Andler, L. Bagge, C.J. Herrlander, J. Hilke, J. Jeansson, A. Kallberg, A. Nilsson, A. Paal, K.-G. Rensfelt, U. Rosengird, J. Starker and M. af Ugglas, Phys. Rev. Lett. 72 (1994) 3775. [6] For a review, see: A. Miiller, in: Physics of Ion Impact Phenomena, Springer Series in Chemical Physics, vol. 54, ed. Deepak Mathur (Springer, Berlin, 1991) p. 13. [7] J. Kentner, J. Linkemann, C. Broude, D. Habs, G. Hofmann, A. Miller, E. Salzborn, D. Schwalm, and A. Wolf, these Proceedings (7th Int. Conf. on the Physics of Highly Charged Ions (HCI-94), Vienna, Austria, 1994) Nucl. Instr. and Meth. B 98 (1995) 142. (81 J. Linkemann et al., presented at this Conference (7th Int. Conf. on the Physics of Highly Charged Ions (HCI-94), Vienna, Austria, 1994). [9] K.J. LaGattuta and Y. Hahn, Phys. Rev. A 24 (1981) 2273. [lo] R.E. Marrs, S.R. Elliot and D.R. Knapp, Phys. Rev. Lett. 72 (1994) 4082; See also, R.E. Marrs, S.R. Elliot and J.H. Scofield, presented at this Conference (7th Int. Conf. on the Physics of Highly Charged Ions (HCI-941, Vienna, Austria, 1994); Also see S.R. Elliot, invited paper, [ll] W.G. Graham, W. Fritsch, Y. Hahn and J.A. Tanis, eds., Recombination of Atomic Ions, Proc. of a NATO Advanced Research Workshop (Plenum, New York, 19921.
G.H. Dunn et al. /Nucl. Instr. and Meth. in Phys. Rex B 98 (1995) 107-113 [12] J. Linkemann,
J. Kenntner, A. Miiller, A. Wolf, D. Habs, D. Schwalm, W. Spies, 0. Uwira, A. Frank, M.S. Pindzola, N.R. Badnell, Ref. [7], p. 154. [13] S. Asp et al., presented at this Conference (7th lnt. Conf. on the Physics of Highly Charged Ions (HCI-94), Vienna, Austria, 1994). [14] W. Spies et al., Ref. [7], p. 158. [15] 0. Uwira et al., Ref. [7], p. 162. [16] A.R. Young, L.D. Gardner, D.W. Savin, G.P. Lafyatis, A. Chutjian, S. Bliman and J.L. Kohl, Phys. Rev. A 49 (1994) 357. [17] D.S. BeliC, G.H. Dunn, T.J. Morgan, D.W. Mueller and C. Timmer, Phys. Rev. L&t. 50 (1983) 339. [18] B.A. Huber, C. Ristori and D. Kichler, AIP Conf. Proc. 274, 6th lnt. Conf. on the Physics of Highly Charged Ions, eds. P. Richard, M. Stiickli, C.L. Cocke and C.D. Lin (1993) p. 455. [19] B.A. Huber, C. Ristori, C. Guet, D. Jalabert, M. Maurel and J.C. Rocco, AIP Conf. Proc. 295, 18th Int. Conf. on the Physics of Electronic and Atomic Collisions, eds. T. Andersen, B. Fastrup, F. Folkmann, H. Knudsen and N. Andersen (1993) p. 820. [20] J.B. Greenwood, B. Srigengan, R.W. Newell, J. Geddes, I.D. Williams, Ref. [7], p. 125. [21] R.A. Phaneuf, AIP Conf. Proc. 295, 18th Int. Conf. on the Physics of Electronic and Atomic Collisions, eds. T. Andersen, B. Fastrup, F. Folkmann, H. Knudsen and N. Andersen (1993) p. 405. [22] E.W. Bell, Ph.D. Thesis, Univ. of Colorado, Boulder, 1993. Available through University Microfilms International @MI), P.0 Box 1764, Ann Arbor, MI 48106, USA. [23] C. Guet, B.A. Huber, D. Jalabert, M. Maurel, C. Ristori, J.C. Rocco, presented at this Conference (7th Int. Conf. on the Physics of Highly Charged Ions, Vienna, Austria, 1994). [24] J.B. Greenwood, B. Srigengan, R.W. Newell, J. Geddes and I.D. Williams, Ref. [7], p. 125. 1251 Unpublished, see E.K. W%hlin, Ph.D. thesis, University of Colorado, 1990, available through UMI, Order no. AAC 9117090. [26] E.K. Wtihlin, J.S. Thompson, G.H. Dunn, R.A. Phaneuf,
[27]
[28] 1291 [30]
1311
[32] [33] [34] [35]
[36]
[37] [38] [39] [40]
113
D.C. Gregory and A.C.H. Smith, Phys. Rev. Lett. 66 (1991) 157; in: Atomic Physics of Highly Charged Ions, eds. E. Salzborn, P.H. Mokler and A. Miller (Springer, Berlin, 19911 p. 35. X.Q. Guo, E.W. Bell, J.S. Thompson, G.H. Dunn, M.E. Bannister, R.A. Phaneuf and A.C.H. Smith, Phys. Rev. A 47 (1993) R9; in: 6th Int. Conf. on the Physics of Highly Charged Ions, eds. P. Richard, M. Stockli, C.L. Cocke and CD. Lin, AIP Conf. Proc. 274 (AIP, New York, 1993) p. 463. E.W. Bell et al., Phys. Rev. A 49 (1994) 4585. M.E. Bannister, X.Q. Guo, T.M. Kojima and G.H. Dunn, Phys. Rev. Lett. 72 (1994) 3336. S.J. Smith, A. Chutjian, J. Mitroy, S.S. Tayal, R.J.W. Henry, K.F. Man, R.J. Mawhorter and I.D. Williams, Phys. Rev. A 48 (1993) 292. J.L. Forand, C.A. Timmer, E.K. Wlhlin, B.D. DePaola, G.H. Dunn, D. Swenson and K. Rinn, Rev. Sci. Instr. 61 (1990) 3372. P.O. Taylor, D. Gregory, G.H. Dunn, R.A. Phaneuf and D.H. Crandall, Phys. Rev. L&t. 39 (19771 1256. D. Gregory, G.H. Dunn, R.A. Phaneuf and D.H. Crandall, Phys. Rev. A 20 (1979) 410. D.S. Belic, R.A. Falk, G.H. Dunn, D. Gregory and C. Cisneros, Bul. Am. Phys. Sot. 26 (1981) 1315. For a summary see: G.H. Dunn, in: The Physics of Ionized Gases, ed. M. Matic (Boris Kidric, Belgrade, 19801, p. 49. See also Refs. [21] and [22]. N.H. Magee Jr., J.B. Mann, A.L. Merts and D.L. Robb, Los Alamos Scientific Laboratory Report no. LA-6691-MS, 1977 (unpublished). N.R. Badnell, M.S. Pindzola and D.C. Griffin, Phys. Rev. A 43 (1991) 2250. M.S. Pindzola, D.R. Schultz and D.C. Griffin, Phys. Rev. A 48 (1993) 4333. T.W. Gorczyca, M.S. Pindzola, N.R. Badnell and D.C. Griffin, Phys. Rev. A, in press. D.C. Griffin, M.S. Pindzola, F. Robicheaux, T.W. Gorczyca and N.R. Badnell, Phys. Rev. Lett. 72 (1994) 3491.
3.1. COLLISIONS
WITH ELECTRONS
Beam Interactions with Materials&Atoms
ELSEVIER
Collisions of electrons with highly-charged G.H. Dunn a3*, N. DjuriC ‘, Y-S Chung a, M. Bannister
ions
b, A.C.H. Smith ’
a JILA of the National Institure of Standards and Technology and the lJnit,ersity of Colorado, Boulder, CO 80309-0440, ’ Oak Ridge National LaboraIm): Oak Ridge, TN 37831, USA ’ UtGersity College, Londott WCIE6BT, United Kingdom
USA
Abstract This progress report, in addition to describing recent work in the authors’ laboratory, highlights the general character and importance of electron collisions with highly-charged ions (HCI) and describes major advances in the field since the previous conference on the subject. Thus, while the authors’ principle efforts are currently directed toward investigation of excitation of HCI, there have been very notable advances by others in the areas of ionization and recombination and an attempt is made to put these into context of the field in general. Also, for the first time, significant progress is now being made by others in experimental investigation of elastic scattering of electrons from HCI.
1. Introduction Infinite numbers of infinite series of resonances enrich the study of collisions between electrons and highlycharged ions (HCI), which then takes on the mantle of being both intensely interesting and vitally important. Resonances can and do alter cross sections enough that their presence substantially modifies the behavior of plasmas such as those in hot astrophysical environments, controlled fusion devices, and X-ray lasers, i.e. the environments where HCI are major species. Thus, the modelling of these environments is crucially dependent upon electron-HCI collision data including resonance effects. Further enriching this scene is the fact that under some circumstances the resonances in electron-HCI collisions can be varied (controlled) by the presence of external fields or collisions - a feature which is sometimes very dramatic for dielectronic recombination. As noted, there are many motivations for the study of such collisions, and one currently stimulating our own work is the need to obtain experimental benchmarks so that theory can be confidently used to obtain the data necessary to model the edge plasma [I] of controlled fusion reactors. The edge plasma plays an important role in the heating and stability of fusion plasmas. The plasma near the walls of a fusion device is typically characterized by low temperatures in the region T = 2-200 eV and particle densities in the range 10”-10’5 cm-a. Character-
* Corresponding author, tel. + 1 303 492 7824, fax + 1 303 492 5235, E-mail: [email protected].
istic of the low temperatures and proximity to the vessel walls, particle constituents are atoms, molecules and ions of hydrogen, helium, carbon, oxygen, and a host of metal and other impurities of low fractional content coming from walls, limiters and divertors. Ions are typically in charge states up to about 10. Supposing charge neutrality and comparable electron and ion temperatures, electron collisions dominate over those between heavy particles such as atoms or ions, since the collision frequencies are greater than those between heavy particles by the ratio of velocities, N (1836 A)‘/’ where A is the atomic mass. Only highly-resonant heavyparticle collisions, such as resonant charge transfer, will have cross sections large enough to offset the velocity factor and give a rate comparable to that for electron collisions. In a preponderance of cases, resonances in electron-ion collisions may be thought of as starting with a “dielectronic capture”. Consider an electron incident on an ion with just E less energy than E,,, the energy needed to excite a core electron from the initial state i to an excited state j. In the attractive Coulomb field, the incident electron gains kinetic energy, so that in close proximity to the ion there is more than enough energy to excite the core electron. Supposing that it does so, however, the incident electron is left bound with energy E - there has been a capture of one electron associated with the excitation of another. Obviously, due to quantization of energy, this can occur only if E corresponds to a bound level - i.e. the process is “resonant”. The resulting doubly excited state is referred to by various terms: resonance, compound state, complex, etc. Stabilization of the compound state can occur along a variety of paths: (1) If the two electrons
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00084-4
3.1. COLLISIONS WITH ELECTRONS
108
G.H. Dunn et al. /Nucl. Instr. and Meth. in Phys. Res. B 98 (199.5)107-113
share their energy, the incident electron may go out again with energy, Ei, - E, and a resonance feature will appear in the cross section for elastic scattering. (2) If one of the excited electrons radiates some energy, the system stabilizes and dielectronic recombination has occurred. (3) If the core electron which became excited was an inner-shell electron, there may be enough energy in the compound state that the electron can share its energy both with the incident electron and another outer shell electron(s), leading to double (multiple) autoionization, and resonant-excitation-double-autoionization (REDA) has occurred. (4) The excited core electron may share its energy with the incident electron thus ejecting it, but if, in the process, it moves into state k rather than returning to state i as in (1) above, then resonant excitation to state k will have occurred - now appearing as a resonance feature in the excitation cross section. In each of these cases the cross section to obtain the stabilized product can approximately be expressed as a multi-step process, so that
As Aan +A, + . . +A,
.
(1)
I
Here a,” is the dielectronic capture cross section with the incident electron’s being captured into level n. It is proportional ( 5 >, through detailed balance, to the autoionization rate A,” of the doubly excited state. The branching ratio to the final state considered B, is equal to the ratio shown in brackets involving decay rates via various channels including the rate A, to the final state considered, and the sum is over all n. When A, is a radiative rate (A,), as in the case of dielectronic recombination (DR), the sum in Eq. (1) becomes sensitive to the relative size of A, and the autoionization rate A, , and it has been shown [2,3] and observed [4] that elect& fields can dramatically affect the number of terms contributing in a significant way to the sum. Thus, for dielectronic recombination one can “tune” the value of the cross section with external fields. However, this tuning effect is not likely to be present to any great extent for the other stabilization routes, and such an effect has been neither seen nor predicted.
2. Ionization, recombination
and elastic scattering
This progress report primarily focuses on work in the authors’ laboratory in the area of electron-ion excitation. However, in this volume there are no other reviews or progress reports on electron-ion processes. Given that there have been very significant recent strides in observing ionization, recombination, and elastic scattering, we here take the opportunity to briefly summarize some of the major advances in those other areas which have occurred since the Sixth Conference on the Physics of Highly
Charged Ions. In so doing, we call attention in some instances to other papers in this volume. Before discussing individual processes, it is important to emphasize a major advance in the technology of electron coolers at ion storage rings, since this has been the venue for most of the recombination work in recent years, and - as noted below - is now becoming important for ionization work as well. The critical stride [5] was the improvement of the efficiency of electron cooling by adiabatically expanding the electron beam in a decreasing magnetic field, thereby lowering the transverse electron temperature. This, of course, has resulted in vastly improved electron-energy distributions in electron-ion studies. The improvement has been implemented at Stockholm, where it was invented, at Heidelberg, and at Aarhus. 2.1. ionization The experimental study of electron-impact ionization of ions has been pursued successfully and with great expertise over some years [6] and the techniques and understanding are relatively mature. Nevertheless, there have been some very notable advances recently, and two stand out in particular. First, ion-storage-ring technology has now been applied to ionization by taking the rather obvious step of installing a detector in the appropriate location inside the ring after the cooler (this, as opposed to outside the ring for recombination studies). Taken together with the implementation of the improved perpendicular cooling mentioned above, extraordinary results have been obtained on Li-like C114+ and Si”’ [7], and on Na-like Fe”+ [8]. Observation of the clear REDA peaks is especially gratifying for the latter case, since it was for Fet5+ that the process was first hypothesized [9]. The exciting detailed experimental data will now provide a standard against which the theory can be judged. Comparisons at this point indicate that it is not routine to obtain agreement, and theoretical development and experimental exploration still are necessary. The second breakthrough which we call attention to is the measurement of ionization cross sections for very-high Z hydrogen like ions at high energies [lo] in Super EBIT. This testing of ionization theory under highly relativistic conditions suggests through the early data that the theory is missing something - agreement between theory and experiment is not good. 2.2. Recombination As already mentioned, the study of electron recombination with ions is now almost exclusively performed using ion-storage rings. An excellent overview of the field covering work over the past decade can be found in the NATO monograph [ll] on the subject. Again, the field has become relatively mature, but there are a number of outstand-
G.H. Dunn et al. /Nacl. Instr. and Meth. in Phys. Res. B 98 (1995) 107-113 ing questions and issues, and there have been recent advances in the field which will be mentioned. Because the process in its entirety involves resonances, there are already dramatic results [7,12,13], and the field will continue to benefit greatly from the recent perpendicular cooling innovation mentioned above in terms of obtaining much more highly-resolved resonance structures. Indeed, resolution is good enough that precision spectroscopy and QED tests are being seriously considered [14] using dielectronic recombination resonances. Measurements on radiative recombination “at zero” relative energy of electrons and ions continue to produce anomalously large cross section values [13,15]. This anomaly, which has been reported a number of times reaching as far back as four years, remains to be explained. Three-body processes and interference of radiative and dielectronic recombination have been variously invoked in unsuccessful attempts to resolve this. Finally, in this brief discussion of recombination advances and outstanding issues, it should be mentioned that there is only one clear-cut experiment [4] which tests the theory of field enhancement of DR. This important phenomenon has suffered benign neglect since the nearly sole means for studying DR has come to reside at storage rings. An important exception to this is a recent experiment [16] on C3’ using a crossed beams method and detecting photons and product ions in coincidence [17]. Just as in earlier experiments at Oak Ridge where anomalously large field enhancements of DR cross sections were found for Li-like ions, (summarized in Ref. [ll]) so also is it the case in the recent Harvard experiment. Contrary to the Oak Ridge experiments, however, the ambient electric field in which the collisions take place is well-defined and known. The statistical uncertainty in the measurement is, however, large enough that the disagreement between experiment and theory is inconclusive; i.e. the disagreement is only suggestive. The interesting physics involved in this enhancement and the potential importance of it in plasma environments invites further investigation. One would hope for a means to achieve this at storage rings. 2.3. Elastic scattering
It seems paradoxical that complex processes such as already discussed have been studied over a period of many years and that it is only in the past few years that seemingly-more-simple elastic scattering of electrons from ions has been measured. These studies were ushered in by Huber et al. [l&19] who measured relative differential elastic cross sections for electron scattering from Xe6+ and from Ba2+ using a colliding beams technique. Recently, another method has been introduced [20] which leads to measurements of integrated elastic backscattering. Both methods give results with significant deviations from Rutherford scattering, but the limited results so far seem in all cases to agree with more complete theory. As dis-
cussed, the field is new and no dielectronic have as yet been observed.
3. Excitation
109 resonances
- methods
Electron-impact excitation of HCI has been studied by numerous techniques over a period of about twenty five years; yet despite this, there remains a serious need for experiments which will adequately test theoretical calculations, especially when resonances play a role. The topic has recently been reviewed by Phaneuf [21], and a complete discussion of techniques and listing of cases studied can be found in the thesis by Bell [22]. Here, we merely list the different techniques and give only brief comments on most of them. The reader is referred to the references above for more detail and for further references. 3.1. CBFR The crossed beams with forced radiation method was used early to measure excitation of the 2s state of hydrogen-like ions. The method yielded relative cross sections, and results were normalized to Born approximation calculations at high energy. 3.2. CB The crossed beams with fluorescence detection has been used for a great fraction of the absolute total cross section measurements for ion excitation. Absolute accuracies and precisions are good, but with detection sensitivities in the neighborhood of 10e4, the method is tedious and difficult, requiring absolute radiometry and detection of low signal levels in the presence of high backgrounds. 3.3. PL‘AS The plasma rate method was used in the late 1960’s and early 1970’s. Observations of fluorescence in a plasma along with electron density and temperature and ion density, coupled with modelling of the plasma with various assumptions allows extraction of the excitation rate coefficient. There are substantial uncertainties in the method, and it seems the method is no longer being pursued. 3.4. EA When an inner-shell electron is excited, autoionization may result. Thus, the observation of structural “features” in the ionization cross section at electron energies where there are inner shell excitation thresholds can often lead to information about the inner-shell excitation cross section. This EA method has the advantage that one generally collects 100% of the ionized products of the collision. It has the disadvantage that the branching ratios for autoion-
3.1. COLLISIONS WITH ELECTRONS
110
G.H. Dunn et al. /Nucl. lnstr. and Meth. in Phys. Rex El 98 (1995) 107-113
ization must be assumed or calculated, and the (uncertain) background of underlying ionization must be subtracted.
In the crossed beams energy loss method electrons which have lost an amount of energy equal to the excitation energy are detected at what may typically be a variable angle. Thus, it is used to measure differential cross sections, supplying valuable information for testing theory which isn’t available in total cross section measurements. The angular range through which data can be collected is generally limited, and the results are relative cross sections which must then be normalized - typically to elastic cross sections. Progress with this method is reported in this volume [23]. A variant of the CBEL method in which electrons are collected over a broad angular range has recently been introduced for study of singly charged ions [24] and it is intended that it will be used for study of HCI as well. 3.6. EBIT/S The electron-beam ion trap (EBIT) and electron-beam ion source (EBIS) are used successfully to study a number of electron-ion collisions, including excitation. The Xradiation from the device is observed as a function of electron energy (which is momentarily changed from the equilibrium value). Cross section values are obtained by normalizing the signal to another signal for which the cross section is thought to be known - for example, radiative recombination in the case of EBIT. This method allows excitation measurements on very-highly-charged ions; and though the results are relative and normalized, it is generally felt that the normalization is quite secure. The electron energy resolution is quite bad - several tens of eV - but for processes being measured with thresholds at several keV, this probably isn’t as serious a deficiency as it sounds. 3.7. MEIBEL The merged-electron-ion beams energy loss method is currently being used in our laboratory for electron excitation of HCI. Progress using this technique will occupy the remainder of the discussion here, aside from summary remarks With this method, absolute total cross sections are measured near threshold, and gross features of differential cross sections are extracted. The technique features near total collection of collision products, resulting in a detection efficiency of about 70%, and an electron-energy resolution of about 0.2 eV. It has been used in our laboratory for measurements on C+ [25], Si3+ [26], Ar’+ [27], 0” [28], and Krbf [29]. A similar approach has been used by Chutjian et al. [30] for singly-charged ions, and implemen-
Fig. 1. Schematic view of the MEIBEL apparatus. The uniform magnetic field is in the z direction, the electric field in the y direction and E X B is in the Y direction.
tation of changes to enable measurements on HCI are in progress. The MEIBEL technique utilizes crossed electric and magnetic fields, E = Ej and B = Bk, and the properties of the trochoidal paths of charged particles in such fields. For these trajectories, we have, x = p/w, [ w, t - sin( w, t)], y = p/w, [l - COS(W,t)l, 2 = i,t, i = p [l - COS(W,t)], j = p sin( w, t), and i = i,, where p = E/B is the drift velocity in the x direction. It can be seen that after an integral number n of cyclotron periods, nT, = 2nn/w,, the particle velocity is equal to its initial velocity, its y coordinate has its initial value, and its x and z coordinates are advanced by pnT, and i,nT, respectively. Fig. 1, which is a schematic of the MEIBEL apparatus, illustrates how these properties are implemented in our laboratory. The apparatus is immersed in a uniform solenoidal magnetic field parallel to the incident ion beam. Electrons from an electron gun are focused into a region (the merger) having a transverse electric field of about 10 V/mm. Referring to the discussion above, for our case n is always 2; and after two periods, the electron velocity is again along the z axis, but the trajectory has been displaced from its initial x position by 2pT,. Multiply-charged ions from the Oak Ridge National Laboratory Electron Cyclotron Resonance Ion Source are merged with the electrons at the merger exit. Ions and electrons then travel together in an electric-field-free region (about 63.5 mm long) where the collisions take place. At the end of this collision region, the primary electrons and forward-travelling inelastically scattered electrons are separated by the action of a second pair of parallel plates (the demerger) with an electric field of about 2.5 V/mm. As in the case of the merger, the demerger plates are biased positive and negative with respect to the median plane. The demerger acts as an electron velocity-dispersion device, where the net velocity in the z direction and the drift velocity p in the x direction determine a position in a plane parallel to the y-z plane and at an x distance d from the beam axis. Unscattered electrons, deflected by the demerger through a
G.H. Dunn et al. /Nucl.
111
Instr. and Meth. in Phys. Rex B 98 (1995) 107-113
relatively small angle, are collected by a Faraday cup and their current is measured. Scattered electrons, deflected through much larger angles in the demerger, strike a position-sensitive detector (PSD) and are counted. Ions are deflected and collected in a Faraday cup and their current is measured. The operating pressure is approximately 1.5 X 10-s Pa. The measurement of the extent of electron and ion beam overlap (form factor) along the merge path is accomplished using a movable beam probe [31] employing fluorescent screen and digitized video techniques. Electrons scattered elastically at large angles by ions in the merge path could in principle also reach the detector, but are blocked from entering the demerger by a series of apertures. The signal on the PSD is accompanied by large background countrates due to electron and ion scattering on gas and surfaces. Because of the low signal-to-noise ratio (less than lo-* 1, both beams are chopped at 2 kHz in a phased four-way chopping scheme [28], and the detector output is accumulated in four histogramming memories according to position and temporal block. The four temporally distinguished memories correspond to different combinations of the beams’ being on and off so that (after correction for detection-system dead times) the memory contents can be appropriately added and subtracted to obtain the signal as a function of position. The excitation cross section is determined from the expression
where R is the observed signal countrate from detection of inelastically scattered electrons by the PSD, E the measured PSD detection efficiency, F the form factor, and lze, ~1~.I,, and Ii are the velocities and currents of the electrons and ions of charge e and qe, respectively. All quantities in the equation are absolutely determined so that the resultant measured cross sections are absolute.
LLiiiii Electron Energy IeVl Fig. 2. Absolute cross section versus electron energy for emission of 2p-2s radiation (15.5 nm) by electron impact on ground state C3+ ions. Points are from Ref. [32], theory (dashed curve. 2 state close coupling with exchange) is from Ref. [36] and is convoluted with the experimental energy distribution (solidcurve).
latter it is from a 7-state close coupling R-Matrix calculation [37]. Given the quality of agreement, there appears to be no good reason to pursue further experiments with this class of transition - theory appears to have the situation well in hand. However, some equivocation must be made in that in none of the experiments noted above were strong resonances encountered. In the cases of Si3+ [26] and Ar7+ [27] the experiments were limited to energies below the positions of predicted resonances. In the Ar7+ case there is a hint in the experimental rest&s of a resonance at 19 eV - below the 19.7 eV energy at which the first resonance is predicted, but the evidence is not clear.
2
4. Excitation
- results
Using the CB method, we have in the past measured excitation cross sections for the resonance lines of Li-like C3+ [32] and N4+ [33] and for Na-like Al’+ [34] and for a host of singly-ionized ions [35]. As already noted, with the MEIBEL technique we have measured excitation cross sections for resonance transitions for Li-like 05+ and Na-like Si3+ and Ar7+. In all these cases for resonance excitations, the agreement between experiment and theory is quite satisfactory and within combined uncertainties. Typical examples of results showing both experiment and theory are shown for the fluorescence measurements on C3+ [32] and the energy loss experiments on Ar’+ 1271 in Figs. 2 and 3 respectively. In the former case, the theory is two-state-close coupling with exchange [36], while in the
E ”
‘:
‘0 1 0 -
4: J-
.:
2-
Electron
Energy
(eV)
Fig. 3. Measured (Ref. 12711 total absolute cross sections for electron-impact excitation of Ar ” (3s --) 3~) using the MEIBEL technique. The solid curve represents a seven-state close coupling R-matrix calculation (Ref. [37]) after convolution with an electron energy distribution of 0.2 eV FWHM.
3.1. COLLISIONS
WITH ELECTRONS
112
C.H. Dunn et al./Nucl.
Kr@+(4s* 'S) -
6 +
Krw(4s4p
Instr. and Meth. in Phys. Rex B 98 (1995) 107-113
'P) .
I
L.~.~.~.~.J
84.0
14.5
IS.0
Electron
lS.5
16.0
Energy
163
17.0
17.5
(eV)
Fig. 4. Absolute total cross sections for electron-impact excitation of the 4s’ ‘S + 4s4p 3P transition in Kr6+ as a function of the collision energy using the MEIBEL technique (Ref. [29]).
The MEIBEL technique is not carried to higher energies because at a defined scattered electron energy defined by the ion velocity, backscattered electrons in the center of mass (CM) frame will also be backscattered in the laboratory frame and then be lost from the detector. Indeed, we have made use of this effect to deduce gross features of differential excitation cross sections for Ar7+ [27] and 05+ [28]. We showed that near threshold the inelastic scattering is predominantly in the backward quadrants. This was an unexpected result which has since been confirmed by theoretical calculations [38]. When resonances are measured in excitation, there is evidence that much more theoretical effort is needed to obtain agreement. Fig. 4 shows results [29] using the MEIBEL technique for the intercombination excitation 4sz1S + 4s4p 3P in Kr6+. No theoretical results are shown in the figure, since the results are just now in press [39]. Agreement between theory and experiment was obtained only after much effort with the theory. Originally, ten state close coupling (1OCC) calculations in L-S coupling gave a set of results predicting the two major resonances as observed in the experiment. Twenty CC gave results that also predicted two major resonances, but agreement with experiment was significantly worse. Full Breit-Pauli 14state close coupling calculations give reasonable agreement after careful treatment of perturber resonances. It is now known that the two major resonances are associated with n = 9 and 10. These resonances are strongly perturbed by 4d and 4f resonances and the final results are extremely sensitive to the exact location and size of these perturbers [39]. Griffin et al. [40] have recently emphasized that there may be much greater sensitivity to interactions between resonances when the interaction is direct, as in excitation, as opposed to when the interaction is through a continuum, as in DR. The Kr”+ case seems to be a paradigm of such sensitivity.
5. Summary remarks There seem to be strong reasons to experimentally pursue more cases where resonances play a strong role in the excitation process in order to give further guidance to theoretical developments in the excitation of HCI. There is less incentive to experimentally investigate strong transitions unless there is good reason to believe that resonances will be affecting the cross sections, since theory seems able to make adequate calculations of such excitations. Differential cross sections for ion excitation are proving to be interesting, and may be quite meaningful in guiding theory in further development.
Acknowledgements We are grateful for support from the Office of Fusion Energy of the US Department of Energy, Contract no. DE-A105-86ER532237 with the National Insitute of Standards and Technology and Contract no. DE-ACOS840R21400 with Martin Marietta Energy Systems.
References [l] G. Dunn, At. Plasma-Material Int. Data for Fusion 2, (19921 25, Suppl. .I. Nucl. Fusion. [2] K. LaGattuta, I. Nasser and Y. Hahn, Phys. Rev. A 33 (19861 2782. [3] C. Bottcher, D.C. Griffin and MS. Pindzola, Phys. Rev. A 34 (1986) 860. [4] A. Miiller, D.S. BeliC, B.D. DePaola, N. DjuriC, G.H. Dunn, D.W. Mueller and C. Timmer, Phys. Rev. A 36 (1987) 599. [5] H. Danared, G. Andler, L. Bagge, C.J. Herrlander, J. Hilke, J. Jeansson, A. Kallberg, A. Nilsson, A. Paal, K.-G. Rensfelt, U. Rosengird, J. Starker and M. af Ugglas, Phys. Rev. Lett. 72 (1994) 3775. [6] For a review, see: A. Miiller, in: Physics of Ion Impact Phenomena, Springer Series in Chemical Physics, vol. 54, ed. Deepak Mathur (Springer, Berlin, 1991) p. 13. [7] J. Kentner, J. Linkemann, C. Broude, D. Habs, G. Hofmann, A. Miller, E. Salzborn, D. Schwalm, and A. Wolf, these Proceedings (7th Int. Conf. on the Physics of Highly Charged Ions (HCI-94), Vienna, Austria, 1994) Nucl. Instr. and Meth. B 98 (1995) 142. (81 J. Linkemann et al., presented at this Conference (7th Int. Conf. on the Physics of Highly Charged Ions (HCI-94), Vienna, Austria, 1994). [9] K.J. LaGattuta and Y. Hahn, Phys. Rev. A 24 (1981) 2273. [lo] R.E. Marrs, S.R. Elliot and D.R. Knapp, Phys. Rev. Lett. 72 (1994) 4082; See also, R.E. Marrs, S.R. Elliot and J.H. Scofield, presented at this Conference (7th Int. Conf. on the Physics of Highly Charged Ions (HCI-941, Vienna, Austria, 1994); Also see S.R. Elliot, invited paper, [ll] W.G. Graham, W. Fritsch, Y. Hahn and J.A. Tanis, eds., Recombination of Atomic Ions, Proc. of a NATO Advanced Research Workshop (Plenum, New York, 19921.
G.H. Dunn et al. /Nucl. Instr. and Meth. in Phys. Rex B 98 (1995) 107-113 [12] J. Linkemann,
J. Kenntner, A. Miiller, A. Wolf, D. Habs, D. Schwalm, W. Spies, 0. Uwira, A. Frank, M.S. Pindzola, N.R. Badnell, Ref. [7], p. 154. [13] S. Asp et al., presented at this Conference (7th lnt. Conf. on the Physics of Highly Charged Ions (HCI-94), Vienna, Austria, 1994). [14] W. Spies et al., Ref. [7], p. 158. [15] 0. Uwira et al., Ref. [7], p. 162. [16] A.R. Young, L.D. Gardner, D.W. Savin, G.P. Lafyatis, A. Chutjian, S. Bliman and J.L. Kohl, Phys. Rev. A 49 (1994) 357. [17] D.S. BeliC, G.H. Dunn, T.J. Morgan, D.W. Mueller and C. Timmer, Phys. Rev. L&t. 50 (1983) 339. [18] B.A. Huber, C. Ristori and D. Kichler, AIP Conf. Proc. 274, 6th lnt. Conf. on the Physics of Highly Charged Ions, eds. P. Richard, M. Stiickli, C.L. Cocke and C.D. Lin (1993) p. 455. [19] B.A. Huber, C. Ristori, C. Guet, D. Jalabert, M. Maurel and J.C. Rocco, AIP Conf. Proc. 295, 18th Int. Conf. on the Physics of Electronic and Atomic Collisions, eds. T. Andersen, B. Fastrup, F. Folkmann, H. Knudsen and N. Andersen (1993) p. 820. [20] J.B. Greenwood, B. Srigengan, R.W. Newell, J. Geddes, I.D. Williams, Ref. [7], p. 125. [21] R.A. Phaneuf, AIP Conf. Proc. 295, 18th Int. Conf. on the Physics of Electronic and Atomic Collisions, eds. T. Andersen, B. Fastrup, F. Folkmann, H. Knudsen and N. Andersen (1993) p. 405. [22] E.W. Bell, Ph.D. Thesis, Univ. of Colorado, Boulder, 1993. Available through University Microfilms International @MI), P.0 Box 1764, Ann Arbor, MI 48106, USA. [23] C. Guet, B.A. Huber, D. Jalabert, M. Maurel, C. Ristori, J.C. Rocco, presented at this Conference (7th Int. Conf. on the Physics of Highly Charged Ions, Vienna, Austria, 1994). [24] J.B. Greenwood, B. Srigengan, R.W. Newell, J. Geddes and I.D. Williams, Ref. [7], p. 125. 1251 Unpublished, see E.K. W%hlin, Ph.D. thesis, University of Colorado, 1990, available through UMI, Order no. AAC 9117090. [26] E.K. Wtihlin, J.S. Thompson, G.H. Dunn, R.A. Phaneuf,
[27]
[28] 1291 [30]
1311
[32] [33] [34] [35]
[36]
[37] [38] [39] [40]
113
D.C. Gregory and A.C.H. Smith, Phys. Rev. Lett. 66 (1991) 157; in: Atomic Physics of Highly Charged Ions, eds. E. Salzborn, P.H. Mokler and A. Miller (Springer, Berlin, 19911 p. 35. X.Q. Guo, E.W. Bell, J.S. Thompson, G.H. Dunn, M.E. Bannister, R.A. Phaneuf and A.C.H. Smith, Phys. Rev. A 47 (1993) R9; in: 6th Int. Conf. on the Physics of Highly Charged Ions, eds. P. Richard, M. Stockli, C.L. Cocke and CD. Lin, AIP Conf. Proc. 274 (AIP, New York, 1993) p. 463. E.W. Bell et al., Phys. Rev. A 49 (1994) 4585. M.E. Bannister, X.Q. Guo, T.M. Kojima and G.H. Dunn, Phys. Rev. Lett. 72 (1994) 3336. S.J. Smith, A. Chutjian, J. Mitroy, S.S. Tayal, R.J.W. Henry, K.F. Man, R.J. Mawhorter and I.D. Williams, Phys. Rev. A 48 (1993) 292. J.L. Forand, C.A. Timmer, E.K. Wlhlin, B.D. DePaola, G.H. Dunn, D. Swenson and K. Rinn, Rev. Sci. Instr. 61 (1990) 3372. P.O. Taylor, D. Gregory, G.H. Dunn, R.A. Phaneuf and D.H. Crandall, Phys. Rev. L&t. 39 (19771 1256. D. Gregory, G.H. Dunn, R.A. Phaneuf and D.H. Crandall, Phys. Rev. A 20 (1979) 410. D.S. Belic, R.A. Falk, G.H. Dunn, D. Gregory and C. Cisneros, Bul. Am. Phys. Sot. 26 (1981) 1315. For a summary see: G.H. Dunn, in: The Physics of Ionized Gases, ed. M. Matic (Boris Kidric, Belgrade, 19801, p. 49. See also Refs. [21] and [22]. N.H. Magee Jr., J.B. Mann, A.L. Merts and D.L. Robb, Los Alamos Scientific Laboratory Report no. LA-6691-MS, 1977 (unpublished). N.R. Badnell, M.S. Pindzola and D.C. Griffin, Phys. Rev. A 43 (1991) 2250. M.S. Pindzola, D.R. Schultz and D.C. Griffin, Phys. Rev. A 48 (1993) 4333. T.W. Gorczyca, M.S. Pindzola, N.R. Badnell and D.C. Griffin, Phys. Rev. A, in press. D.C. Griffin, M.S. Pindzola, F. Robicheaux, T.W. Gorczyca and N.R. Badnell, Phys. Rev. Lett. 72 (1994) 3491.
3.1. COLLISIONS
WITH ELECTRONS