complete momentum balance for single ionization of helium by … · 1999. 1. 29. · tors or even...

PHYSICAL REVIEW A AUGUST 1997VOLUME 56, NUMBER 2

Complete momentum balance for single ionization of helium by fast ion impact: Experiment

R. Moshammer,1 J. Ullrich,2 H. Kollmus,1 W. Schmitt,2 M. Unverzagt,1 H. Schmidt-Bocking,1 C. J. Wood,3 and R. E. Olson31Institut fur Kernphysik, August-Euler-Strasse 6, D-60486 Frankfurt, Germany

2Gesellschaft fu¨r Schwerionenforschung, m.b.H., Planckstrasse 1, D-64291 Darmstadt, Germany3Department of Physics, University of Missouri-Rolla, Rolla, Missouri 65401

~Received 11 February 1997!

The collision dynamics of He single ionization by 3.6 MeV/u Se281 impact was explored using the reactionmicroscope of the Gesellschaft fu¨r Schwerionenforschung, a high-resolution integrated multielectron recoil-ionmomentum spectrometer. The complete three-particle final-state momentum distribution~nine Cartesian com-ponentspi! was imaged with a resolution ofDpi'60.1 a.u. by measuring the three momentum componentsof the emitted electron and the recoiling target ion in coincidence. The projectile energy loss has been deter-mined on a level ofDEp /Ep'1027 and projectile scattering angles as small asDq'1027 rad becameaccessible. The experimental data which are compared with results of classical trajectory Monte Carlo calcu-lations reveal an unprecedented insight into the details of the electron emission and the collision dynamics forionization of helium by fast heavy-ion impact.@S1050-2947~97!01908-2#

PACS number~s!: 34.101x, 34.50.Fa

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I. INTRODUCTION

When energetic charged projectiles interact with neuatoms, the ejection of a target electron is the dominant retion channel occurring with cross sections on the order10215 cm2. The detailed understanding of the facets of tarionization, therefore, has a strong impact on any applicawhich is based on energy deposition in matter by fast ioAmong them are the radiation damage of biological aother materials, track formation and bulk modifications,development of radiation detection devices, and the invegation of plasmas. One important source of systematic dcontributing to our understanding of the collision dynamare measurements of ionization cross sections doubly diential in ejected electron energy and angle~for a review see,e.g.,@1#!. As stated in@1#, however, there are only a few seof reliable data for the emission of low-energy electrons~see,e.g., @2,3#! with energies below 20 eV which contributabout 50% to the total single-ionization cross section. Indition, most of these investigations were performed uslow-charged projectiles such as electrons@4# and protons@5#.Recently, highly charged heavy ions~for an upcoming re-view on existing data see@6#! gained increasing interest concerning applicational aspects in connection with the cantherapy project at the Gesellschaft fu¨r Schwerionenforschung~GSI! @7#.

Despite its outstanding importance, no kinematicacomplete experimental investigation has been publishedprovides information on the electron emission, the recoil-scattering, and the energy loss, as well as the angular sgling of the projectile for single ionization by ion impacOnly one study has been presented recently where the lotudinal momentum balance was completely determined@8#.In contrast, single ionization by electron impact has beextensively investigated in kinematically complete so-cal(e,2e) experiments~for a review see@4#!. Even for doublephotoionization a considerable amount of kinematicacomplete (g,2e) studies have been performed since the pneering experiment@9# in 1993.

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The complete lack of such data for ion impact is duetwo reasons: First, for most collision systems the changeprojectile energy and transverse momentum~scatteringangle! in a typical ionization encounter is by far smaller thathe momentum spread of ion beams from modern acceltors or even storage rings where the ions are cooled byinteraction with electrons or lasers. Thus, the momentchange of the projectile has only been accessible experimtally with sufficient resolution for light~hydrogen, helium!and slow (Ep,500 keV) ions~see, e.g.,@10#!. One study hasbeen performed for 2.1 MeV/u C61 on Ne where the relativeenergy loss as well as the projectile scattering has been msured for neon multiple ionization@11,12#. In a few otherexperiments projectile scattering angles have been detein coincidence only with the emitted electron~see, e.g.,@13#!, the recoil-ion charge state@13,14#, and its transversemomentum@15–18#. All these studies severely suffered frolimited resolution.

Second, conventional electron spectroscopy, whereenergy distribution of secondary electrons is scanned stestep in energy and angle, faces tremendous difficulties indetection of slow electrons@1# and, more importantly, suffersfrom small solid angles on the order of 1023 of 4p. Both aresevere restrictions, because most of the emitted electronsoft electrons which contribute significantly to the total crosection, and measurements coincident with the projectilethe recoil ion are extremely difficult@13#. Usually, neitherthe charge state of the recoil ion nor that of the outgoprojectile is determined.

Due to these reasons the only possible strategy leadinkinematically complete experiments is the coincident, chastate selective detection of the recoiling target ion andemitted electron where the final momenta of both are demined with sufficient resolution. Experimentally this ischallenging task since, as mentioned before, nearly 50%the electrons are emitted with energies below 20 eV andrecoiling target ions of interest have energies in the sub-mregime. Only during the last few years efficient recoil-iodetection techniques have been developed, based on ucold supersonic jet targets, which are sensitive to such sm

1351 © 1997 The American Physical Society

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energy transfers to the target nucleus~see, e.g.,@19–22# andfor an upcoming review see@23#!. Moreover, efficient meth-ods for the detection of low-energy electrons have beenveloped recently at GSI@8,24#. By using a superposition oelectric and solenoidal magnetic fields all electrons withergies below 50 eV including for the first time those wiEe50 eV were projected on large area position sensitivetectors. From their position and time of flight~TOF!, mea-sured in an electron recoil-ion projectile coincidence, thtrajectory has been calculated and, thus, their initial momtum vector ~all three spatial dimensions! was obtained.~Similar projection techniques have been applied morecently providing either only the total energy of the electro@25# or two out of three momentum components@26,27#.! Upto now only longitudinal momentum balances have bepublished since the transverse recoil-ion momentum restion was limited to 0.5 a.u. in these first experiments. In tpaper we report on the kinematically complete experimestudy of target single ionization by ion impact with a reslution of Dpi'60.1 a.u. for all nine final momentum componentspi . Single differential cross sections, as well as tcomplete momentum balance for the longitudinal andtransverse direction, are presented.

From the theoretical point of view considerable progrehas been achieved within the last decade in the descriptioionization collision dynamics on a quantum-mechanicalsis ~for a review see@28#! as well as with semiclassical treaments @29,30#. In the perturbative regime where the Boapproximation is applicable, methods have been develoto calculate three-body kinematics@31–33#. In the nonper-turbative regime the ‘‘hidden crossing’’ method@34# hasbeen developed for slow, adiabatic collisions~vp,ve , vp :projectile velocity,ve : velocity of the active electron!. Morerecently the time dependent Schro¨dinger equation of theelectron in the field of the two nuclei moving on classictrajectories has been solved numerically by discretizationing a Cartesian mesh@35,36#. In both methods, however, thprojectile motion is separated and approximated by a straline.

At higher projectile velocities (vp.ve) for nonperturba-tive collisions~q/vp.1, q: projectile charge! three-body in-teractions also termed ‘‘two-center effects’’ strongly inflence the electron emission characteristics@6,37#. Very low-energy electrons were found to be emitted into the forwdirection due to the ‘‘postcollision interaction’’ with themerging projectile@8,38,39#. In addition, as will be demonstrated in this paper, the projectile scattering can no lonbe treated assuming a central interaction potential, butcomplete three-particle problem has to be solved. Twcenter effects on the electron emission have been inclurecently ~for an overview see@28# and references therein!and total ionization cross sections as well as the details ofelectron emission were successfully calculated~see also@40,41#!. In the longitudinal direction even recoil-ion momenta as well as the momentum change of the projechave been deduced from calculated electron momenta aping momentum conservation laws@42#. Since, however, thecomplete three-particle problem is not solved, the transvescattering of the recoil ion and of the projectile is not accsible within this approach. Thus, the very fundamental thrparticle problem, single ionization of a target atom by an

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in the nonperturbative regime~which is the most importanone if slowing down of ions in matter is considered awhich, in essence, leads to the Bragg maximum in the eneloss! is still out of the capabilities of most calculational tecniques.

On the other hand tremendous progress has been achusing semiclassical methods. Classical trajectory MoCarlo ~CTMC! calculations are the only method in the noperturbative regime that treats the full three-particle problwithout any approximation beyond classical scatteringthe interaction of the charged particles. Quantum behavioincluded statistically by using a momentum distributionthe electron in the bound state of the target atom determby potentials based on Hartree-Fock calculations. Methhave been developed for treating many electron transiti~n-body CTMC! accounting for the electron-electron interation in the ground state. More sophisticated techniques wreported to treat the (e-e) interaction during the collisionaccounting for the monopole part of the interaction~dynami-cal screening: dCTMC@43#! as well as on its direct implementation in the postcollision dynamics for transfer ioniztion and double ionization collisions@44#.

II. EXPERIMENTAL METHOD

The recently developed combined multielectron recoil-imomentum spectroscopy@24# was used to control and analyze with high resolution the reaction products after targionization. One substantial part guaranteeing an interncold and well defined He target is a two stage supersonicThe He gas expands through a 30mm diameter nozzle form-ing a supersonic atomic beam. With two skimmers of 0mm and 0.4 mm diameter, respectively, the innermost parthis beam is cut out providing a localized (Dx'2 mm) anddense (1012 cm22) He target. The atomic beam is crosswith a well collimated beam~1 mm 3 1 mm! of3.6 MeV/u Se281 ions delivered from the universal linear acelerator ~UNILAC ! at GSI. The projectiles were chargstate analyzed after the collision and Se281 ions ~no chargeexchange! were recorded by a fast scintillation counter wia rate up to 1 MHz. Recoiling target ions and electrons pduced in the reaction zone are extracted along the ion binto opposite directions by a weak uniform electric field1–5 V/cm applied over a length of 22 cm~Fig. 1!. An addi-tional homogenous magnetic field of typical 10–20 Gau

FIG. 1. Schematic drawing of the combined recoil-ion manelectron momentum spectrometer.

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56 1353COMPLETE MOMENTUM BALANCE FOR SINGLE . . .

generated by two Helmholtz coils~1.5 m diameter!, is ap-plied almost parallel to the electric field which forces telectrons on cyclotron trajectories. In this way the electroare efficiently guided onto the detector and a high detecsolid angle is guaranteed. After acceleration in the electfield recoil ions and electrons both drift over 22 cm befothey are postaccelerated~2000 V for recoil ions and 200 Vfor electrons! and detected by two-dimensional position sesitive ~2D PS! channel-plate detectors. With this focusingeometry the time of flight becomes independent in firstder on the extension of the reaction zone considerablycreasing the resolution in the longitudinal direction. Fromposition of detection and the TOF, measured in an elecrecoil-ion projectile coincidence, the recoil-ion charge stand the three momentum components of both, the recoiland the emitted electron, can be deduced. All recoil ionsinterest and all electrons~DV54p for energies up to 50 eV!are projected onto the detectors. Due to detector efficienand grid transmissions a total triple coincidence efficiencyabout 20% was achieved. Details about the spectrometeadvantages and limits, and how to extract unambiguouslytrajectories and the initial momenta of the reaction producan be found in@24#.

If a double-ionization event occurs one is faced with tproblem that the position and the TOF of both electronsto be recorded. This is not a simple task since both electrhit the detector within a time gap of less than 200 ns. Wour new three-fold electron detector device, which consof three independent~2D PS! detectors@45#, we can easilyfulfill this requirement under the specific condition that eaelectron hits a different detector. If both electrons arrivethe same detector we lose the position information butcan still determine their time of arrival if their spacingtime is more than 8 ns. This allows us to extract the lontudinal momenta of both electrons in coincidence withcomplete momentum vector of the He21 recoil ion. Recentimprovements of the electron spectrometer, time focusingwell as the threefold detector, are described in more deta@45#. Results of double ionization have partly been publish@44# and will be discussed in a forthcoming publication.

Besides the unique advantage of a 4p solid angle andlarge momentum acceptance, which is necessary for codence measurements, our technique for low-energy elecdetection removes many of the tremendous experimentalficulties of conventional spectrometers. The target extensis well defined by the supersonic jet. Electrons from thesidual gas are completely suppressed in the triple coidence spectra. The influence of electric fringe fields amagnetic distortions is drastically reduced by extractingelectrons. The final charge state of the target and that ofprojectile ion are well defined. Furthermore, since theQvalue of the reaction is measured in addition, simultaneelectronic excitation of the heavy projectile is excluded.

We want to emphasize, that for the investigation of mtiple ionization or collision induced reactions where mothan one electron is emitted, like in target ionization accopanied by electron loss from or electron capture to the pjectile, large active diameter 2D PS electron detectors wfast multihit capable delay-line readout@46# will be imple-mented in the near future. This then allows kinematica

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complete experiments for a large variety of collision inducmultiple-ionization reactions.

III. THEORETICAL MODEL

The experimental data presented here will be compawith results obtained with the CTMC theory. As mentionin the Introduction, this theory treats the nonperturbatthree-particle problem completely concerning the intertions between all particles, yielding the complete nindimensional final momentum space for single ionization.this section we give a brief description of the theoreticmodel and shortly discuss the implemented improvemeand its natural limits. The semiclassical model has been donstrated to be an adequate approach to describe ion indtarget single and multiple ionization for a large range of ipact velocities and projectile charge states. Moreover, sinelectron capture from laser aligned initial states with tcomplete determination of productn, l , andml quantal lev-els has been successfully benchmarked against experimline emission measurements which includes polarizationanisotropy@47#. Recent studies for target single ionizationhelium @8# and multiple ionization of neon@39# using fastheavy ions as well as investigations for slow highly chargion and proton impact ionization of helium@26,27# demon-strated the capabilities of the CTMC approach. From anperimentalists point of view the fact that experimentally acessible highly differential cross sections can be calculaeasily and in a clear manner is a further advantage.

The theoretical method used here includes inherentlythree-particle dynamics: the interaction between all partpating particles during and after the collision is directly icorporated in the calculations. The bound-electron inistate of helium is taken to be in a model potential determinfrom Hartree-Fock calculations. This same model potentiaincorporated in the interaction of the projectile and the tarnucleus so that all charges are asymptotically correct at bthe separated and united atom limits. Moreover, the etron’s Compton profile is in reasonable agreement withperimental values.

IV. RESULTS AND DISCUSSION

The dynamics of single ionization of an atom by chargparticle impact is completely determined by the measument of six out of nine momentum components of the thparticles in the final state. The three missing momentcomponents as well as the inelasticity~the Q value! of thereaction can be deduced from momentum and energy convation. For the overwhelming part of ion-atom collisionleading to ionization of the target atom only little momentuand energy compared to the initial momentum (pP) and en-ergy (EP) of the incoming heavy projectile is transferreduring the encounter. Under these conditions the longitud~along the ion-beam direction! and transverse momenta adecoupled and can be calculated separately on the basnonrelativistic energy and momentum conservation. Thefore, the transverse momentum balance in the laboraframe of reference has to fulfill

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gies between the initial and final atomic states, is direcconnected to the longitudinal momentum transfer. Moreovthe longitudinal recoil-ion momentum is related to the cotinuum energyEe of the ejected electron demonstrating tclose linkage between recoil-ion momentum spectroscand electron spectroscopy@48#.

Once theQ value is known, a quantity which is detemined experimentally, then the process of single ionizatiofully determined by the specification of a fivefold differenticross section. Several projections out of this many dimsional space onto specific physically relevant quantitiesbe discussed in order to elucidate the dynamics of collisinduced ionization. Since all reaction products are detecsimultaneously, the absolute cross section is easily obtaby normalizing the sum of all events to the measured tosingle-ionization cross section of s115(3.360.5)310215 cm2 @49#. This same value has been used to normize the CTMC calculations which lie 27% below the acepted experimental value.

In this section experimental results for single ionizationhelium due to the impact of 288 MeV~3.6 MeV/u! Se281

FIG. 2. Illustration of the collision geometry and declaratioused throughout this paper.

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will be discussed in detail and compared with results otained by CTMC calculations. Since one cannot presentthe possible projections and cuts out of the nine-dimensiomomentum space~i.e., the square of the complete threparticle final-state wave function! a subjective selection odata is presented which in the authors opinion illuminatesmain features of the underlying collision dynamics. Figureillustrates the geometrical conventions used throughoutpaper. The projectile moves along thez direction~this is thelongitudinal direction!. The transverse plane is the (x-y)plane. The collision plane is defined by the incoming projetile vector and the recoil-ion transverse momentum goalong the negativex direction ~see Fig. 2!.

A. Longitudinal momentum balance

The cross-section differential in longitudinal momentathe recoil ion, the electron, and the projectile is shown in F3 together with predictions obtained from theory~lines!. Asin a previous measurement@8# with 3.6 MeV/u Ni241 projec-tiles the electrons are found to be emitted dominantly ithe forward direction with a most likely forward energy oonly 2.5 eV. Their longitudinal momentum is almost completely balanced by the backscattered recoil ions. Thus,projectile momentum change shows a narrow distributwhose width is mainly determined by our experimental relution. Nevertheless, the tail on the left-hand side canattributed to the electron energy distribution@theEe /vP termof Eq. ~4!#.

The target atom ‘‘dissociates’’ in the strong electric fieof the passing projectile which delivers energy but only velittle momentum. Therefore, the action of the fast heavy pjectile reveals similarities to photoionization where the eletron perfectly balances the recoil-ion momentum to thetent of the negligibly small momentum transferred by tabsorbed photon. In fact, the field of a swift charged projtile can be described as an intense electromagnetic pulsetaining a broadband of photon frequencies. In the framewof the Weizsa¨cker-Williams method target ionization is de

FIG. 3. Longitudinal momentum distributions of recoil ions ansoft electrons together with the projectile’s momentum loss~histo-gram!. Smooth lines: CTMC calculation multiplied by a factor o1.4.

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scribed as absorption of those virtual photons by the a@50#. Since almost no momentum is carried by the incidphotons only those whose energy corresponds to the momtum of the electron in the bound state at the instant ofsorption can interact. Hence, the obtained momenta ofelectrons and the recoil ions are directly related to the innal momenta of the electrons in the helium atom at thestant of the collision with the projectile ion.

The remarkable forward-backward asymmetry of tionic target fragments can be ascribed to the strong, lorange potential of the outgoing projectile leading to a ‘‘puing behind’’ of the electron and a ‘‘pushing away’’ of thremaining target ion~the so-called ‘‘postcollision interaction’’: PCI!. This behavior is predicted by theory~see Fig.3!. In a recent theoretical study Wood and Olson@51# haveshown that the longitudinal emission characteristics of reion and electron change dramatically if the sign of the pjectile charge is changed. For antiproton collisions with hlium the electron is predicted to be emitted in the backwdirection whereas the recoil ion emerges with positive mmenta due to the reversed sign of the PCI.

B. Low-energy electrons

The total electron emission is dominated by low-eneelectrons with energies well below 50 eV contributingmore than 85% to the total single-ionization cross sectiThe cross section singly differential in electron energies~in-tegrated over all emission angles! is shown in Fig. 4 in com-parison with the theoretical results~full lines! for single ion-ization of helium by 3.6 MeV/u Se281. Electrons arecoincident with He11 ions and projectiles without charge echange in their ground state. As in a previous experiment@8#a weak maximum appears around 2 eV which is neither

FIG. 4. Singly differential electron emission cross sectionsingle ionization of helium by 3.6 MeV/u Se281. Full line: CTMCresult scaled up by a factor of 1.4. Dotted line: 1.Born approximtion @52#.

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produced by any theory~Born approximation@52#, CTMC!nor by any other experimental investigation. For electronergies above 4 eV the obtained shape of the distribution iagreement with CTMC, slightly steeper than predicted by

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FIG. 5. Singly differential cross section for emission of lowenergy electrons withEe,50 eV as a function of the ejected eletron’s polar angle. Full line: CTMC calculation multiplied by 1.4

FIG. 6. Transverse momentum distributions of recoil ions, eltrons, and projectiles for single ionization of helium. The transveprojectile momentum exchange is directly associated with the stering angle~upper scale!. Smooth lines: CTMC calculation multi-plied by 1.4.

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FIG. 7. ~Color! pe' vs pR' for helium single ionization by 3.6 MeV/u Se281 impact. The cluster size represents the doubly differencross sectiond2s/(dpe'dpR') plotted on a logarithmic scale.

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first Born approximation and similar to results of other eperimental investigations@53#.

We want to emphasize that our results cannot be cpared directly to results of any other measurements atelectron energies where neither the final charge state ofprojectile nor that of the target was controlled. To the besour knowledge, the intensity of these very low-energy eltrons ~the first data point in Fig. 4 comprises all electrowith 0<Ee,400 meV! has never been investigated expementally and it is questionable whether some of the electrin the very low-lying continuum at the target might recombine radiatively. This is one of the questions that willaddressed in further experiments. Reducing the magnitudthe electric extraction and the magnetic guiding fieldsenergy resolution of a few meV can be achieved with o

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spectrometer at a bandwidth of 0<Ee,5 eV. ~Such experi-ments have been performed recently and will be publisseparately.!

The preference of the forward direction of low-enerelectron emission is obvious in the differential cross sectas a function of the electron’s polar angle~Fig. 5!. Here thedoubly differential cross section is integrated over electenergies withEe,50 eV. The angular dependence cleademonstrates the forward peaked electron emission anreduction of the cross section by more than one ordermagnitude into the backward hemisphere. Althoughagreement between experiment and CTMC predictionsquite good for the longitudinal momenta and the electrenergies, a slight overestimation is observed in the forw

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FIG. 8. ~Color! Projections in momentum space of all particles in the final state after helium single ionization onto the plane deteby the incident projectile and the outgoing He11 recoil-ion momentum vector~i.e., the collision plane!. The cluster size represents thcorresponding doubly differential cross sectiond2s/(dpxdpi) on a logarithmic scale. For the recoil ion this is equal tod2s/(dpR'dpRi)since the recoil-ion momentum component pointing out of the paper plane is zero due to the specific projection.

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direction along with a significant underestimation of bacward emission.

C. Transverse momentum balance

In contrast to the longitudinal direction where recoil-ioand electron momenta are linked via the energy-conservaequation@Eq. ~3!# the transverse direction reveals the futhree-body dynamics. Here, the transverse recoil-ion mmentum compensates the transverse momentum ofejected electron and in addition the internuclear momenexchange between the target and the projectile. In Fig. 6single-ionization cross section differential in transverse mmenta of all outgoing particles is displayed in compariswith predictions obtained from CTMC calculations. Wpoint out that the projectile momentum is deduced frommeasured electron and recoil-ion momenta and that thetracted projectile scattering angles in the sub-mrad regime arenot accessible by analyzing the outgoing projectile direcThis would require the measurement of a deflection of 1 mon a detector placed 10 km behind the target region. It wofurther necessitate a beam quality which is beyond the meof the best available ion accelerators or storage rings.

Surprisingly, within our experimental resolution, thereno difference between the transverse momentum distrtions of recoil ions and electrons. Moreover, the transvemomentum transfer to the projectile is smaller than the

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served momenta of the atomic fragments. Thus, similarlyin the longitudinal direction they almost completely balaneach other. This is possible only if recoil ion and electronemitted into opposite directions. The experimental resuvalidate the statement that the total momentum transfeby the projectile is small compared to the final momentaboth the ejected electron and recoil ion. One important csequence is that there is no direct relationship betweenimpact parameter and the transverse recoil-ion momentumthe projectile scattering angle. Theory predicts typical impparameters for single ionization of about 4 a.u. being larthan the mean spatial extension of the helium atom. Ththe target nucleus is almost perfectly shielded by its electrand polarization of the atom becomes important duringinward part of the projectile trajectory which, based on tsemiclassical results, should even result in negative defltion angles@30,54#: the projectile was predicted to be scatered to the same side as the emitted recoil ion for a mpart of the total single-ionization cross section.

In Fig. 7, where the transverse momentum of the electis plotted versus that of the recoil ion, those events woappear above the diagonal line withpR'5pe' . This is trueonly if electron and recoil ion are perfectly emitted backback in the azimuthal plane~the plane perpendicular to thprojectile beam!, which will be discussed in more detail ione of the following sections. In conclusion, the momenta

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FIG. 9. ~Color! Momenta of emitted electron and scattered projectile projected onto the (py-pi) plane. In this representation the outgoinrecoil-ion momentum vector stands perpendicular to the paper plane corresponding to a rotation of the coordinate system definedby 90° around thepi axis ~i.e., a ‘‘side view’’ of Fig. 8!. Plotted are the doubly differential cross sectionsd2s/(dpydpi) for the electron andprojectile ions, respectively, on a logarithmic scale.

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electron and recoil ion are strongly coupled in the longitunal as well as in the transverse direction: if the electronemitted with a high momentum then the recoil-ion mometum is also large. In addition, for the overwhelming partall collision events the momentum transfer from the protile is comparably small. This is true in the transverse as was in the longitudinal direction.

D. Three-particle dynamics

A convenient representation to illuminate the complthree-particle momentum balance is to project the momeof all outgoing reactants onto the collision plane~see Fig. 2!defined by the incident projectile~pi direction! and the trans-verse recoil-ion momentum vector~2px direction! ~Fig. 8!.Several of the main features characterizing the dynamictarget single ionization by fast heavy ions can be dedufrom this representation. First, the forward-backward asymetry of recoil ion and electron which, according to theois a result of the long-range interaction with the recedprojectile ion~PCI effect!. Second, the momentum imparteby the projectile is small in comparison to the momentathe atomic fragments revealing similarities with ionizatiby photoabsorption. Third, the recoil ion and electronpreferably emitted back to back balancing their momentaa level which corresponds to the small momentum traferred by the projectile.

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The tail observed in the projectile distribution towarpositivepx momenta in Fig. 8 can be attributed to the direinteraction of the projectile with the target nucleus. Only fthose encounters is the momentum transfer related toimpact parameter, but this is a minor fraction of all collisioleading to single ionization of helium~cross sections are onlogarithmic scale in Fig. 8!. This fact is further supported bythe representation chosen in Fig. 9 where the recoil-ion mmentum vector is pointing out of the paper plane. Here eltron and projectile momenta are projected perpendicularlthe above defined collision plane corresponding to a ‘‘sview’’ of Fig. 8 from thex direction. If the projectile deflec-tion would be caused mainly by interaction with the targnucleus this projection would deliver narrow distributiocentered along thepz axis. Instead, a considerable amountmomentum transfer out of the collision plane is observexperimentally. This implies that the recoil ion and electrare not perfectly emitted back to back. Moreover, the amuthal angle enclosed by the electron and recoil ion shoshow a distinct distribution. This point together with the agular correlation between all participating particles in tazimuthal plane will be discussed in more detail in the flowing section.

There has been a lively recent discussion on the so-ca‘‘asymmetry of the soft electron emission’’ in collisions witstrong perturbations. Analyzing data sampled with conv

eteredons


FIG. 10. ~Color! The momenta of~a! outgoing projectile ion and~b! ejected electron projected onto the azimuthal plane~the planeperpendicular to the incoming projectile velocity vector!. The orientation is defined by the He11 recoil ion which is scattered along thnegativepx axis as indicated by the arrows. In~c! the projected electron momentum distribution is shown with respect to the scatprojectile which is deflected towards the negativepx direction defining the rotation in this plot. The doubly differential cross sectid2s/(dpxdpy) are presented on a logarithmic scale.

etectsiethhe

on.ar-

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ro-ed

tional electron spectrometers for electron energies aboveV @2#, it was found that most of these electrons are emitinto the forward direction as a result of two-center effe@53,55#. Exploring the full three-particle collision dynamicwith our method illuminates that this asymmetry indeedtwofold. In addition to the distinct forward emission of thsoft electrons another asymmetry becomes obvious inthe maximum of the electron momentum distribution in t

1ds

s

at

scattering plane is found opposite to the recoil-ion emissiAs will be shown in a subsequent theoretical paper this chacteristic changes dramatically as a function of the collisvelocity.

E. Azimuthal angular correlations

In this section we want to restrict the discussion to pjections of the full three-particle momentum space obtain

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after helium single ionization onto the azimuthal plane,plane perpendicular to the incoming projectile velocity vetor @i.e., the (px-py) plane according to the convention usso far#. The projections of the outgoing projectile and temitted electron momentum with respect to the recoil iondisplayed in Figs. 10~a! and 10~b!. The distributions are ori-ented such that the momentum vector of the scattered H11

recoil ion is pointing along the negativepx direction as indi-cated by the arrows without additional condition on tlength of this vector.

A very narrow distribution centered around the originobtained for the projectile ion demonstrating again the wmomentum exchange between projectile and target nuclHelium single ionization is dominated by small-angle sctering of the projectile which is deflected almost isotropicawith respect to the recoiling target nucleus. Moreover, wfinite probability negative scattering angles occur andprojectile is scattered to the recoil-ion side~2px direction!.Within the experimental resolution for the projectile mometum change of aboutDpp''60.1 a.u. corresponding topolar scattering angle resolution ofDqp'657 nrad no sig-nificant shift of the center of the projectile scattering distbution towards the recoil-ion side can be observed.

A quite different behavior is obtained for the ejected eletron to be emitted preferentially into the opposite directionthe recoil ion@Fig. 10~b!#. Thus, we again observe a stronlinkage between recoil ion and electron but, on the othand, there is almost no azimuthal angular correlationtween the projectile and the ionic target fragments. Thisilluminated by plotting the electron momentum distributioprojected onto the azimuthal plane with respect to the stered projectile in Fig. 10~c!. Only a weak correlation is observed such that the electrons slightly tend to be scattopposite to the projectile. For a better comparison thesesults are compiled in the polar diagrams of Fig. 11 showthe corresponding angular distributions for the azimutangles between all ejected reactants.

Exploring the characteristics of the three-particle momtum exchange in even more detail, it is instructive to plotazimuthal angle between recoil ion and electronw re versusthe angle enclosed by recoil ion and projectilew rp calculatedfor each single event~Fig. 12!. In this representation thedifferent collision mechanisms contributing to target singionization can be separated in a simple and illustrative mner since the dominance of any possible two-body intertion can be assigned to specific regions in this plot. Foroccurrence of a direct nucleus-nucleus interaction, whereelectron takes up the part of a spectator, recoil ion and p

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jectile are emitted back to back into opposite directioThus those events are characterized to appear along thewith w rp5180°. Following the same argumentation binaencounter electron emission, which is a two-body interactbetween projectile and electron, shows up along the diagow rp5180°2w re , whereas a strong coupling of recoil ioand electron, which can be associated with ‘‘photoioniztion,’’ appears with the typical angle ofw re5180°. Allevents inside these boundary lines experience momentumchange between all participating particles on the basis othree-body interaction. Thus, the observed pattern cledemonstrates the importance of the three-body momenexchange. It also shows, however, that the kinematicssingle ionization by fast heavy-ion impact is dominatedelectronic dipole transitions where the recoil-ion electrtwo-body interaction dominates the three-body momentexchange.

Many of the discussed features, such as the small momtum loss of the projectile, the preferred back to back emsion of the recoil ion and electron, and the fact that theserved momenta compare well to the internal momenta oftarget atom, are inherently included in the simple pictuwhere ionization is the result of the interaction with thequivalent photon field of the passing projectile ion. Athough the Weizsa¨cker-Williams formalism and the firstorder Born approximation fail in reproducing, e.g., the tocross section for the present collision system since theyvalid only in the limit of high velocities~at largevp andsmall perturbations both formulations are identical!, the as-sumption that dipole excitations contribute mainly to ioniztion is still valid in the present regime of fast collisions wilarge perturbation strengths.

V. CONCLUSIONS

We have performed a kinematically complete experimfor single ionization of helium by charged particle impausing advanced many particle detection techniques. Themomentum vectors of all participating reactants were msured with high resolution and the dynamics of helium sinionization by fast heavy ions was explored. The resultsour work are manyfold.

First, a fast highly charged projectile is an extreme‘‘soft’’ and ‘‘sensitive’’ tool to ionize the target. It merelytransfers momentum to the target electrons, acting very mlike a photon field. Moreover, since no momentum or eneexchange between the two electrons is required to obdouble ionization the final two electron momentum distrib

nal--

alm

FIG. 11. The angular distributions betweethe three outgoing particles in the azimuthplane perpendicular to the initial projectile direction. Polar representation of the singly differential cross section as function of the azimuthangleds/dw between the transverse momentuvectors of the specified particles.

are the


FIG. 12. ~Color! The azimuthal angle between recoil ion and electron plotted vs that between recoil ion and projectile. Indicatedkinematical lines assuming the specified two-body interactions and considering the third particle as a spectator~see text!. The region belowthe diagonal line is forbidden because of simple kinematical reasons.

f tth

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ementthe

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tions have been demonstrated to be a sensitive probe o(e-e) correlation in the ground state as well as duringcollision @44#.

Second, the strong and long-ranging potential of the ogoing projectile ion causes a considerable forward-backwasymmetry of the recoil ion and electron. The asymmetrythe electron emission which has been discussed beforfound to be twofold: In addition to being scattered forwathe electrons are emitted opposite to the recoil ion inscattering plane. One can easily show that, for the presituation, all particles strongly interact in the continuuwhich is an ideal situation to investigate the three-body Clomb continuum. As expected, semiclassical calculations

hee

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ent,--

herently including all the interactions among the particlcorrectly describe the continuum.

Third, the attempt to separate the many particle problinto several two-body interactions shows that for the prescollision system the strongest correlation occurs betweenrecoil ion and the electron and not, as might be expecbetween the recoil ion and the projectile via nuclear Colomb deflection. Thus, and very importantly, it is definiteimpossible for the major part of all collisions resultingsingle ionization to extract the impact parameter fromobservable quantities. This has been demonstrated beforproton on helium singly ionizing collisions at energies btween 0.5 MeV@18# and 3.0 MeV@16,56#, i.e., at consider-

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ably smaller perturbations. As far as theories are concermany particle interactions between the electrons and theclei have to be incorporated and the impact-parametermulation using a classical trajectory in the~screened! poten-tial of the target is not adequate for the present situatRecent experiments and calculations@27# show that such anapproximation may be partly applicable for single ionizatiat very low projectile velocities comparable to orbital veloity of outer-shell electrons.

Fourth, the comparisons with results obtained froCTMC calculations demonstrate that this semiclassmodel is reliably applicable in the present regime of hiperturbations. In spite of the approximative descriptionbound many electron atomic states~actually this is also truefor all quantal calculations on bound many electron state! itclearly predicts the underlying collision dynamics and allothe extraction of highly differential cross sections. It is tonly model available that includes many particle interactioand the coupling between electronic and nuclear motionconsistent way. The inclusion of the full (e-e) interactionduring the collision and in the final state was shown toessential to come to a reasonable agreement with experimtal data in the case of double ionization@44#.

VI. FUTURE PERSPECTIVES

Since several other experimental groups are now ussimilar techniques, in the near future many new experimewill be performed over the wide range of projectile energavailable at different accelerator facilities. As will be dtailed in a subsequent theoretical paper the characteristicthe three-body collision dynamics undergo dramatic chanas a function ofvp andqp . Regimes are found where any othe mutual two-body interactions dominate the three-partmomentum exchange as well as ‘‘true’’ three-body situatioare present. A flavor of the rich variety to be expected canobtained by comparing the present results with a similarperiment for 5–15 keV proton impact on helium@57#. There-fore, it would be most desirable that full three-particquantum-mechanical calculations are developed in thefuture giving consistent results over the whole range of pturbations.

Even more, applying our experimental technique, it isbe expected that the complete momentum vectors of ufive continuum electrons emerging from a collision candetermined simultaneously in the near future. The first kimatically complete experiment on helium double ionizati

d.

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en-

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ofes

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has been already performed@44# and further results will bepublished soon. They certainly will be followed by moinvestigations using protons or electrons as projectiles, asummarized in an upcoming review on the field of recoil-imomentum spectroscopy@23#.

Recently similar experiments have been performed us1 GeV/u U921 projectiles from the SIS~heavy-ion synchro-tron! at GSI extending the investigations to the highest psible perturbation in the high velocity limit.~The results willbe published separately in a forthcoming paper.! Then, onone hand, relativistic effects become important and escially the magnetic interaction of the relativistic projectiwith the target might be strong enough to consideramodify the collision dynamics. At the same time, the mofication of the electron spectra by the final-state interactwith the receding projectile will be reduced by at leastfactor of 5, so that the mapping of the correlated motionthe electrons from the initial to the final state is expectedbe less influenced by PCI.

We would like to emphasize that fast GeV/u highcharged ions are a unique, unsurpassed source of light dering attosecond (10218 sec), exawatt/cm2 (1018 W/cm2),and broadband pulses of virtual photons. These featuresbeen exploited in nuclear physics to investigate nuclstructure~halo nuclei, giant resonances, etc.!. Combined withkinematically complete experiments on double~multiple!ionization this reveals an ‘‘attosecond microscope’’ for tinvestigation of the correlated many-electron motion withparts of typical revolution times in bound states. In additiomolecules, clusters, or even solids can be used as tarThus, one might envisage that this method will becomestandard technique for the investigation of bound-stmany-electron correlations in atoms, molecules, clusters,solids.

ACKNOWLEDGMENTS

This work was supported by GSI, DFG, and BMFT. Wwould like to thank our colleagues and friends A. CassimC. L. Cocke, R. Do¨rner, S. Hagmann, M. Horbatsch, O. Jautzki, S. Keller, R. Mann, V. Mergel, and L. Spielberger fmany stimulating discussions. The excellent work of tUNILAC crew of GSI for providing the ion beam and thtechnical support by A. Bardonner are acknowledged. Tauthors would like to thank the Alexander von HumboStiftung for their support and acknowledge the financial sport of NATO.

s.

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r-

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