Complete single-ionization momentum spectra for strong perturbation collisions
R. E. Olson and C. J. WoodDepartment of Physics, University of Missouri-Rolla, Rolla, Missouri 65401
H. Schmidt-BockingInstitut fur Kernphysik, University of Frankfurt, D-60486 Frankfurt/Main, Germany
R. Moshammer and J. UllrichUniversitat Freiburg, Fakultat fur Physik, D-79104 Freiburg, Germany
~Received 11 August 1997!
The combination of recoil ion and ionized electron momentum spectroscopy provides an unparalleledmethod to investigate the details of ion-atom collision dynamics in kinematically complete experiments. Topredict single ionization scattering behavior at the level now realized by experiment, the classical trajectorythree-body Monte Carlo method has been used to obtain complete momenta information for the ionizedelectron, recoil ion, and projectile in the collision plane defined by the incident projectile and outgoing recoilion. Strongly coupled systems were considered where the charge state of the projectile divided by the speed ofthe collision q/v is greater than unity. Illustrated are 3.6-MeV/nucleon Se281 and 9.5-MeV/nucleon Ni261
collisions on He where experimental data are available. The theoretical results are in good agreement withthese data and calculations have been performed for 165-keV/nucleon and 506-keV/nucleon C611He tocompare results for the sameq/v perturbation strengths, but at much lower velocities. In all cases the ejectedelectrons are found to be preferentially emitted opposite to the recoil ion in the projectile-recoil collision plane.The 165-keV/nucleon C61 spectra are especially rich in that electron capture strongly contributes to the overallelectron loss process. Here, the electron capture to the continuum~ECC! spectrum is observed to have not onlythe known asymmetry in the longitudinal direction, but also has an almost complete asymmetry in the collisionplane opposite to the recoil ion. Collision plane spectra differential in the transverse momenta of the recoil iondepict the transition from soft electrons for low transverse recoil momenta, to two-center, and ECC electronsfor increasing transverse recoil ion momenta.@S1050-2947~98!10006-9#
PACS number~s!: 34.50.Fa, 34.10.1x
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I. INTRODUCTION
The experimental application of recoil ion momentuspectroscopy has rapidly matured in the last decade. Onally, recoil ions were used as a source of slow, multicharged ions that were then employed in subsequent csion measurements. Studies were also made of the aveenergies of the recoil ions as a function of charge state. Hever, by the 1980s, the first measurements were being mon the transverse momentum distributions of recoil ioThese early momentum measurements were severely limby the thermal motion of the target atoms, which markerestricted the precision of the observations~see Ref.@1# for areview!.
The development of ‘‘cold’’ targets and position-sensitidetection has removed many of the impediments ofmethod ~see Ref. @2# for a detailed description of themethod!. As examples, Do¨rner et al. @3# displayed the inter-play of three-body collision dynamics for H11He singleionization collisions by comparing recoil ion transverse mmenta against projectile scattering angle. The Kansas Sgroup lead by Cocke used recoil ion spectroscopy to meatheQ values for electron transfer collisions@4,5# and clearlyobserved the mass transfer of the electron@6# in multipleelectron capture collisions of F911Ne. These measuremenwere followed by the direct observation in the recoil mmenta spectra of the signatures for the electron-electron
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electron-nuclear interactions in He1,O711He projectile ion-ization @7,8#. Unverzagtet al. at GSI @9# and Jardinet al. atCaen @10# then provided both longitudinal and transverrecoil momentum spectra for single and up to sevenfold iization of Ne and Ar, which displayed the collective behaior of the ionized electrons. Very recently, Moshammeret al.have combined recoil ion and electron spectroscopy to pform the first completemomentum determination of thproducts in single ionization collisions for ion impact@11,12#and have clearly observed the importance of the electrelectron interaction in multiple ionization collisions@13#.@For a review of the numerous experimental investigatioon kinematically complete (e,2e) experiments for electronimpact, see Ref.@14#.# The French group at Caen@15# hasmade high precision state-selective electron capture measments using recoil ion momentum spectroscopy for loenergy collisions involving Ne101 and Ar181, while theRIKEN group has performed similar investigations at muhigher energies@16#.
Presently, recoil ion momentum measurements madecoincidence with the projectile scattering angle measuments by Mergelet al. @17# illuminate the electron-electronThomas mechanism for transfer ionization in H11He colli-sions, while Kraviset al. @18# have studied saddle-point electron production in low-energy collisions involving multiplcharged ions. Furthering the development of the field isinvestigation by Do¨rner et al. @19# who observed collision
PRA 58 271COMPLETE SINGLE-IONIZATION MOMENTUM SPECTRA . . .
plane information for slow electron production in 10- a15-keV H11He collisions, and Tribediet al. @20# who haveobtained longitudinal momentum spectra for atomic and mlecular hydrogen differential in the angle of the ejected eltron.
Unfortunately, theoretical methods that describe the coplete final state momentum information for single and mtiple electron removal as a result of ion impact havemade the spectacular advances as those of the experimeists. The major impediment is the lack of anab initio quantaltheory that can provide the coincidence information ofproducts for even the three-body single ionization reactilet alone multiple ionization processes. In fact, there is ooneab initio quantal theory that includes electron correlatito accurately describe total cross sections for twofold ionition of the simplest many-electron target, the helium at@21#. Conventional basis set expansion methods, while pviding excellent accuracy for two-body interactions suchexcitation and electron capture, are unable to provide mmentum information for ionized electrons since the psdostates used to represent the ionization channel do notsufficient angular information. Only in the limit of high velocities for small perturbations where the first Born appromation is valid, has it been possible to include bothprojectile-electron and the projectile-target nucleus intertions to obtain three-body kinematics@22–24#. With increas-ing perturbation strengthsq/v.1, the dipole approximationbreaks down and three-body interactions strongly influethe product state momentum balance. In much of this laregime, the continuum distorted wave~CDW! method pro-vides an accurate portrayal of postcollision and two-cencollisional effects~see Ref.@25# for a review!. In the CDWmethod, by invoking conservation of momentum and enewith the assumption that the recoil ion’s energy is smcompared to that of the electron and to the energy changthe projectile, accurate longitudinal momentum spectrasingle ionization products can be obtained@26#.
In order to fill the gap and provide interpretation and pdictions of scattering dynamics, we have been lead tovelop then-body classical trajectory Monte Carlo~CTMC!method for single and multiple electron removal collisio@27#. In the CTMC method, the collision is evolved usinclassical mechanics, while the initial conditions contain nessary quantal information. A merit of the method is thatpairwise electron-nuclear and nuclear-nuclear interactiare included so that it is possible to provide a completetermination of the momenta of the product states of a cosion, even for multiple ionization. In order to maintain parwith the experimental progress noted above, extensions hbeen made to the original CTMC method so that now mopotentials based on Hartree-Fock calculations can be usedescribe the electron-nuclear interactions@28#, electrons onboth target and projectile centers can be incorporated@7#,dynamical screening of the nuclei during the collision mbe included@29#, and direct incorporation of the electronelectron interaction in the postcollision regime has beenplied @13#.
The motivation for the work reported here is to predsignatures of single ionization dynamics using coincideprocedures that are now within reach of experiment. Trange of projectile charge state over collision speedq/v is
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varied between 1.33 and 5.14. This is in contrast to a lperturbation strengthq/v50.5 study published for protonand antiproton collisions at 100 keV. In the latter, stroasymmetries in the collision plane for the antiproton cawere predicted, and the impact parameter dependence foformation of soft, saddle point, ECC, binary encounter, abackwards ejected electrons were illuminated@30#. Thesestudies were recently extended to 300 and 500 keV to pvide predictions@31# needed to design the recoil ion spetrometer for antiproton experiments conducted at the LEnergy Antiproton Ring in CERN. In the latter paper thelectron longitudinal spectra for proton impact were copared to data from pioneering studies made using convtional electron spectroscopy methods@32#.
II. THEORETICAL METHOD
For a simple three-body collision system comprised ofully stripped projectile~a!, a bare target nucleus~b!, and anactive electron~c!, the application of the CTMC method irelatively straightforward. One first writes down the classicHamiltonian for the system
H5pa
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Za
r ac1Vbc~r bc!,
~1!
wherepi are the momenta andVi j (r i j ) are the pairwise in-teraction potentials between the individual particles. FrEq. ~1!, one obtains a set of 18-coupled, first-order differetial equations arising from the necessity to determinetime evolution of thexyz Cartesian coordinates of each paticle,
dqi
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and their corresponding momenta,
dpi
dt52
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Five random numbers, constrained byVbc(r bc) and the bind-ing energy of the target atom, are used to initialize the plaand eccentricity of the electron’s orbit, and another is usedetermine the impact parameter within the range of intertion. For our work, we utilize a fourth-order Runge-Kutintegration method because of its ease of use and its abto vary the time step size. This latter requirement is essensince it is not uncommon for the time step to vary by throrders of magnitude during a single trajectory.
In essence, the CTMC method is a computer experimTotal cross sections for a particular process are determby
sR5S NR
N Dbmax2 , ~4!
whereN is the total number of trajectories run within a givemaximum impact parameterbmax, andNR is the number of
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272 PRA 58R. E. OLSONet al.
positive tests for a reaction such as electron capture orization. Momentum differential cross sections are easily geralized from the above.
For single electron removal reactions with a He taratom, it is adequate to treat the problem within a onelectron model and employ the independent electronproximation to approximate atomic shell structure. Foraccurate calculation, it is necessary to use an interactiontential that simulates the screening of the target nucleusthe electrons. One can simply apply a Coulomb potenwith an effective chargeZeff , such as obtained from Slaterrules. Then, the computational procedure is the same ashydrogenic case. However, the boundary conditions forlong-range and short-range interactions are poorly satisfi
To improve the electronic representation of the target,tentials derived from quantum-mechanical calculations wused. Here, the simple solution of Kepler’s equation canbe applied. However, Peachet al. @33# and Reinhold andFalcon @34# have provided the appropriate methods that yia target representation that is correct under the microcancal distribution. For our work, we employ the methodReinhold and Falco´n because of its ease of use and flexibity. Moreover, we have standardized our codes for a mopotential of the form
Vbc~R!52@Zb2NbS~R!#
R~5!
with the screening of the core given by
S~R!512H S h
j D @exp~jR!21#11J 2 1/2
. ~6!
In Eqs.~5! and~6!, Zb andNb denote the nuclear charge annumber of nonactive electrons in the target core, andh andjare screening parameters.
The major reason for our choice of this interaction potetial is that Garveyet al. @35# have performed a large set oHartree-Fock calculations and have parametrized their resin the above functional form. Screening parameters are gfor all ions and atoms forZ<54. This potential can also bused for the representation of partially stripped projecions. Moreover, in order to predict spectra differential in tmomentum of all outgoing particles, it is necessary thatinteraction potentials are accurate in both the unitedseparated atom limits.
III. RESULTS
A. Longitudinal momentum spectra
In order to illustrate the collision dynamics as a functiof perturbation strengthq/v, we will concentrate on 9.5MeV/nucleon Ni261 and 3.6-MeV/nucleon Se281 single ion-ization collisions with He. Here, theq/v values are 1.33 and2.34, respectively. Moreover, there are complete experimtal momentum spectra for these two systems with whichcompare the calculational results. These measurementsmade at GSI Darmstadt by the authors using the experimtal setup recently described in Ref.@12#. Since the perturbation strength cannot completely specify a system, we wcontrast these results with those of 506- and 165-k
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nucleon C61, which have the sameq/v values. As will beshown, the 165-keV/nucleon C61 spectra are especially ricbecause electron capture is a major component of the etron removal processes, in turn, this strongly affectsthree-body ionization spectra. Finally, lest we begin to fthat the collision dynamics are well understood, we wcompare the CTMC results to the 34-, 48-, and 66-kenucleon C611He longitudinal momentum spectra of Kravet al. @18#, which haveq/v values of 5.14, 4.33, and 3.69respectively. Here, electron capture dominates over iontion and the agreement between experiment and theorpoor.
In Fig. 1 our experimental and theoretical results are psented for the 9.5-MeV/nucleon Ni261 system, whereq/v51.33. The CTMC values, which are known to underesmate the total ionization cross sections at high energiescause of the poor classical description of large impact pareter collisions that give rise to slow electrons, have benormalized to the experimental results. In turn, the expmental data are absolutely normalized by extrapolatingabsolute data of Berget al. @36#, which are accurate to630%. For the recoil ion spectra, there is reasonable oveagreement between theory and experiment with the mmum value of the longitudinal momentum found20.2 a.u. The calculated electron spectra are found to pat approximately 0.3 a.u. The forward shift is due to the po
FIG. 1. Longitudinal momentum spectra for single ionizati9.5-MeV/nucleon Ni2611He collisions. Our experimental electroand recoil ion spectra are given by filled and open circles, resptively. The CTMC values for the electron and recoil ion spectragiven by the solid and long-dashed line, respectively. The theoical change in longitudinal momentum of the projectile is giventhe short-dashed line. The CTMC cross sections have been mplied by a factor of 2.41 to the experimental value2.6310215cm2.
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PRA 58 273COMPLETE SINGLE-IONIZATION MOMENTUM SPECTRA . . .
collision interaction with the highly charged projectile. Thasymmetry between the recoil and electron longitudinal mmentum, with the electrons having a larger cross sectiopositive values of the longitudinal momentum than the cresponding values at negative momenta for the recoil ioncaused by the momentum change of the projectile, whichonly be negative. The calculated momentum change ofprojectile is also given in Fig. 1. The loss of projectile mmentum is very sharply peaked with the maximum occurrat Q/v520.046 a.u., the value that corresponds to zeroergy ionized electrons. The experimental electron spectradicate that the electrons are more backwardly scatteredgiven by the calculations, with a maximum value atpz'0.1 a.u. As a check we have verified that the full threbody calculations are preserving conservation of momenand energy.
As the perturbation strength is increased toq/v52.34 forthe 3.6-MeV/nucleon Se281 system, the overall trends of thlongitudinal momentum spectra remain similar to that for9.5-MeV/nucleon Ni261 case. The calculated and experimetal recoil ion spectra are again in good agreement withanother, and are found to maximize at approximat20.4 a.u., Fig. 2. The same disagreement as before efor the electron spectra. Here the calculations maximizeapproximately 0.55 a.u., while the experimental valuearound 0.3 a.u. For the CTMC results, the asymmetry inrecoil ion versus the electron spectra is further enhancecomparison to the 9.5-MeV/nucleon results. This is becathe projectile momentum loss broadens considerably asspeed of the projectile decreases. As expected, the chanprojectile momentum is negative, and is found to peak aQ/v value of20.075 a.u.
FIG. 2. Longitudinal momentum spectra for 3.6-MeV/nucleSe2811He single ionization collisions. The notation is the samethat in Fig. 1. Here, the CTMC cross sections have been multipby a factor of 1.38 to the experimental value of 3.3310215 cm2.
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The 3.6-MeV/nucleon Se281 system is very similar to the3.6-MeV/nucleon Ni241 system that was studied previous@11#. In that work, there was good agreement betwen-CTMC calculations and the experiment in the peak potions of the recoil ion, and electron longitudinal momenta.series of continuum distorted wave calculations have brecently carried out for the Ni241 system, where good agreement has been demonstrated for the absolute cross sec@37#. These calculations tended to underestimate the forwshift of the electron, and backward shift of the recoil iospectra. The authors stated that this discrepancy with expment and CTMC calculations may be due to the neglecthe nuclear-nuclear distortion in the calculations.
It is illustrative to consider another collision system ainvestigate the momentum spectra at the same values ofturbation strength as those used above. For this comparwe have used C61 at an energy of 506 keV/nucleon (q/v51.33) and 165 keV/nucleon (q/v52.34). Their longitudi-nal momentum spectra are given in Fig. 3. For both casesprojectile momentum loss is found to significantly influenthe three-body spectra, and has a width that approaches~506keV/nucleon! and even exceeds~165 keV/nucleon! that ofthe recoil ion.
The 165-keV/nucleon C61 case differs greatly from the3.6-MeV/nucleon Se281 collision system mainly because it iinfluenced by electron capture, which is not appreciable
sd
FIG. 3. Calculated values for the longitudinal momentum sptra for C611He at 165 and 506 keV/nucleon. The electron arecoil ion spectra are given by solid and long-dashed lines, wthe change in momentum of the projectile is given by the shdashed line.
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274 PRA 58R. E. OLSONet al.
the higher-energy Se281. This is apparent from several chaacteristics, one of which is the electron-capture-to-tcontinuum~ECC! shoulder on the electron spectrum that ocurs at the projectile speed of 2.57 a.u. A complementshoulder is also apparent on the projectile momentumdistribution at21.63 a.u. The onset of electron capturealso displayed in the recoil ion momentum, in that a shcutoff in momentum is found at20.93 a.u. This value corresponds to the ECC process, with recoil momenta at mnegative values being discrete, and corresponding to eleccapture to the ground and excited states of C51.
Experimental electron longitudinal momentum spectraist for C611He collisions at 66, 48, and 34 keV/nucleo(q/v53.69, 4.33, and 5.14, respectively!. In Fig. 4, the com-parison between CTMC results and the measurementKravis et al. @18# are displayed. Here, even though tCTMC calculations very nicely reproduced the out-of-placomponent of the ionized electron spectra~Fig. 7 of Ref.@18#!, the longitudinal momenta differ considerably. Nothat the CTMC results have been shifted by a constant10.4a.u. in each case. With this shift, the widths of the longidinal spectra are in accord with one another. To verify tthe calculations were encompassing the ECC componenthe ionized electrons, the integration routine was changefollow each ECC event to 107 a.u., or 0.5 mm, past thecollision center. Thus, the lack of a strong component
FIG. 4. Longitudinal electron momentum spectra for 34-, 4and 66-keV/nucleon C611He. The data of Kraviset al. @18# aregiven by the open circles. The CTMC calculations are given byfilled circles. Note that the CTMC results have been shifted to mpositive values ofpz by a constant 0.4 a.u. at each energy.
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ECC electrons in the calculations could not be reconcilMoreover, we have calculated the state selective eleccapture cross sections for these systems, since it is posto Stark ionize high C51 Rydberg states in the deflectoplates of the experiment. However, we find the C51 electroncapture distributions narrowly peaked aboutn5324, withinsufficient highn values needed to reconcile the differenwith experiment.
A process that may explain the difference is the douexcitation channel. This process is not included in our oelectron calculations, but will give rise to;35-eV electrons(v'1.60 a.u.) with a cross section that is approximately210% of the total ionization value. Such a reaction yieldHe1 recoil ion, as detected in the coincidence measuremMoreover, these electrons will reside in the cusp regionthe electron spectra, and may be further focused to thisby the slow highly charged C61 projectile. Further work onthis topic will be required.
To investigate the possibility of a clear signature of ECor saddle point electrons in the electron longitudinal momtum spectra, calculations for H1 and C61 projectiles havebeen carried out for collision speeds of 1 to 12 a.u. Trelative peak positionsv* 5vmax
el /vproj , where vmaxel is the
maximum in the longitudinal velocity distribution of themitted electron andvproj is the projectile velocity, were thenplotted as a function of projectile speed. In such a plotECC electrons occur atv* 51, and saddle-point electronare located atv* 5@11(qp /qt)
1/2#21, whereqp is the finalprojectile charge andqt is the final target charge. The resulare inconclusive; see Fig. 5. At high speeds, the longitudforce induced by the projectile on the ionized electron bances to zero, with the transverse force causing most etrons to be ejected around 90° with apz value close to zero.As the collision energy is lowered, two-center effects bcome more prominent with the longitudinal momentumaximizing near the saddle point velocity at calculated vues of 1.9 a.u. for H1 ~90 keV!, and 3.6 a.u. for C61 ~325keV/nucleon!. Interestingly, within statistical errors thCTMC calculations tend to a maximum, then decreaseward the saddle-point velocity at very low collision speedThis behavior is also demonstrated in the CDW calculatioof Fainstein@26# and is borne out by the measurementsKravis et al., which show a similar behavior for C61, but areinconclusive for H1.
B. Collision plane studies
A major attribute of the momentum spectroscopy methis that it is now possible to perform collision plane studithat more fully elucidate the various scattering mechanisIn the data presented here, we will use a collision pladefined by the incident projectile momentum (1z coordi-nate! and the outgoing transverse momentum of the recion (1x coordinate!. This is a collision plane that is mosamenable to the experimental setup, since there is no dmeasurement on the outgoing projectile at these energieslower energies where it is feasible to measure the projecdeflection it will be possible to use a collision plane definby the projectile scattering. Either coordinate system canutilized in the calculations since all nine final-state mometum components are determined.
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PRA 58 275COMPLETE SINGLE-IONIZATION MOMENTUM SPECTRA . . .
In Fig. 6 theoretical results for 9.5-MeV/nucleon Ni261
are shown, and in Fig. 7 the comparison between theoryexperiment is given for the 3.6-MeV/nucleon Se281 system.Here, thex andz momentum components for all the reactioproducts of each ionizing collision are presented. The ovegeneral trends are well reproduced by the calculations. Hever, differences are apparent in that the calculated trverse momentum components of the recoil ion and ionielectron are more broadly distributed than in the Se281 ex-perimental observations, with the ionized electrons mlikely to be scattered in an azimuthal direction oppositethat of the recoil ion. The change in momentum for the pjectile is relatively sharp, with the calculations being mohighly peaked than the experiment. The experimental demination of the projectile loss is deduced from the coincidobservation of the recoil ion and ionized electron, andeffected by finite resolution, so this difference is not consered significant.
Even though the perturbation strengths for 3.6-Menucleon Se281 and 165-keV/nucleon C61 are identical, the
FIG. 5. Energy dependence of the position of the maximumthe electron longitudinal momentumvmax
el as a function of projectilespeedvp . The reduced functionvmax
el /vp for the ordinate is used sothat the ECC position is constant at unity. Likewise, the positionthe saddle point velocity SP is given for the two systems unconsideration. The CTMC calculations for H1 and C611He areshown by the solid line. Experimental data from Kraviset al. @18#and Dorner et al. @38# are denoted by solid circles and squarerespectively.
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C61 system differs significantly from Se281 when one con-siders the collision plane information. In Fig. 8 the electrspectra are presented for electrons just in the projectile-recollision plane. Here, we have restricted they component ofelectron momentum to be less than 0.05 a.u. In the upperfigure, all counts are given with no other restrictions. Tspectrum is asymmetric with the electrons being prefertially emitted opposite to the recoil ion. Local maxima apresent for the slow electrons and the ECC electrons.ECC electrons have the known asymmetry to smaller valof pz around the cusp at the projectile velocity. They are a
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FIG. 6. Calculated three-body momentum spectra for 9.5-Menucleon Ni2611He single ionization collisions. The collision planis defined by the incident projectile momentum, and the transvemomentum of the outgoing recoil ion. Thex- and z-momentumcomponents of the collisions products are presented. The plotsmade using a linear scale where each contour line represenequal portion of the cross section.
FIG. 7. Calculated and experimental three-body momentspectra for 3.6-MeV/nucleon Se2811He single ionization colli-sions. The experimental projectile change momenta are dedfrom the coincident observation of the momenta of the ionized etron and recoil ion. Notation is the same as in Fig. 6.
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276 PRA 58R. E. OLSONet al.
found to be very asymmetric in thepx plane with the ECCelectrons being preferentially emitted at an azimuthal anof 180° from the recoil ion.
In order to follow the collision dynamics further, the upper left spectrum has been cut in terms of the transvemomentum of the recoil ion. By so doing, small transverecoil ion momenta roughly correspond to large impactrameters, and large transverse momenta relate to the mviolent small impact parameter collisions. Each of the thcoincident spectra given in Fig. 8 contribute equally to ttotal cross section. For small recoil transverse momenta,large impact parameters, primarily slow electrons are form~upper right figure!. In this case, there is a slight tendency fthe electrons to be produced azimuthally opposite to thecoil ion in the projectile’s direction. For intermediate collsions ~lower left figure!, considerable two-center electronare produced with a significant tendency for the electronbe emitted opposite to the recoil ion. This behavior is evmore accentuated for the hard collisions with large rectransverse momenta~lower right figure!. Electrons aroundthe ECC cusp now dominate. It is significant that these etrons are found to have an almost complete asymmetry incollision plane with azimuthal angles opposite to that ofrecoil ion, and with that of the projectile. Such an asymmeis very surprising because the projectile scattering is onorder of tens of microradians, while the electron asymmeis on the order of tens of degrees. From this, one would inthat these ECC electrons not only have the known asymtry in energy about the cusp, but are also strongly polariin the projectile scattering plane.
C. Azimuthal angle dependence
A convenient way to follow the angular correlation in ththree products of the single ionization reaction is to plot
FIG. 8. Calculated electron collision plane results for the 1keV/nucleon C611He system. Here, the spectra are coincident welectrons whose perpendicular momentum components are bet60.05 a.u. The upper left figure has all recoil ion transverse mmenta counts. For soft collisions, the upper right figure restrictstransverse momentum of the recoil ion to be less than 0.6Intermediate collisions are given in the lower left figure, while hacollisions with recoil transverse momenta greater than 1.2 a.u.in the lower right figure. The ranges of the transverse momentumthe recoil ion were chosen so that each of the three latter figrepresented an equal portion of the total cross section.
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azimuthal angle between the projectile and recoil ion verthat of the recoil ion and ionized electron. For small impaparameter or low-energy collisions, there will be a stro180° correlation between the recoil ion and projectile, wthe counts appearing along the top horizontal section ofplot. For large impact parameter or high energy collisiothe projectile transfers energy to ionize the target but dnot appreciably participate in the postcollision momentusharing. For these cases, the recoil ion and electron ioback-to-back with a 180° correlation between each otwhere the counts appear along the right-hand vertical porof the graph. If there is a hard collision between the projtile and electron so that binary electron production occuthe projectile and ionized electron will scatter at 180° to eaother and the counts will appear along the diagonal portof the graph.
In Fig. 9 the 9.5-MeV/nucleon Ni261 system is investi-gated. The CTMC calculations portray the general aspectthese collisions with most of the counts found along the vtical section which reflects momentum sharing betweenrecoil ion and ionized electron. In such fast collisions there
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FIG. 9. Azimuthal angle dependencies between the recoiland ionized electron, abscissa, and recoil ion and projectile, onate, for the 9.5-MeV/nucleon Ni261 system. The CTMC results arin the upper figure and the experimental values in the lower figuA logarithmic scale was used for the eight contour lines.
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PRA 58 277COMPLETE SINGLE-IONIZATION MOMENTUM SPECTRA . . .
very little change in momentum of the projectile, so that ttarget products primarily explode back-to-back. We do nthat the measurements indicate that the correlation betwthe ionized electron and recoil ion is somewhat more diffuthan that calculated. Interestingly, both experiment atheory display a small island of counts in the upper left stion of the plots where there is a 180° correlation betwerecoil ion and projectile along with a near 0° correlatibetween recoil ion and electron. These events occur in rtively small impact parameter collisions where the projectat its distance of closest approach, passes between the rion and ionized electron. The transverse impulse givenproducts causes the positively charged projectile and reion to repel one another, while the electron is attractedward the projectile. After the collision, the projectile’s tranverse momentum is then found to be balanced by the sumthat of the recoil ion and ionized electron.
The azimuthal angle dependencies for the 3.6-Menucleon Se281 are very similar to that of Ni261, Fig. 10.Again theory yields a sharper pattern than that of the expment, with a dominance of recoil ion–ionized electron bato-back scattering. Both theory and experiment showstrong maximum in the lower right hand corner whererecoil ion and electron are at 180° to one another, and
FIG. 10. Azimuthal angle dependencies for the 3.6-Menucleon Se281 system. The notation is the same as in Fig. 9.
eeened-n
a-,coiltoil-
of
/
i--aee
projectile, and recoil ion are near 0°. Analysis of the CTMresults indicate that these are primarily large impact paraeter collisions where the electron’s transverse momentumbalanced by the transverse momenta of the projectile, whis attracted toward the electron at the distance of closestproach and that of a very low momentum recoil ion, whipartially absorbs some of the deflection of the projectile.
To study the evolution of azimuthal angle dependenccalculations are presented for C61 at 66, 165, and 506 keV
/
FIG. 11. Calculated azimuthal angle dependencies for the C61
system at 66, 165, and 506 keV/nucleon. Notation is the same aFig. 9.
tiheeVmhe
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teite
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278 PRA 58R. E. OLSONet al.
nucleon, Fig. 11. These energies correspond to perturbastrengthsq/v of 3.69, 2.34, and 1.33, respectively. For tlargest perturbation strength corresponding to 66 knucleon, two-body heavy particle nuclear scattering donates, with the ionized electron having little effect on ttransverse momentum balance~top figure!. At the intermedi-ate energy of 165 keV/nucleon, the electron becomesequal partner in the momentum balance with three lomaxima apparent in the three corners of the azimuthal acorrelations~middle figure!. As the collision energy is fur-ther increased to 506 keV/nucleon, the projectile contribua minor fraction to the transverse momentum balance wthis now controlled by the back-to-back explosion betwethe recoil ion and ionized electron, lowest figure.
IV. CONCLUDING REMARKS
The field of momentum spectroscopy has matured rapin just the last several years. This progress now makepossible to perform kinematically complete experiments acalculations for single ionization collisions induced by ioimpact. Such studies provide insight into the dynamics amomentum sharing of three-body reactions.
In this paper we concentrated on large perturbatstrength collisions where the charge state of the projecdivided by collision speedq/v was greater than unity. Ingeneral, theq/v parameter characterized many of the mmentum spectra. However, the presence of a strong eleccapture channel leads to rich structure displaying soft, twcenter, and ECC electrons at lower velocities. Collisplane studies differential in the transverse momentum ofrecoil ion provide a method to separately probe soft cosions where the recoil ion momentum is small, to thosevolving small impact parameter violent collisions where trecoil ion momentum is large. Such studies, when combiwith the azimuthal angle dependencies between the threaction products, leads to an improved understanding ofization collisions.
.
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.
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Many detailed questions arise when direct comparisare made between theoretical calculations and experimedata. Since the CTMC method incorporates all the pairwCoulomb forces between the particles for a three-body sinionization reaction, it is possible to do a kinematically complete calculation. This has not been feasible by any quamethod that is applicable to the collision systems presenhere. However, the many discrepancies between theoryexperiment indicate that further theoretical developmenneeded.
In particular, there is notable disagreement betwetheory and experiment for the very strong perturbatstrength 34–64-keV/nucleon C611He collisions. Here,CTMC calculations underestimate the position of tmaxima in the longitudinal electron spectra, while CDW rsults overestimate its position and the width of the transvespectra@39#. Both of these methods are three-body theoriwhich probably infers that a more complete four-body stuof this system is necessary.
As pointed out in this paper and in Ref.@31#, probably themost interesting systems of study will be those at intermeate energies such as 165-keV/nucleon C611He. Here, theelectron capture and ionization channels are both equallyportant, giving rise to nice illustrations of soft, saddle-poiand cusp electron dynamics. The experimental studiespresent have primarily concentrated on either relatively henergy MeV/nucleon collisions, or those below 100 kenucleon where electron capture dominates. Further expments in this area from the Kansas State and Freiburg laratories are now under way.
ACKNOWLEDGMENTS
The authors would like to thank the Office of Fusion Rsearch of the Department of Energy, GSI, the Deutsche Fschungsgemeinschaft, the Bundesministerium fu¨r Bildungund Forschung, and the Alexander von Humboldt Stiftufor their support.
er-
. P.
r-
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