3.1 Laser Spectroscopy of Antiprotonic Helium Atoms

D. Horvath, B. Juhasz, E. Takacs (ASACUSA collaboration)

In 2002, laser spectroscopy studies ofantiprotonic helium atoms (p – e− –He++ ≡pHe+) were carried out at the Antiproton De-celerator (AD) of CERN in July and Au-gust. The experiments used both the directAD antiproton beam (energy: 5.3 MeV) andthe decelerated beam (energy: 20–120 keV),which were produced using the Radio Fre-quency Quadrupole Decelerator (RFQD), aunique device which both decelerates and fo-cuses the antiproton beam. Unlike the pre-vious year, this time an S-shaped achromaticspectrometer line was added between the exitof the RFQD and the entrance of our cryostat.This spectrometer line only transports the de-celerated antiprotons to the cryostat, while theundecelerated antiprotons (appr. 50% of thebeam) annihilate far from the cryostat, thusreducing a major source of background in theannihilation time spectrum.

Another new equipment we started to usewas a high-pressure, high-purity target cham-ber for room temperature measurements. Thechamber has one stainless steel window forthe antiproton beam, and three quartz win-dows for the laser beams to allow both tradi-tional collinear single-photon spectroscopy andDoppler-free two-photon spectroscopy. Thischamber can be used with the direct 5.3-MeVantiproton beam.

Using the old and new equipment, the fol-lowing experiments have been made:

High-precision measurements of the wave-lengths of transitions between five pairs ofmetastable and short-lived antiprotonic statesin low-density (0.1–5 mbar) 4He and 3He [1].Using the above-mentioned achromatic spec-trometer line to increase the signal-to-noise ra-tio, the precision of the measured transitionwavelengths will likely to increase, which inturn can improve our previously obtained pre-cision of the mass and charge of the antiproton,a test of the CPT invariance [2,3].

The above-mentioned measurements at lowdensities (<1 mbar) revealed that the average

lifetime of antiprotons (which can be deducedfrom the average decay rate of the delayed an-nihilation time spectra) increases to ∼5 mi-croseconds compared to 3.5 microseconds athigher densities (>100 mbar) [4]. This reflectsthe reduced collisional influence at such lowdensities.

We also found that at even lower densi-ties (<0.1 mbar), the decay lifetime of thelaser-induced annihilation spike becomes sig-nificantly longer (∼10 ns vs. ∼ns) [4]. This in-dicates that the p –He++ ≡ pHe++ ion, whichis created after the Auger transition from thedaughter state of the laser-induced transition,has a longer lifetime due to a reduction of thecollisional Stark mixing in such ultra-low den-sity environments.

Discovery of four new laser resonant tran-sitions between antiprotonic states, one in 4Heand three in 3He [4]. The wavelengths ofthese transitions were also measured. A high-resolution scan of one of the transitions re-vealed a double peak, which is caused by thehyperfine splitting of the parent and daughterstates (see Fig. 1).

0.504 0.506 0.508 0.51 0.512 0.514 0.516

Pea

k to

tota

l

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Wavelength (nm) - 525

0.504 0.506 0.508 0.51 0.512 0.514 0.516

Pea

k to

tota

l

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Figure 1. High-resolution scan of a resonancetransition with a doublet splitting.

The precision of our previous single-photonmeasurements was limited by Doppler broad-

29

ening, which can be eliminated using Doppler-free two-photon laser spectroscopy technique.The feasibility of this method was tested in2002 using the high-pressure target chamberand two collinear laser beams. The mea-surements had to made at room temperature,where Doppler broadening is larger than thelaser bandwidth so that we can see a narrowingof the resonance line due to Doppler cancelling.The transition was successfully observed, butthe measured linewidth was much larger andthe signal-to-noise ratio was much smaller thanthose of the single-photon transitions. Thepossible reasons for the poor experimental re-sults can be the increased i) collisional broad-ening, ii) laser bandwidth, iii) laser wavelengthand power fluctuations.

Investigation of the temperature depen-dence of quenching of metastable states in col-lisions with H2 and D2 molecules [5]. Accord-ing to the theoretical calculations of Sauge andValiron [6], a state-dependent activation bar-rier exists for this kind of quenching reaction,which means that the quenching cross sectionσq should increase with increasing temperaturefollowing the Arrhenius law:

σq = σ0 exp(−Eb/kT ), (1)

where σ0 is the cross section at infinitely hightemperatures (this we expect to be close to thegeometrical cross section), Eb is the height ofthe activation barrier, k is the Boltzmann con-stant and T is the temperature. However, allprevious measurements of quenching by hydro-gen and deuterium molecules were done at 30K [7]; therefore, in order to test the above tem-perature dependence, we made measurementsat several temperatures: at room tempera-ture using the high-pressure target chamberand at 25–100 K using our usual high-densitycryostat, and we found that indeed there is asignificant temperature dependence. In caseof one antiprotonic state, we could systemati-cally study this dependence by measuring thequenching cross section with deuterium at sixtemperatures. The collected data, however,favour a different model:

σq = σ0 exp(−Eb/kT ) + σc, (2)

where σc is independent of the temperature.This term is most likely related to the quantumtunnelling of the colliding impurity moleculethrough the activation barrier. Fig. 2 showsthe quenching cross section versus the inversetemperature. A deviation from the Arrheniuslaw is clearly visible (note the logarithmic scaleof the vertical axis). The plotted line is the re-sult of fitting Eq. (2) to the data points.

T (K)2030405060708090

1/T (1/K)0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

)2 c

m-1

6 (

10qσ

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 2. Quenching cross section versus the in-verse temperature.

The analysis of the data collected in 2000and 2001 was partially completed and the re-sults were published [7-10].

Almost all of the support structures of theexperimental devices were designed and man-ufactured in Hungary.

[1] M. Hori et al., in preparation.

[2] M. Hori et al., Phys. Rev. Lett. 87 (2001) 093401.

[3] K. Hagiwara et al., Phys. Rev. D 66 (2002) 010001.

[4] H. Yamaguchi et al., in preparation.

[5] B. Juhasz et al., in preparation.

[6] S. Sauge and P. Valiron, Chem. Phys. 283 (2002)433.

[7] B. Juhasz et al., Eur. Phys. J. D 18 (2002) 261,and references therein.

[8] M. Hori et al., Phys. Rev. Lett. 89 (2002) 093401.

[9] H. Yamaguchi et al., Phys. Rev. A 66 (2002)022504.

[10] E. Widmann et al., Phys. Rev. Lett. 89 (2002)

243402.

30

3.2 An improved description of the multiple ionizationKβLi satellite energy spacings

I. Torok, T. Papp, S. Raman a)

In analytical works, and in basic atomicphysics research one needs the data of thesatellite lines, therefore we began to make anew compilation of the energy shifts of theKαLiMmNn ..., KβLiMmNn ... satellites,and K2αLiMmNn ..., K2βLiMmNn ... hy-persatellites. A byproduct of this compilationis a test of the ”classic” description of their en-ergy spacings as a function of Z [1]. The largerdatabase we have now, made it possible, to ob-tain a better description. For KαLi satellitessee Ref. [2]. The old version gave equidis-tant spacing also for the KβLi satellites, usingan average effective Z seen by the electrons:∆E(KβL) = 4.38ZL = 4.38(Z − 4.15), ourversion uses an effective Z changing with thenumber of spectator L vacancies:

∆E(KβLi) = i×3.37[Z + (i− 1)×0.5− 5.37]i = 1, 2, 3, ..., 7

This equation, obtained by fitting a rep-resentative portion of our compiled data isin agreement with experimental data, perhapsthe i = 7 case is a little bit underestimatingthem, probably because of the significant num-ber of additional M, N vacancies. Full accountis given in a paper in preparation.

The work was supported by OTKA No.T016636.

∗ ORNL is managed by Lockheed MartinEnergy Research Corporation under contractNo. DE-AC05-96OR22464 with the U.S. De-partment of Energy.

a) Oak Ridge National Laboratory (ORNL),∗ OakRidge, TN, USA 37831

[1] D. Burch, L. Wilets, W.E. Meyerhof, Phys. Rev.A 9 (1974) 1007.

[2] I. Torok, T. Papp, S. Raman, Nucl. Instrum.Meth. B150 (1999) 8.

31

3.3 On the measurements of K2βLi hypersatellites

I. Torok

Although we gave a short publication inour institute’s Ann. Rep., there was statedin the literarure, that such new formulae forthe KβLi, and K2βLi satellites and hyper-satellites are not existing. In [1] we gave asemiempirical formula for the KαLi satelliteenergies, and in [2] for the KβLi lines, thislatter report we republish in this Ann. Rep.,with the original title, containing the symbolβ (which was lost during the editorial processin the case of first publication), emphasisingthe new content. Regarding the K2βLi hy-persatellites they were not measured at all bycrystal spectrometers.

The K2βLi hypersatellites are very weaklines. They are regarded, as not availablefor measurements by crystal spectrometers.Nowadays the situation is changing, the betterand better resolution and the use of high effi-ciency position sensitive detectors makes thesehypersatellites to become investigable. In apair of spectra (Ca and Ti) - I got from the au-thors (the group of prof. J.-Cl. Dousse) priorto publication [3], - there were a few weak,

but definite, although unassigned lines, whichcomparing to our multiple ionization satelliteenergy systematics [2], turned to be such hy-persatellites, including their K2βLi satellites.We found also an indication of such hypersatel-lites for Ti in the literature [4], dated about tenyears earlier. The Dousse-group was informedabout our observation in their spectra, and asto my knowledge, now a project is running suc-cessfully to measure such hypersatellites in therange of elements around Cr.

[1] I. Torok, T. Papp, S. Raman: Energy systemat-ics of the KαLi satellite transitions, Nucl. Instr.Meth. B150 (1999) 8.

[2] I. Torok, T. Papp, S. Raman: Energy systematicsof the KLi satellite transitions, ATOMKI Ann.Rep. 1999 (2000) p. 38.

[3] M. Kavcic, privat communication, 1998.

[4] Y. Awaya, T. Kambara, Y. Kanai, T. Mizogawa,

A. Hitachi, B. Sulik: Multiple inner-shell ioniza-

tion of target atoms by 0.8-26 MeV/u heavy ion

impact, RIKEN Accel. Prog. Rep. 22 (1988) p.

55. Fig. 1.

32

3.4 Electron emission from H02 in collisions with He atoms

L. Sarkadi, L. Lugosi, B. Paripas a) and B. Palasthy a)

The electron emission in energetic ion-atom(atom-atom) collisions has been widely studiedin the past decades, and now it is well under-stood theoretically. At the same time, the in-formation for the electron emission in collisionsinvolving molecules is rather scarce.

In the present work we studied the electronejection from the neutral H2 molecule in colli-sions with He atoms at impact energy 150 keVamu−1. The work was motivated by a recentexperiment [1] in which evidence was found forthe coherent electron emission from the two Hatoms of the H2 molecule collided with 60 MeVamu−1 Kr34+ ions.

Our measurements were performed at the1.5 MV Van de Graaff accelerator of ATOMKI.We produced neutral H2 beam by charge ex-change of the H+

2 beam of the accelerator withthe residual gas of the beam channel. For nor-malization we used a H0 beam of the same ve-locity. We measured the energy spectra of theejected electrons at 0. The electron emissionfrom H0

2 and H0 was indentified by detectingthe electrons in coincidence with the outgoingH+

2 and H+ ions, respectively. The spectrawere taken in the cusp region, i.e., we mea-sured the distributions of those electrons whichwere ejected with small relative kinetic energywith respect to the projectile. The cusp elec-tron production associated with projectile ion-ization is called electron loss to the continuum(ELC). It was an interesting question whetherELC is affected by any interference effect formolecule projectile.

The obtained electron spectra are displayedin Fig. 1. Surprisingly, the width of the ELCpeak for the molecular emission is considerablysmaller than that for the atomic emission. Theratio of the corresponding cross sections ex-hibits a pronounced, narrow peak centered atthe cusp maximum.

We applied the classical trajectory MonteCarlo (CTMC) method to the description ofthe ELC process in collisions of H0

2 and H0

with He. The coherent electron emission from

H02 was treated as it is proposed in Ref. [2].

CTMC predicts a weak dependence of themolecule/atom cross section ratio on the elec-tron energy, in a strong disagreement with theexperiment.

Electron energy [eV]0 20 40 60 80 100 120 140 160

DD

CS

[arb

. uni

ts]

0.01

0.1

1

Electron energy [eV]0 20 40 60 80 100 120 140 160

DD

CS

(H

20 ) / D

DC

S(H

0 )

1

2

3

4

5

6

ELC, H20

ELC, H0

CTMC Experiment

Figure 1. Upper part: Measured relative doubledifferential cross sections (DDCS) for the ELC cuspproduced in H0

2 + He (open circles) and H0 + He(full circles) collisions. Lower part: Ratio of themeasured and calculated DDCS values as a func-tion of the electron energy. The notations: –o–,experiment; —, CTMC theory. The experimentaldata are normalized to the theorerical curve at 150eV electron energy.

a) Department of Physics, University of Miskolc,Hungary

[1] N. Stolterfoht et al., Phys. Rev. Lett. 87, 023201(2001).

[2] L. Sarkadi, J. Phys. B, submitted for publication

(2003).

33

3.5 Strong nondipole effect in 5s photoionization of xenon

S. Ricz, R. Sankari a), A. Kover, M. Jurvansuu a), D. Varga, J. Nikkinen a), T. Ricsoka, H. Aksela a),S. Aksela a)

Dipole approximation has often been usedsuccessfully to describe the angular distribu-tion of photoelectrons and also to evaluatethe experimental angular distribution results.The validity of the dipole approximation comesfrom the dominance of the dipole interactionat low photon energies (hν ≤ 5 keV). Untilrecently the contribution of the higher ordermultipole components were assumed to be neg-ligible.

Intensive theoretical investigations relatedto nondipole effects at low photon energies be-gan during the last decade. Recent experimen-tal investigations of the photoionization angu-lar distribution [1][2], extending down to 250eV photon energies, suggested that nondipoleeffects are of importance at low photon ener-gies.

In present work, the angular distributionof the 5s photoelectrons of xenon was mea-sured with linearly polarized light in the 90-225 eV photon energy range in order to de-termine the dipole (β) and nondipole (δ andγ) parameters. The measurements were car-ried out at the beam line I411 on the thirdgeneration MAX-II storage ring in the Max-Lab, in Lund, Sweden [3][4]. Emitted elec-trons were detected by 20 channeltrons usingESA-22 electron spectrometer [5], which wasinstalled before the permanent end-station intoso called one-meter section. For present mea-surements the relative energy resolution of theanalyzer was set to ∆E/E = 2.4 ∗ 10−3. Thisresolution and the bandwidth of the photonbeam (bandwidth using 120µm exit slit variedbetween 0.09 and 0.3 eV depending on inci-dent photon energy) ensured that the Xe 5sphotoline could be separated from the closestsatellite line.

The correct intensity calibration therelative efficiencies of the detectors weredetermined by using isotropic Ar L2 −M2,3M2,3

3P0,1,2 Auger transitions.The angular anisotropy parameters were

extracted from the experimental, efficiencycorrected intensities using equation [6]

dσnl

dΩ=

σnl

4π1 + βP2(cos θ) (1)

+[δ + γ cos2(θ)] cos(φ) sin(θ)

that describes angular distribution of photo-electrons for linearly polarized light. P2 isthe second order Legendre polynomial, σnl isthe photoionization cross section of the nl or-bital, β is the anisotropy parameter of thedipole interaction (E1), δ and γ are the pa-rameters related to the quadrupole interaction(E2), whereas θ and φ define the polar andazimuthal angles relative to the polarizationvector, respectively.

80 100 120 140 160 180 200 220-0.25

0.00

0.25

0.50

0.75

1.00

1.25

Gam

ma

Photon energy (eV)

Figure 1. Comparison of the experimentalnondipole γ parameters (open circles) with the cor-responding theoretical values as a function of thephoton energy. Theory: RIPM [8] (dot line), 13-channel RPAE [11] (dash-dot-dot line), 13-channel(dash line) and 20-channel RRPA (solid line) [9]

The dipole and nondipole parameters wereobtained by the least squares fitting proce-dure to Eq. (1). Due to used geometry theδ and γ parameters could be determined sepa-rately, however, the δ parameter was found to

34

be very close to zero as expected theoretically(see e.g.[6] and references therein). The valueof the fitted β and γ parameters did not changepractically either the δ-parameter was includedor not. Figure 1. compares our experimen-tal and theoretical [8][9][12] nondipole γ pa-rameters. The RIPM approximation [8] showsslightly increasing line without any structure,while the γ parameter values calculated with13 or 20-channel RRPA [9] show an enhance-ment with maximum around 160 eV. Our ex-periment shows similar structure than thesetheoretical predictions. The shape of the ex-perimental cusp is similar to the 20-channelcalculation but the maximum of the experi-mental values is smaller. Comparison betweentheoretical [8][9][12] and present experimentalvalues shows that the inclusion of the Xe 4sand 4p channels is important in the descriptionof the energy dependence of the γ parameter in5s ionization. The contribution created by the4p channel is, however, slightly overestimated[9]. This is not surprising as the Xe 4p−1 isknown to correlate with 4d−2nf, εf states andthis correlation is not included in the calcula-tions.

Amusia et al [12] presented theoretical val-ues for γ parameter in Xe 5s photoionization.Their RPA calculations with exchange (RPAE)included coupling between 4d, 5s and 5p chan-nels. The values are smaller over the wholeenergy range of interest than the correspond-ing values of Johnson and Cheng [9] indicatingthat relativistic effects are of some importance.

Remaining discrepancies between experi-ment and theory may be related to the omis-sion of the satellite channels of the type5p−2nd, εd and 4d−1nf, εf related to the 5sand 4p ionizations, respectively, in the calcu-lations.

Figure 2. compares the present and theprevious [7] experimental β parameters andthe corresponding theoretical values [9][10] inthe 90-220 eV photon energy range. The re-sults of the relativistic independent particle ap-proximation (RIPA) [8], which omits the cou-pling between the continuum channels, do notshow any sudden changes and β has a constantvalue of about 2. However, all calculations

which take the channel interaction into ac-count predict a broad minimum around 150 eVphoton energy. The minimum is deeper in 13-channel than in 20-channel RRPA calculation[9]. The depth further decreases in predictionsbased on the relativistic time-dependent den-sity functional theory (TDDFT) [10], which in-clude also the correlation related to satellitechannels in an average way by a model poten-tial. The present experimentally determined βparameters are between 20-channel RRPA andTDDFT values, slightly closer to the results ofthe 20-channel RRPA calculations. This indi-cates that the influence of the 4p channel isimportant in the Xe 5s ionization but that theTDDFT fails in accounting the additional cor-relation correctly. In general, experimental βparameters agree well with theoretical ones [9]except in the 90-130 eV photon energy rangewhere experimental and theoretical values de-viate significantly (∼10%).

1.6

1.8

2.0

Bet

a

100 120 140 160 180 200 220

1.4

Photon energy (eV)

Figure 2. Comparison of the present experimen-tal angular distribution β parameters (open circles)with the earlier experimental results of Hemmers etal [7] (diamonds) and with the theoretical values:RIPM[8] (dot line), 20-channel RRPA [9] (dash-dotline), TDDFT [10] (solid line).

Recently Hemmers et al [7] published ex-perimental β parameters in this energy region.The agreement with our experimental resultsis good at the low-energy side of the dip (seeFig. 2), but not on the high-energy side. Their

35

beta values show narrower and shallower dipthan ours or the calculated ones [9]. Further-more the position of the minimum is shifted tolower photon energies. The difference betweenthe two experimental results requires furtherinvestigations.

The effects of the nondipole interaction areremarkable over a wide photon energy range.Especially, at 155 eV photon energy, wherethe γ parameter reaches its maximum, thenondipole contribution to total angular distri-bution is as high as 20%. It is clearly enoughto question the validity of the dipole approxi-mation in photoionization of the Xe 5s subshellrelative far from the ionization threshold.

AcknowledgementsThe staff of MAX-laboratory is acknowl-

edged for assistance during the measurements.This work has supported by the ResearchCouncil for Natural Sciences and Technol-ogy of the Academy of Finland. The workwas also supported by the Hungarian Scien-tific Research Foundation (OTKA Grant No:T025325) and by the European Community’sARI-Program.

a) Department of Physical Sciences, P.O. Box 3000,90014 University of Oulu, Finland

[1] M. Jung, B. Krassig, D. S. Gemmell, E. P. Kan-ter, T. LeBrun, S. H. Southworth,and L. Young,Phys. Rev. A 54, 2127 (1996).

[2] O. Hemmers, G. Fisher, P. Glans, D. L. Hansen, H.Wang, S. B. Whitfield, R. Wehlitz, J. C. Levin,I. A. Sellin, R. C. C. Perera, E. W. B. Dias, H.S. Chakraborty, P. C. Deshmukh, S. T. Man-son,and D. W. Lindle, J. Phys. B 30, L727(1997).

[3] J-H. Guo, S. M. Butorian, C. Sathe, J. Nordgen,M. Bassler, R. Feifel, S. Werin, M. Georgsson,A. Andersson, M. Jurvansuu, R. Nyholm, andM. Eriksson, Nucl. Instr. and Meth. A 431,285 (1999).

[4] M. Bassler, J-O. Forsell, O. Bjorneholm, R. Feifel,M. Jurvansuu, S. Aksela, S. Sundin, S. L.Sorensen, R. Nyholm, A. Ausmees, and S. Svens-son, J. Electron Spectrosc. Relat. Phenom.101-103, 953 (1999).

[5] S. Ricz, A. Kover, M. Jurvansuu, D. Varga, J.Molnar, and S. Aksela, Phys. Rev. A 65, 042707(2002).

[6] J. W. Cooper, Phys. Rev. A 47, 1841, (1993).

[7] O. Hemmers, S. T. Manson, M. M. Sant’Anna, P.Focke, H. Wang, I. A. Sellin, and D. W. Lindle,Phys.Rev. A 64 022507 (2001).

[8] A. Derevianko, W.R. Johnson, and K.T. Cheng,At. Data and Nucl. Data Tables 73, 153 (1999).

[9] W. R. Johnson and K.T. Cheng, Phys. Rev. A 63022504 (2001).

[10] D. Toffoli, M. Stener and P. Decleva, J. Phys. B35, 1275 (2002).

[11] M. Ya. Amusia, A. S. Baltenkov, L.V. Cherny-sheva, Z. Felfli, and A. Z. Msezane, Phys. Rev.A 63, 052506, (2001).

[12] M. Ya. Amusia, A. S. Baltenkov, Z. Felfli, and A.Z. Msezane, Phys. Rev. A 59, R2544, (1999).

36

3.6 X-ray imaging of ECRIS plasmas

E. Takacs a,b), S. Biri, A. Valek, J. Palinkas a), Cs. Szabo b), L.T. Hudson b), B. Juhasz, T. Suta,J. Imrek a) and B. Radics a)

Introduction

Highly charged ion plasmas generated inthe ATOMKI ECR ion source had been im-aged using an X-ray CCD device of the Na-tional Institute of Standards and Technology(NIST). The motivations for the experimentscame from possible future high-resolution X-ray spectroscopic measurements using X-raymicrocalorimeters and crystal spectrometers.In the present set of experiments, the generaldistribution of the emitting highly charged ioncloud and its systematic dependence on var-ious operating parameters were the focus ofour interest. Understanding the details of theion production and confinement provides in-sight into the operation of the ECR ion sourceand gives important information for our futurespectroscopic plans. In addition to its sourcediagnostic value, the X-ray imaging and spec-troscopy of highly charged ion plasmas can alsobe utilized for the laboratory investigation ofplasmas of astrophysical and other interests.

X-ray imaging

The NIST CCD camera used in these ex-periments has 1152x1242 pixels in a rectangu-lar arrangement. The imaging was achievedusing an appropriately positioned 70 microm-eter diameter X-ray pinhole. The CCD chipwas thermoelectrically cooled to about −45Cto reduce thermal noise. Each pixel can beused in single photon detection mode with anenergy resolution of about 180 eV. This fea-ture allows the post detection filtering of theobtained images according to the wavelengthof the detected X-ray photons. This can beused to discriminate certain characteristic lineemission features in the spectra to determinetheir distribution in the plasma [1]. The dataacquisition and analysis system was partly de-veloped by us using the ROOT data analysislibrary.

ECR plasmasFor our imaging studies, we have operated

the ECR under different running conditions inorder to better understand the dynamics ofthe ion generation. We used working gases ofAr, Xe, O2, and solid ferrocene (an organiccompound containing Fe). In order to have aclear view of the source the injection side endcap of the plasma chamber has been modified.The pinhole was mounted 91 cm from the cen-ter of the plasma and the pinhole – CCD dis-tance was 25 cm forming an X-ray camera withdemagnification of 3.6. This permitted morethan half of the plasma volume to be imagedthrough a course mesh; considered to be suf-ficient because of the 120 degree symmetry ofthe ECRIS.

Figure 1. Image generated by an Ar plasma inthe ATOMKI ECRIS.

Systematic studiesIn these first sets of imaging measurements,

the basic features of the ECR plasma X-rayemission were studied under different runningconditions. An image generated by an Arplasma is shown in Figure 1. The upper partof the source is vignetted by a horizontal cutdue to the design of the injection side endcap. The two arms showing strong emission

37

are mainly due to bremsstrahlung and charac-teristic X-rays generated by high-energy elec-trons impinging onto the opposite side endcap. The circular aperture of the extractionhole is clearly visible in the center. In a com-pletely different process the more or less circu-lar plasma cloud emits characteristic radiationof the Ar working gas caused by core vacancycreation due to electron impact. An interest-ing feature is the upside down triangle show-ing reduced intensity emission, which we ten-tatively attribute to X-ray absorption withinthe plasma column.

En er gy ( ke V)

1 2 3 4 5 6 7 8

C o

un

ts

0

500

1000

1500

2000

2500

3000

En er gy ( ke V)

1 2 3 4 5 6 7 8

C o

un

t s

0

500

1000

1500

2000

Al K α α α α

Ar K α α α α

Figure 2. X-ray spectra from different parts ofFigure 1.

Several sets of images similar to Figure 1have been taken under different running con-ditions in order to study the origin of the differ-ent features in the pictures. These include run-ning the ECRIS in low and high power modes,at different magnetic field settings, and turningthe ion extraction on and off etc. We took pic-tures of mixed plasmas (Ar + Xe, Ar + O2) aswell. In addition to the images that have sev-

eral X-ray photons hitting a single pixel duringthe exposure, we have also taken low light levelimages. In these cases, the collected charge in asingle CCD pixel is proportional to the energyof the detected X-ray photon, therefore, underthese conditions spectral analysis of the X-raysis also possible. As an example Figure 2 showstwo of such spectra obtained under the samerunning conditions as Figure 1. The spectraare from two different regions of the image, theupper corresponding to one of the bright armsand the lower to a region of the Ar plasmacloud. The difference in the strength of thedifferent characteristic emission lines is clearlyvisible indicating the size and distribution ofthe plasma (Ar emission) as contrasted withthe Al emission from electrons striking the endwalls of the plasma chamber. The analysis ofthe large amounts of data and model calcula-tions are under way.

ConclusionsX-ray images taken under different ECRIS

running conditions reveal the hottest, most en-ergetic regions of the plasma. Spectral fil-tering allows us to study the origin of cer-tain spectral features (e.g. characteristic lines,bremsstrahlung continuum) in the plasma,which can help to improve modeling of thesource and other magnetically confined plas-mas.

a) Department of Experimental Physics, University ofDebrecen, Hungary

b) National Institute of Standards and Technology,Gaithersburg, MD, USA

[1] P. Grubling et al., Rev. Sci. 69 (1998) 1167.

38

3.7 Cascade transition x-rays from electron capture into highly charged ions incollisions with neutral gas targets

H. Tawara a), E. Takacs a,b), L.P. Ratliff a), J.D. Gillaspy a) and K. Tokesi

In collisions of low energy (few keV/u),highly charged ions (HCIs) with neutral atoms,the electron capture process is far dominantover other processes such as excitation or ion-ization. It is well established that an elec-tron from a target atom is usually capturedinto high a Rydberg state of the projectileion [1]. Even in multi-electron target atoms,single electron capture is generally dominant,though the contribution of double and tripleelectron capture becomes significant for higherion charge states. In the case of multiple elec-tron capture, Auger electron emission becomesan important first step of the relaxation pro-cess [2]. In essentially all cases (single or mul-tiple capture), however, the stabilization endsin a cascade of photon emitting transitions.When the projectiles are highly charged, thephotons emitted in these final steps are x-rays.The observation of these x-rays can provide in-formation on both the electron capture and thefollowing cascade. Recently, the unexpectedobservation of x-rays from comets and otherobjects of the solar system [3] brought the col-lisions of highly ionized projectiles with neutralgases into the forefront of research.

Using the electron beam ion trap (EBIT)[4] and extraction facility [5] at the NationalInstitute of Standards and Technology (NIST),we have performed a series of systematic colli-sion studies with different projectile and tar-

get combinations. X-rays originating froma series of the cascades after electron cap-ture into highly excited Rydberg states havebeen observed from low energy, highly chargedKrq+ ions (q=27-36) colliding with neutral Aratoms. We found that the intensity ratio be-tween L (n=32) x-rays and the sum of M x-rays (n=43, n=53, n=63 etc.) is drasticallychanged from Kr27+ to Kr28+ and constantfor higher ion charge states (q=29-36). Thisfeature can be understood to be due to themetastable states formed during cascades af-ter electron capture into Kr27+ ions. This isalso supported by time-dependent populationcalculations.

a) NIST, Gaithersburg, MD 20899-8421, USA

b) Debrecen University, Debrecen, Bem t 18/a H-4026

[1] R.K. Janev, L.P Presnyakov, and V.P. Shevelko,Physics of Highly Charged Ions (Springer, 1985)

[2] M. Barat and P. Roncin, J. Phys. B 25 (1992) 2205

[3] C.M. Lisse, D.J. Christian, K. Dennerl, K.J.Meech, R. Petre, H.A. Weaver, and S.J. Wolk,Science, 292 (2001) 1343

[4] J.D. Gillaspy, Y. Aglitskiy, E.W. Bell, C.M. Brown,C.T. Chantler, R.D. Deslattes, U. Feldman,L.T. Hudson, J.M. Laming, E.S. Meyer, et al.Phys. Scr. T59 (1995) 392.

[5] L.P. Ratliff, E.W. Bell, D.C. Parks, A.I. Pikin,

and J.D. Gillaspy,Rev. Sci. Instrum. 68 (1997)

1998.

39

3.8 Double 1s ionization of Mg and Si induced in collisions with fast heavy ions

M. Kobal a), M. Kavcic a), M. Budnar a), J.-CI. Dousse b) and K. Tokesi

The Kα x-ray emission spectra of Mg andSi excited with 34 MeV C ions and 50 MeV Neions have been measured with a von Hamoscrystal spectrometer [1]. The energy reso-lution of approximately 0.5 eV was achievedenabling us to distinguish contributions orig-inating from states with different number ofholes in K and L shells. In order to deter-mine the intensity of the hypersatellite andsatellite lines the model spectra based on theMCDF calculations was constructed and fittedto the measured spectra. The intensities of themeasured hypersatellite and satellite lines wereused to determine the yield of the KXLN va-cancy states produced in the collision, takinginto account whole decay scheme of the par-ticular initial KXLN ionized state. The decayscheme has been calculated using the initialrates of the radiative and nonradiative transi-tions from [2, 3] which were then corrected foradditional vacancies in the inner shell accord-ing to statistical approach, first proposed byLarkins[4].

From the yield of the doubly 1s ionizedstates (K2XLN ) produced in the collisions rel-ative to the singly 1s ionized states (K1LN ) theratio of double to single 1s ionization cross sec-tion has been obtained. The double to single1s ionization cross section has been also calcu-lated in the independent electron model usingthe one electron ionization probabilities calcu-lated within the three body classical trajectoryMonte-Carlo simulation (CTMC). The calcu-lated values are presented in Table 1. In suchnearly symmetric collisions electron capture bythe projectile is actually the dominant ioniza-tion mechanism. Since the capture in the 1sshell of the projectile is by far the strongest theionization cross section depend significantly on

the charge of the projectile. In Table 1 wecan find the calculated values for the projectilewith 0, 1, 2 electrons in its K shell and for theprojectile with the average equilibrium chargein the solid target used in our experiment.

Table 1. Double to single 1s ionization cross sec-tion, σd/σs, (in %) calculated with the CTMCmodel for the measured collisions. Tabulated arethe calculated values for the projectile with 0,1,2K shell electrons and for the projectile with the av-erage equilibrium charge in the solid target usedin the experiment. a: 34 MeV C6+ → Mg, b: 50MeV Ne10+ → Mg, c: 34 MeV C6+ → Si, d: 50MeV Ne10+ → Si.

(0) (1) (2) (av.)a 16.6 12.3 10.2 15.8b 24.1 12.5 11.7 15.3c 12.2 8.4 7.6 11.6d 12.2 7.5 8.2 9.0

We found, except for the case of 34 MeVC6+ → Mg collision, a relatively good agree-ment between the experimental and calculateddata.

a) Jozef Stefan Institute, Ljubljana

b) Physics Department, University of Fribourg

[1] J. Hoszowska, J.-Cl. Dousse, J. Kern, Ch. Rheme,Nucl. Instrum. Methods A 376, 129 (1996).

[2] S.T. Perkins et al., Tables and Graphs of atomicshell relaxation data derived from the LLNLevaluated atomic data library Z=1-100, LLNLReport UCRL 50400 Vol. 30, 1991.

[3] J.L. Campbell, T. Papp, At. Data Nucl. DataTables 77 (2001) 1.

[4] F.P. Larkins, J. Phys. B: J. Phys. B 4, L29 (1971).

[5] I.P. Grant et al., Comput. Phys. Commun. 21,

207 (1980).

40

3.9 Fermi-shuttle acceleration in low and intermediate velocityion-atom collisions

B. Sulik a), R. Hellhammer b), Z.D. Pesic b) and N. Stolterfoht b)

We have been performing a systematic searchfor accelerating multiple scattering sequencesof electrons emitted in ion-atom collisions (orFermi-shuttle type ionization [1]). In thisprocess, the liberated electron is repeatedlybackscattered by the projectile and the tar-get center (denoted by P and T respectively).With the impact velocity of the projectile V,scattering sequences starting with target ion-ization produce electrons emitted with themean velocity 2nV in both forward and back-ward directions, where n is the number of en-counters with the projectile. Starting withprojectile ionization, the corresponding meanvelocity is (2n+1)V.

In a recent work [2], experimental evi-dence has been found for consecutive P-T-P (projectile-target-projectile) and P-T-P-Tping-pong-like scattering of ionized target elec-trons in single C+ + Xe collisions at 150 and233 keV/u impact energies. Distinct signa-tures for triple and quadruple electron scat-tering have been separated. Typical signaturewas the excess electron intensity emitted for-ward and backward in the expected velocityregions.

In the present work, we search for longersequences in a significantly lower impact veloc-ity range. In an earlier experimental study [3],distinct structures of excess electron yields atforward and backward directions have been ob-served in collisions of 50-400 keV O+ ions withAr target. These structures appeared to beshifted with the projectile velocity [3]. In ourpresent experiments, performed at the beam-line of the ECR ion source of the Ionen-StrahlLabor (ISL) in Hahn-Meitner Institute Berlin,we studied the spectra of electrons emitted incollisions of 15 keV N+ ions with Ar atoms un-der single collision condition. At this low ve-locity, we enter the impact energy range, wherethe accelerating electron ”orbits” may be con-sidered as specific molecular orbitals, and theFermi-shuttle process might be treated as a

promotion mechanism [4]. Our preliminaryresults show a a significant forward-backwardenhancement in the yield of continuous elec-trons in the 20-100 eV energy range, indicatingthe presence of 6-12-fold accelerating multiplescattering in the collisions (Fig. 1). Furtherexperimental and theoretical work is neededto confirm these findings.

10-2

10-1

100

101

102

101 102

Electron Energy (eV)

Nor

mal

ised

Cro

ss S

ectio

n (a

rb. u

nits

)

15 keV N+ + Ar

Ar MNN

Ar LMM

30o

90o

135o

6V|

8V|

12V|

Figure 1. Double differential cross sections forelectron emission in 15 keV N+ + Ar collisions,normalized to the Ar LMM Auger group. Mul-tiples of the projectile velocity are indicated.

AcknowledgementsWe acknowledge support from the OTKAGrant No. T032942, and the Hungarian-German Intergovernmental S&T Collabora-tion No. D17/99.

a) A significant part of the work was performed dur-ing a guest-scientist period in Hahn-Meitner In-stitute, Berlin.

b) Hahn-Meitner Institute, Glienickerstr. 100, D-14109 Berlin, Germany

[1] E. Fermi, Phys. Rev. 75, 1169 (1949).

[2] B. Sulik et al., Phys. Rev. Lett. 88, 073201 (2002).

[3] N. Stolterfoht and D. Schneider, IEEE Trans.Nucl. Sci. 26, 1130 (1979).

[4] S. Yu. Ovchinnikov and J. H. Macek, Nucl. Instr.

Meth. B 154, 41 (1999).

41

3.10 Electron emission from collisions of H+2 molecule ions with inert gas targets:

Search for interference patterns

B. Sulik, T. Ricsoka, O. Turak and N. Stolterfoht a)

In recent years, particular attention has beendevoted to charged particle induced ionizationof the H2 molecule. Since the two atomic cen-ters in this simple molecule can not be distin-guished, their electron emission contributionsadd coherently. First experimental evidencefor such interference effects has been foundin the electron emission spectra in collisionsof very fast and highly charged (60 MeV/uKr34+) projectiles with H2 molecules [1]. Insubsequent theoretical studies [2,3], the basicfeatures have been analyzed. In a recent ex-perimental study, some of their prediction hasbeen verified [4].

The simplest molecular system, however, isnot H2 with two electrons, but the H+

2 molecu-lar ion. At first sight, the symmetries of the H2

molecule are also present in this one-electronsystem, but electron-electron interactions donot alter the picture.

In the present work, we studied electronemission from H+

2 molecule ions colliding withHe and Ar targets (the inverse collision sys-tem). A beam of 1.5 MeV/u H+

2 ions was di-rected to gas jet targets, and electron spec-tra were collected in the entire 0-180o angularrange. The experiments have been performedat the beamline of a 5 MV Van de Graaff ac-celerator in ATOMKI, Debrecen. For referencepurposes, we also collected spectra in collisionsof 1.5 MeV H0 atoms with the same targets.

In Ref. [2], interference was treated withina two-effective center approximation, whichpartially accounts the correlation between theemitted and bound electrons. It is not clear,whether interference is only due to symmetryproperties, or electron correlation in H2 alsoplays a significant role.

Our present experiments are expected toanswer this question too. We have found cleardifferences between atomic (H0) and molecular(H+

2 ) bombardment with the same impact ve-locity. Preliminary results are shown in Figure1, comparing the cross sections for H0 and H+

2

impact at 165o. Beyond the shape-difference, acrossing point exhibits at 1140 eV, indicatingthe presence of interference effects. The os-cillation frequency seems to be doubled com-pared to first order expectations [1,2]. Thisis in agreement with the picture that electronloss at backward angles is due to hard colli-sions. Our data also resemble a recent obser-vation of double frequency components for H2

[5]. Further analysis is in progress.

10-22

10-21

10-20

500 1000 1500 2000

Electron Energy (eV)

DD

CS

(cm

2 /eV

sr)

1.5 MeV/u H2+ + Ar

165o

1.5 MeV H0 + Ar

crossingat 1040 eV

(v = vproj + 1 au)

Figure 1. Double differential electron emissioncross sections at 165o observation angle in collisionsof H atoms and H+

2 molecules with Ar. .

AcknowledgementsWe acknowledge support from the Hun-garian OTKA Grant No. T032942, and theHungarian-German Intergovernmental S&TCollaboration No. D17/99.

a) Hahn-Meitner Institute, Glienickerstr. 100, D-14109 Berlin, Germany

[1] N. Stolterfoht et al., Phys. Rev. Lett. 88, 133201(2002).

[2] M.E. Galassi et al., Phys. Rev. A 66, 052705(2002).

[3] L. Nagy et al., J. Phys. B 35, L453 (2002).

[4] N. Stolterfoht et al., Phys Rev. A, in print (March2003).

[5] N. Stolterfoht, et al., submitted to ICPEAC-03

Abstracts Book

42

3.11 Cascade feeding of the 1s2s2p 4P state in collisions of Li-like O5+ ions withH2 and He targets

B. Sulik, A. Orban, L. Gulyas and T.J.M. Zouros a)

In the collisional formation of the 1s2s2p 4Pstate of Li-like ions, one of the possible mech-anisms is the so-called transfer-loss (TL) pro-cess, in which the loss (ionisation) of a projec-tile 1s electron occurs simultaneously with thetransfer of a target 1s electron to the projectile2p subshell. This process was studied experi-mentally in 0.2-2 MeV/u collisions of O5+ ionswith H2 and He targets [1]:

O5+(1s22s)+He → O5+(1s2s2p4P )+He++e−.

In our earlier analysis [2] we have shown thatthe TL process could be described qualita-tively, within the framework of the indepen-dent particle model (IPM). In the presentwork, we show that inclusion of capture tohigher n shells of the projectile provides signif-icantly improved agreement with experiment.The basic idea is that practically all captureinto higher-lying (n > 2) quartet states de-cay radiatively very quickly to the 1s2s2p 4Pstate. These photon cascades become increas-ingly more likely than autoionization with in-creasing n. Due to the strongly different decayrates, the metastable 1s2s2p 4P state behaveslike a quasi-ground state, collecting all quartetcapture events before decaying itself.

Compared to our earlier study [2], only thetransfer probability was calculated differently:

P 2pmT = PHe(1s)→O(2p) + PHe(1s)→O(n>2)

where the first term is the probability of thecapture of a He 1s electron to the O5+ 2p stateby a He or H2 1s electron (original term fromour earlier work [2]), and the second term rep-resents capture to all O5+ n > 2 shells.

Similarly to our previous work [2], calcu-lations of projectile excitation and ionizationprobabilities were performed by an SCA code[3], while electron transfer probabilities werecalculated in the CDW approximation [4].

In Fig. 1, experimental data for the O5+ +H2 collission system [1] are compared with ourpresent (denoted by ”cascade TL + T2L”) and

earlier calculations (TL + T2L). It is clearlyseen, that the inclusion of the cascade feedinginto the calculations significantly improved theagreement with experiment.

0 5 10 15 20 25 30 350.01

0.10

1.00

10.00

Exp (Ref. [1]) T1: ee (IA) [1]

T2: TL + T2L

T3: cascade TL + T2L

O5+ + H2

1s2s2p 4Pd σ

(0o ) A

ug

er /

dΩ

(

10-2

1 cm

2 /sr)

Projectile Energy (MeV)

Figure 1. Single differential cross sections for zero-degree Auger electron emission from the 1s2s2p 4P

state as a function of projectile energy for collisionswith H2. The symbols are for experimental data[1]. The dotted line represents the earlier TL cal-culations without cascade feeding, while the solidline is the present full TL calculation. The dashedline is a calculation for the dielectronic excitation(eeE) within the electron scattering model [1].

AcknowledgementsWe acknowledge support from the Hun-garian OTKA Grant No. T032942, and theHungarian-Greek Intergovernmental S&T Col-laboration No. GR-08/99.

a) Department of Physics, University of Crete &I.E.S.L.-F.O.R.T.H., Heraklion, Crete, Greece

[1] G. Toth et al., Nucl. Instrum. & Meth. in Phys.Res. B 124,413 (1997).

[2] B. Sulik et al., J. El. Spectr. Rel. Phenom. 114-116, 191 (2001).

[3] G. Schiwietz and P.L. Grande, Radiat. Eff. Solids130–131, 137 (1994).

[4] Dz. Belkic, R. Gayet and A. Salin, Phys. Rep. 56,

279 (1979).

43

3.12 Guided transmission of 3 keV Ne7+ ions through nanocapillaries in PETpolymers: dependence on the capillary diameter

N. Stolterfoht a), R. Hellhammer a), Z.D. Pesic a), V. Hoffmann a), S. Petrov a), D. Fink a), B. Sulik b)

The outstanding progress in nanotechnologyis accompanied by a continuous miniaturiza-tion of interfaces used in microelectronics andrelated fields. Particular attention has beenpaid to linear structures of mesoscopic dimen-sions, such as pores or capillaries. Recently,we started experiments in which PET (Mylar)polymer foils of 10 lm thickness were irradiatedby 400 MeV xenon. Capillaries with a diame-ter of a few hundreds nm in foil were obtainedetching ion tracks using NaOH [1].

To study the capillary interior, we mea-sured the transmission of 3 keV Ne7+ ionsthrough capillaries. Foils with different capil-lary diameters (100 nm [1], and 200 nm) weretilted with respect to the incident beam di-rection. Angular distributions of the trans-mitted Ne7+ ions obtained with PET materialwere found to be essentially different from theresults with capillaries covered by a thin Agmetal film. For the latter case, the Ne7+ an-gular distribution is rather narrow (FWHM of10) and ion transmission vanishes when the foilis tilted (Fig. 1). On the contrary, for the 50

tilted isolating PET foil only about 20the an-gular distribution of the Ne7+ ions is relativelybroad (FWHM of 40-60). Similar effects werefound for tilt angles as large as 250 .

The latter observation suggests a ”guid-ance” of the Ne7+ ion within the capillary [1],providing evidence that the capillary walls be-come charged and close collisions with the sur-face are suppressed. The charge deposition oc-curs by means of a self-organizing process [1]

From Fig. 1 it is seen that the transmissionsof the ions depend both on the tilt angle andthe capillary diameter. Specifically, for 00 tiltangle the transmissions are about equal for thetwo capillary diameters, whereas for 150 tiltangle the transmission through 100 nm cap-illaries is about an order of magnitude largerthan that for 200 nm. This finding strongly

supports the picture of ion guiding in the cap-illary. The higher the aspect ratio of the capil-lary the higher the capability to bend the ionsalong the axis of the capillary and transportthem to its exit.

Experimental studies of the time evolution[1,2] of the transmission also support the pic-ture of ion guiding, and provide possibility toverify and refine the developed linear [1] andnonlinear [2] self organizing charge depositionmodels.

Figure 1.Angular distributions of Ne7+ ions trans-mitted through capillaries in PET. The tilt angleis indicated. Also plotted are data for capillaries inAg. In (a) and (b) results for capillary diametersof 100 and 200 nm are compared.

Acknowledgements

a) Hahn-Meitner Institute Berlin, Glienickerstr. 100,D-14109 Berlin, Germany

b) A significant part of the work was performed dur-ing a guest-scientist period in Hahn-Meitner In-stitute, Berlin.

[1] N. Stolterfoht, J.H. Bremer, V. Hoffmann, R. Hell-hammer, S. Petrov, D. Fink, and B. Sulik, Phys.Rev. Lett. 88, 133201 (2002).

[2] N. Stolterfoht, V. Hoffmann, R. Hellhammer, D.Fink, A. Petrov, Z.D. Pesic, and B. Sulik, Nucl.Instrum. Methods B, in print (2003)

44

3.13 Theoretical study of transfer ionization in O8+ + Ar collisions

L. Sarkadi

We continued the theoretical study of thetransfer ionization (TI) process in energeticO8+ + Ar collisions. TI is a two-electron pro-cess in which the ejection of an electron intothe continuum is associated with capture of an-other electron into one of the bound states ofthe projectile. Particularly we are interestedin a special kind of TI when the electron isejected in forward direction with the velocityof the bombarding particle. For such an elec-tron emission the long interaction time withthe projectile results in a singularity in the en-ergy spectrum of the electrons, known as ‘elec-tron cusp’. The formation of cusp associatedwith target ionization is called electron cap-ture to the continuum (ECC). TI proceedingwith cusp formation is a special kind of doubleelectron capture: one electron is captured to abound state, the other electron is captured toa continuum state of the projectile.

TI has been subject of numerous experi-mental and theoretical investigations, mainlybecause as a two-electron process it may pro-vide information about the role of electron-electron interaction (correlation) in atomic col-lisions. The present theoretical work is con-nected to our previous systematic experimen-tal investigations dealing with cusp-electronemission via TI (for a review see [1]). Thesestudies were carried out with H+, He+, He2+,O7+ and O8+ projectile ions in a broad rangeof the collision velocity (from 4.4 keV amu−1

to 1.5 MeV amu−1).We applied the classical trajectory Monte

Carlo (CTMC) method to calculate the elec-tron spectra of the cusp peak and the TI/ECCcusp-intensity ratios for 0.3 – 2 MeV amu−1

O8+ + Ar collisions. (We mean ECC ‘pure’cusp-electron production, i.e., electron emis-sion without bound-state capture.) We carriedout the calculations in the independent parti-cle model (IPM) by considering a reduced col-lision system consisting of the projectile, anactive electron and the target ion core. Therole of the passive electrons of the target core

was taken into account by an effective poten-tial.

Including the contributions of the L andM shell of the Ar target in the calculations,we showed that the maximum observed exper-imentally [2] in the impact-energy dependenceof TI/ECC cusp-intensity ratios is due to theincreasing role of the L shell with increasingenergy. The obtained results are shown inFig. 1. In the figure experimental and the-oretical data for He2+ ion projectiles are alsoplotted. CTMC succeeded in the descriptionof the 2TI/ECC ratio, too (2TI: electron emis-sion accompanied by bound-state capture oftwo electrons).

Collision velocity [a.u.]1 2 3 4 5 6 7 8 9

TI/E

CC

0.0

0.2

0.4

0.6

0.8

1.0

O8+ + ArHe2+ + Ar

vM vL

Projectile energy [MeV/amu]0.05 0.2 0.5 1.0 2.0

Figure 1. Cusp-electron production by TI relativeto ECC. Experimental data for O8+ on Ar: full cir-cles, Zavodszky et al. [2]; full squares, Breinig etal. [3]. Experimental data for He2+ on Ar: opencircles, Vıkor et al. [4]. CTMC calculations: solidline, O8+ on Ar (L and M shell, present work);dashed line, He2+ on Ar [1] (M shell only). ThevM and vL Bohr velocities of the M- and L-shellelectrons are indicated by vertical lines.

[1] L. Sarkadi et al., J. Phys. B 34, 4901 (2001).

[2] P. A. Zavodszky et al., XIX. ICPEAC,Abstr.: p. 311. (1995).

[3] M. Breinig et al., Phys. Rev. A 25, 3015 (1982).

[4] L. Vıkor et al., Nucl. Instr. Meth. B 124, 342

(1997).

45

3.14 Interference effects in electron emission from 68 MeV amu−1 Kr33+ + H2

collisions

L. Sarkadi

We suggest a simple method for the de-scription of the coherent electron emissionfrom the two H atoms of the H2 molecule in-duced by particle impact. The existence of theinterference effect – an analogy of the Young’stwo-slit experiment in optics – was demon-strated experimentally by Stolterfoht et al. [1].Our method is based on a formalism that sepa-rates the cross section for the electron emissioninto an atomic part describing the independentemission from the two H atoms, and a factorgiving account of the interference caused bythe coherent emission from the two centers:

d3σH2

dq dΩdε=

d3σ2H

dq dΩdε

[1 +

sin(pd)pd

]. (1)

Here d3σH2/dqdΩ dε is the triply differentialcross section for the electron emission fromthe H2 target molecule, and d3σ2H/dqdΩdε isthe corresponding cross section for the electronemission from the two H atoms acting as inde-pendent particles (denoted by the label 2H).q is the momentum transfer vector defined asthe difference between the initial and final mo-mentum of the projectile. The solid angle dΩand the energy dε refer to the ejected electron.The factor in the parentheses describes the in-terference caused by the coherent emission ofthe electron from the two H centers. In theinterference factor p is the modulus of the vec-tor p = k − q, where k is the momentum ofthe electron. d is the internuclear distance inthe H2 molecule. Since in the experiment thevector q was not measured, Eq. (1) has to beintegrated over q.

The above separability allows the use ofa classical ionization theory to determine theatomic part of the cross section. To this weapplied the classical trajectory Monte Carlo(CTMC) method. We showed that withinCTMC the doubly differential cross section(DDCS) for the molecular electron emissioncan be evaluated in a very simple way.

Calculations have been carried out for 68MeV amu−1 Kr33+ on H2 collisions. A reason-able agreement has been found between theCTMC results and the recent experimentaldata obtained by Stolterfoht et al. [2], as wellas the predictions of the first Born approxima-tion (see Fig. 1).

DD

CS

(H

2) /

DD

CS

(2H

)

0.8

1.0

1.2

1.4

1.6

Electron velocity [a.u.]

0 1 2 3 40.8

1.0

1.2

1.4

1.6

0 1 2 3 4 5

(a) (b)

(c) (d)

30o 60o

90o 150o

Experiment(Stolterfoht et al.)Born approx.CTMC

Figure 1. Comparison of experimental and theo-retical DDCS(H2)/DDCS(2H) ratios as a functionof the electron velocity for (a) 30, (b) 60, (c)90 and (d) 150 electron emission angles. Thenotations: •, experimental data [2] normalized toCDW-EIS [3] atomic cross sections; - - -, Born ap-proximation [2]; –o–, CTMC (present work).

[1] N. Stolterfoht et al., Phys. Rev. Lett. 87, 023201(2001).

[2] N. Stolterfoht et al., Phys. Rev. A, in press (2003).

[3] P. D. Fainstein, V. H. Ponce and R. D. Rivarola,

J. Phys. B 24, 3091 (1991).

46

3.15 Classical description of the fragmentation of positronium in collision withHe atoms

L. Sarkadi

Recently Armitage et al. [1] reported onfirst measurement of absolute break-up crosssection for the fragmentation of positronium(Ps) in collision with He atoms in the energyrange between 13 and 33 eV. In addition tothe measurement of total cross sections, theydetermined also the longitudinal energy distri-butions of the emitted positrons. A remark-able feature of the obtained positron spectra isa peak appearing just below 50% of the resid-ual Ps energy (Eres = EPs− 6.8 eV). The peakwas interpreted as an analogy of the electronloss to the continuum (ELC) peak appearingin the energy spectrum of the electrons ejectedin the forward direction in ion-atom (atom-atom) collisions. In a previous experiment therelated process, electron capture to the contin-uum (ECC) has been observed by Kover et al.[2] for positron projectiles.

We applied the classical trajectory MonteCarlo (CTMC) method to the description ofthe collisional fragmentation of PS. The colli-sion system was simplified to a three-body sys-tem consisting of the electron and the positronof Ps, as well as the He atom that was consid-ered as a structureless particle. The interac-tion of e− and e+ with He was approximatedby a static, fully screened Coulomb potential.The calculations were carried out for collisionenergies 13, 18, 25, and 33 eV. Our theory over-estimates the measured total break-up crosssections by a factor of 1.6 – 2.5. At the sametime, it correctly reproduces the peak observedin the longitudinal positron spectra (see Fig.1), supporting a peak formation mechanismsimilar to the ELC process in atomic collisions.

The dependence of the e− and e+ ejectionon the emission energy and angle was also in-vestigated by the CTMC model. A strong e−

– e+ asymmetry was found for the doubly dif-ferential cross sections at low impact energy.This behaviour was explained by the polariza-tion of the Ps atom in the incoming phase ofthe collision. The asymmetry is expected to

diminish at high impact energies.According to the calculations, a significant

e− – e+ difference is expected to occur alsoin the longitudinal energy distributions of theejected particles. CTMC predicts a peak alsoin the electron spectrum, but it is less pro-nounced and shows a larger shift from the ex-pected peak position Eres/2 than the corre-sponding peak in the positron spectrum. Anexperiment is suggested in which the longitudi-nal energy distribution of the electrons emittedin the fragmentation of Ps would be measured.

EPs = 25 eV

Longitudinal positron energy [eV]

0 5 10 15 20 250

10

20

30

40

EPs = 33 eV

0 5 10 15 20 25 300

10

20

30

EPs = 18 eV

0 5 10 15 200

10

20

30

40

50

60

EPs = 13 eV

0 5 10 15

Sin

gly

diffe

rent

ial c

ross

sec

tion

[10

-18 cm

2 eV

-1]

0

10

20

30

40

50

60

70

80

(a) (b)

(c) (d)

CTMC Experiment

Figure 1. Longitudinal energy distributions ofthe positrons emitted in Ps + He collisions forEPs =13, 18, 25, and 33 eV. The experimental data(full circles, Armitage et al. [1]) are normalized tothe maxima of the theoretical curves calculated bythe present CTMC model. The vertical dotted lineshows the expected peak position, Eres/2.

[1] S. Armitage D. E. Leslie, A. J. Garner, and G.Laricchia, Phys. Rev. Lett. 89, 173402-1 (2002).

[2] A. Kover and G. Laricchia, Phys. Rev. Lett. 80,

5309 (1998).

47

3.16 Transition matrix elements for atomic excitations induced by screened Coulombpotentials

A. Orban and B. Sulik

In ion-atom collisions the electrons carriedby the projectile may influence the target elec-tronic transitions. The electric field created bythese electrons screens the Coulomb field of theprojectile nucleus. The transition matrix ele-ments, which take into account the screeningeffect of the projectile are important quanti-ties in the description of such collisions. Inthe literature, there exist codes, which werebuilt up for calculating matrix elements forthe pure Coulomb potential in bound-boundand bound-continuum transitions using hydro-genic wave functions for the atomic states de-scription [1], [2]. Recently, we have publisheda FORTRAN code [3] which calculates tran-sition matrix elements between atomic boundstates with high accuracy as a function of theinternuclear distance. Compared with the for-mer codes mentioned above, the present pro-gram takes into account the screening effectof the projectile electrons. Moreover arbitrarywave functions, given by the user, can be usedfor the target atomic states description. Weapplied the screening model already publishedin Ref. [4]. For an accurate numerical eval-uation of the radial integrals, two main prob-lems appeared. One of them is connected tothe fact that in the expression of the screeningmatrix elements the derivatives of different or-ders of the modified Bessel functions In+1/2(x)and Kn+1/2(x) appear. We developed a rel-ative simple procedure for the calculation ofthese derivatives, by expressing them with thehelp of lower order Bessel functions. Conse-quently, the accuracy of the screening matrixelements depends on the accurate calculationof the modified Bessel functions. We have builtup two subroutines for the calculation of theseBessel functions with a relative accuracy bet-ter than 10−10 in a wide range of order andargument. The other problem is that the tar-get wave functions are given by the user onarbitrary grid leading to numerical inaccura-cies. The radial integral is evaluated in three

phases. The integral between 0 and the firstnon-zero coordinate where the wave functionis given by the user is approximated analyti-cally. The remaining two parts of the integralis evaluated numerically, using the equidistantmethod of Simpson from the first non-zero co-ordinate to the internuclear distance, and fromthe internuclear distance to infinity. Detailedtests have been performed at different levels,for different collision systems using hydrogenicwave functions (in tabulated form). For refer-ence, the same calculations have been done byMathematica [5] using the same wave functionsin analytical form. For illustrating the accu-racy of the code, we present the results for thedipol transitions 1s → 2p of F8+ ion in collisionwith He atom in Table 1. The table containsthe G function (the radial part of the integral)for a few internuclear distances, R. The first,second and third rows of the table contain theG(R) function in the different integration re-gions while the forth row is the full G(R) func-tion. In the last coloumn ’valuable digits’ in-dicates the accuarcy of the present calculationwith respect to Mathematica.We have also applied the code for the inves-tigation of single excited states of the lithiumlike oxygen ion [6].

[1] M.J. Jamieson, Comput. Phys. Comm. 1(1970), 437.

[2] L. Sarkadi, Comput. Phys. Comm. 133(2000), 119-127.

[3] A. Orban, B. Sulik, Comput. Phys.Comm. 151 (2003), 199-215

[4] S. Ricz, B. Sulik and N. Stolterfoht, I.Kadar, Phys. Rev. A, 47 (1993), 1930-1938.

[5] S. Wolfram, Mathematica, (Addison-Wesley, Redwood City, CA, 1991).

[6] A. Orban, T.J.M. Zouros, B. Sulik, Nucl.Instr. and Meth. B (in press)

48

Table 1. The G(R) function for the 1s → 2p transition of the F8+ ion induced by He projectile.

R GSCRMTRX(R) GMathematica(R) valuable digits

0.0023 -0.107049057799E-04 -0.107049010129E-04 7-0.199805146162E-05 -0.199804344447E-05 5-0.657339136625E-01 -0.657339136624E-01 11-0.657466166197E-01 -0.657466166068E-01 (10)

0.005 -0.226515644747E-05 -0.226515543329E-05 6-0.124340968808E-03 -0.124340967886E-03 8-0.142649340630E+00 -0.142649340630E+00 12-0.142775946755E+00 -0.142775946753E+00 (10)

0.05 -0.226355769419E-07 -0.226355661376E-07 6-0.766151624559E-01 -0.766151624560E-01 10-0.121377765792E+01 -0.121377765791E+01 11-0.129039284290E+01 -0.129039284300E+01 (9)

0.2 -0.137156290499E-08 -0.137156185166E-08 6-0.955011528055E+00 -0.955011528055E+00 12-0.134730816477E+01 -0.134730816477E+01 12-0.230231969420E+01 -0.230231969419E+01 (12)

0.5 -0.172240208223E-09 -0.172239971614E-09 4-0.727617188910E+00 -0.727617188908E+00 10-0.100783082547E+00 -0.100783082547E+00 12-0.828400271629E+00 -0.828400271282E+00 (9)

1 -0.195026502900E-10 -0.195026119968E-10 6-0.108977937382E+00 -0.108977937382E+00 12-0.297762915183E-03 -0.297762915182E-03 11-0.109275700317E+00 -0.109275700316E+00 (12)

3 -0.156877691415E-13 -0.156877275463E-13 6-0.929706567589E-04 -0.929706567589E-04 12-0.178615479063E-14 -0.178615479062E-14 11-0.929706567764E-04 -0.929706567763E-04 (12)

4 -0.510756099637E-15 -0.510754690141E-15 6-0.305268495603E-05 -0.305268495603E-05 12-0.325695275035E-20 -0.325695275034E-20 11-0.305268495654E-05 -0.305268495654E-05 (12)

5 -0.169539795300E-16 -0.169539315585E-16 6-0.101867023194E-06 -0.101867023193E-06 11-0.556704727266E-26 -0.556704727265E-26 11-0.101867023211E-06 -0.101867023210E-06 (11)

6 -0.568280695828E-18 -0.568279060849E-18 6-0.342680025760E-08 -0.342680025760E-08 12-0.905673816120E-32 -0.905673816120E-32 12-0.342680025817E-08 -0.342680025816E-08 (11)

49

3.17 Angular distribution of highly charged ions transmitted through metallicmicrocapillaries

K. Tokesi, L. Wirtz a), C. Lemell a), and J. Burgdorfer a)

During the last decades studies of interac-tions between highly charged ions (HCI) andsolid surfaces are in center of interest, whichis partly stimulated by potential future techni-cal application such as nanofabrication. So farthe following picture of the HCI-surface inter-action is emerged: When a highly charged ionapproaches a solid surface, one or more elec-trons are resonantly captured at a characteris-tic distance (dc) into Rydberg states of the pro-jectile. As a result, a multiply excited Rydbergatom with inner shell vacancies, a so-called hol-low atom of the first generation (HA1), is cre-ated. It is, however, usually extremely short-lived because of the image acceleration of theion towards the surface. When the ion reachesthe surface the memory of HA1 is lost and thehollow atom of the second generation (HA2) isformed. Recently, an alternative technique hasbeen introduced to study HA1s by interactionof highly charged ions with internal surfaces ofmicrocapillaries.

0

0.01

0.02

0.03

0.04

0.05

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Angle (deg)

Inte

nsi

ty (

arb

. un

it)

χ=0.05χ=0.1

χ=0.5 χ=1

χ=0

Figure 1. Angular distributions for Xe5+ ions forvarious strength of image acceleration between theion and the Ni capillary surface at 5×107 a.u. dis-tance from the capillary exit.

In this work, angular distributions ofHA1s creating in microcapillary transmissionas function of the interaction strength betweenthe HCI and solid surface are studied. The in-teraction strength is varied from the case of

insulator to the clean metal surface by vari-ation of the surface response function χ =(1 − ε)/(ε + 1) from small values χ << 1(ε ≈ 1) to the metallic limit (χ → 1). Hereε is the bulk dielectric response. The simula-tion is based on the classical over the barriermodel including the neutralization and relax-ation cascade. The electronic dynamics is sim-ulated within a Monte-Carlo approach

We performed theoretical model calcula-tions for the angular distribution of Xe6+

ions with an energy of 800 eV/q transmittedthrough Ni microcapillaries. We have shownthat the angular distributions of transmittedions can be used to identify different phases ofhollow ion formation for clean metal surfaces.We have also investigated the case of surfaceswhich are partly or entirely contaminated bylayers of insulating materials by the reductionof image acceleration. We have found thatwhile the final charge state distributions hardlydepend on the strength of the image accelera-tion the angular distributions change dramat-ically. Decreasing the image acceleration theangular distribution shifts to the lower scatter-ing angles. Completely neglecting the imageacceleration, the angular distribution is cen-tered at zero degree.

AcknowledgementsThe work was supported by the Hungar-

ian Scientific Research Found: OTKA No.T032306, the Austrian Fonds zur Forderungder wissenschaftlichen Forschung, FWF (Aus-tria), the grant ”Bolyai” from the HungarianAcademy of Sciences, TeT A-19/2001, and EUunder contract no. HPRI-CT-2001-50036.

a) Institute for Theoretical Physics, Vienna University

of Technology, Wiedner Hauptstr. 8-10 /E-136/,

A–1040 Vienna, Austria

50

3.18 State slective (n,l) capture distributions in low energy antiproton-heliumcollisions

K. Tokesi and B. Juhasz

Recently the state selective capture crosssections at very low (1-100 eV) projectile ener-gies were presented in antiproton-helium colli-sions [1]. The role of isotope effect was also in-vestigated when the capture cross sections for3He and 4He targets were compared. Thesemeasurements give a sensitive test of varioustheories when the measured cross sections arecompared with the experimental data. Themain difficulty in the calculations are causedby the two-center Coulomb field (created bythe projectile and target) that influences themotion of the particles. The classical trajec-tory Monte Carlo (CTMC) method has beenquite successful in dealing with capture pro-cesses in ion-atom collisions [2,3]. One ofthe advantages of the CTMC method is thatmany-body interactions are exactly taken intoaccount during the collisions. This approxi-mation is able to utilize various model poten-tials between the colliding particles in the samefooting.

The state selective (n, l) cross sections forantiproton-capture as a function of impact en-ergy are calculated for 3He and 4He usingthe CTMC technique. In the present studya three-body CTMC method [4,5] is used.The potentials representing the interactionsbetween the components of the collision sys-tem, the case of Coulomb effective potential

(Model 1) and the Garvey-type model poten-tial [5] (Model 2) are considered.

We found the resulting (n, l) distributionsof captured antiproton in good agreement withthe recent measurements [1] for Model 2. ForModel 1, the target potential is described by apoint-like Coulomb potential. For this poten-tial the maximum in the n distribution of thecaptured antiproton is shifted to the higher nvalues compared to Model 2. This is a strongindication of the importance of screening effectat low energy collisions.

AcknowledgementsWe are grateful to D. Horvath for help-

ful comments and discussions. The work wassupported by the Hungarian Scientific Re-search Found: OTKA Nos. T032306 andT033079, the grant ”Bolyai” from the Hungar-ianAcademy of Sciences and TeT-Jap-4/02.

[1] M. Hori et al., Phys. Rev. Lett. 89 (2002) 093401.

[2] J.S. Cohen, Phys. Rev. A62 (2000) 022512.

[3] J.S. Cohen, Phys. Rev. A65 (2002) 052714.

[4] R. Abrines and I.C. Percival, Proc. Phys. Soc.(London) 88 (1966) 861.

[5] R.E. Olson and A. Salop, Phys rev. A16 (1977)531

[6] R.H. Garvey, C.H. Jackman and A.E.S. Green,

Phys rev. A12 (1975) 1144

51

3.19 Photoionization cross sections of Ne(1s)

X-M. Tong a) and K. Tokesi

The photoionization cross sections in theenergy range between 870 and 1200 eV pho-ton energies of Ne(1s) state are calculated bythe independent particle approximation (IPA)[1,3] and by the time dependent density func-tional theory (TDDFT) [4,5] within the frame-work of linear density response theory. For thephotoionization above the 1s ionization thresh-old, the dipole transition is dominant. As atest we include the multi-pole contributions inthe calculations. We found that the contribu-tion of multi-poles to the total cross sectionsis less than 0.1 %. Fig. 1 shows the total pho-toionization cross sections as a function of thephoton energy.

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

3.5E+05

4.0E+05

0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

Energy (keV)

Cro

ss s

ectio

n (b

arn)

Figure 1. Photoionization cross sections: solidline: IPA, dashed line: TDDFT.

The difference between the two calculations arebetween 10 and 20 %, which can be attributedpartly to the effect of electron correlation. Thedifferential photoionization cross sections canbe expressed by the help of total cross sections(σT )as:

dσ

dΩ=

σT

4π(ΣlB1(l)Pl(cos θ)+

+B2(l)P 2l (cos θ) cos(2φ)

). (1)

The angular distribution coefficients can becalculated for given effective potentials basedon either IPA or TDDFT. Keeping only thedipole transition, Eq. 1 can be simplified forlinear polarized photons as

dσ

dΩ=

σT

4π(1− P2(cos θ)+

+12P 2

2 (cos θ) cos(2φ))

, (2)

and for circular polarized photons as

dσ

dΩ=

σT

4π(1− P2(cos θ)) , (3)

respectively. We note that the polarization ischosen on the x − y plane and the photon ispropagated along the z−direction.

AcknowledgementsThe work was supported by the Hungar-

ian Scientific Research Found: OTKA No.T032306.

a) Physics Department, Kansas State University,Manhatten, Kansas 66506

[1] H.K. Tseng, R.H. Pratt, S. Yu, and A. Ron Phys.Rev. A 17 1061 (1978).

[2] Y.S. Kim, R.H. Pratt, A. Ron, and H.K. TsengPhys. Rev. A 22 567 (1980).

[3] J.H. Sofield, Phys. Rev. A 40 3054 (1989).

[4] X.M. Tong, and S.I. Chu, Phys. Rev. A 55 3406(1997).

[5] X.M. Tong, D. Kato, T. Watanabe and S. Ohtani,

J. Phys. B 33 717 (2000).

52

3.20 The role of projectile double scattering in positron-atom collisions

K. Tokesi

The process of electron capture to the con-tinuum (ECC) can be explained as a result ofthe special case of ionization, where the ionizedtarget electron is strongly influenced by theoutgoing projectile. The ECC peak appears atthe energy where the electron velocity is almostthe same as the projectile velocity. The ECCis well understood when the projectile is heavyparticle. It was shown that the most importantmechanism for ECC is the Coulomb focusingof ejected target electron in the direction of theprojectile and the peak occur for positron im-pact as well in the triple-differential cross sec-tions [1]. Since the mass of the positron andthe electron is the same, the projectile energyis shared equally between the positron andelectron after the ECC. Therefore the nominalvalue of the ECC peak in the electron/positronspectrum is (E−Eb)/2. Contrarily, the exper-imentally obtained positions of the ECC peakalways appear at significantly lower/higher en-ergies. To solve this puzzle model calculationswithin the frame work of classical trajectoryMonte Carlo (CTMC) method are performed.

1E-19

1E-18

1E-17

1E-16

1E-15

0 20 40 60 80 100 120 140 160 180

dσ /

dΩ (c

m2 /s

r)

Angle (deg)

Figure 1. Angular distributions of scatteredpositrons at 50 eV impact energy. full circle: full3-body approximation, open circle: neglecting thescattering on the target nucleus.

The CTMC method has been successful indealing with the ionization process in atomiccollisions for light projectile impact. In this

work, the role of projectile double scatteringin positron-hydrogen atom collisions is investi-gated. Fig. 1 shows the angular distributionsof scattered positrons, and for the case of ion-ization channel at 50 eV impact energy. Forthe case of the full 3-body approximation, theenhancement in the distribution between thescattering 60o and 80o is due to the ionizationthrough double scattering [2].

0.0E+00

5.0E-17

1.0E-16

1.5E-16

2.0E-16

2.5E-16

0 10 20 30 40

d3 σ / d

Ωe /

dΩ

p /d

E (

cm2 /s

r/eV

)

Energy (eV)

Figure 2. Energy distribution of scatteredpositrons at 50 eV impact energy. The scatteringon the target nucleus is neglected.

Fig. 2 shows the energy distribution ofscattered positrons at 50 eV primary energywhen the scattering on the target nucleus is ne-glected. The ECC peak position is at E=18.2eV, which is the nominal value at this impactenergy. In conclusion we can say that the roleof double scattering manifests itself in the en-ergy shift of ECC peak [2].

AcknowledgementsThe work was supported by the Hungar-

ian Scientific Research Found: OTKA No.T032306, the grant ”Bolyai” from the Hungar-ian Academy of Sciences.

[1] K. Tokesi, and A. Kover, J. Phys. B 33 3067(2000).

[2] K. Tokesi, to be published.

53

3.21 Model calculations for positron-helium scattering

L. Lugosi, I.F. Barna a) and K. Tokesi

The comparison between the results oftheoretical and experimental investigationsof positron–atom scattering provide valuabletests of both the quality of the applied modelsand wave funtions used in the calculations aswell as the accuracy of the measured data. Dueto the complex nature of the many-body, mul-tichannel collision processes, very detalied the-oretical studies of positron scattering by atomshave been made only for H and He (see the re-cently developed close–coupling calculations ofCampbell et al. [1]). On the experimental side,the e+-H system can be studied with great dif-ficulties. In contrast, accurate experimentaldata have been obtained for He [2,3]. In thecase of the e+-He scattering, there are four par-ticles and consequently six inter-particle co-ordinates. The wave functions of the targetare not known exactly. These factors compli-cate the calculation procedures in comparisonwith those for e+-H scattering. In order todecrease the complexity of the computationalmethods, reasonably accurate equivalent one–electron and complex optical model potentialsbased on optical theory have been proposed fora variety of scattering processes [4,5].

In the present work we consider the elas-tic and inelastic scattering of positron fromHe at energies above the 21S first excitationthreshold at 20.61 eV, i. e. above the Ore gapenergy region using a complex optical poten-tial model (COPM) and a classical trajectoryMonte Carlo (CTMC) method based on theGarvey–type model potential [6]. It is wellknown that the optical potential, which re-places the many–channel problem and hencecan be used to study the elastic and inelasticscattering mechanism between composit sys-tems, is defined by the Feshbach projection ofthe Schrodinger equation on a subset from acomplete Hilbert–space basis set. The opticalpotential Vopt consists of three terms

Vopt(r,E) = Vstat(r) + Vpol(r, E) ++iVabs(r,E), (1)

where Vstat is the mean static field potentialterm (MSF) which represents the interactionof the positron projectile with the unperturbedHe atom, Vpol and Vabs are respectively thepolarisation and absorption model potentialwhich can be expressed as a function of theprojectile energy E. In Eq. (1) r is the po-sition vector of the positron with respect tothe nucleus. Vpol has been expanded up toquadrupole order and the precision calcula-tions of Bhatia and Drachman [7] were usedfor the polarisability coefficients. For the Vabs

potential term we have adopted the expressionobtained by Gianturco and Melissa [5]. In ourinvestigations, the MSF potential was derivedusing three type of wave functions: Hylleraas(H), Hartree–Fock (HF) and one that was con-structed from the configuration interaction ap-proximation (CI). The objective is an approx-imate representation of the ground state of Hein order to find out which model is capableof giving accurate data for the elastic scatter-ing cross sections. Since, the non-Hermitianoptical potential in Eq. (1) has complex radi-ally symmetric form and short ranged, the par-tial wave decomposition of the total scatteringwave function still makes sense. So, the elasticscattering is described by the regular solutionof the

[d2

dr2− l(l + 1)

r2−

−2Vopt(r, E) + k2

]Fl(k, r) = 0, (2)

radial Schrodinger equation, but the l-th radialwave function Fl(k, r) is complex. For neutraltarget systems this regular solution vanishesat the origin and has the following asymptoticbehaviour

Fl(k, r → 0) → 0, Fl(k, r →∞) →→ sin

(kr − lπ

2+ δl(k)

). (3)

54

Separating the l-th partial complex phase shiftδl(k) into its real and imaginary terms, one canwrite

δl(k) = λl(k) + iµl(k). (4)

The imaginary component of the phase shiftcorresponds to absorption, i. e. the loss of par-ticle flux from the incident channel. The totalelastic cross section is given according to (forexample, Bransden [8])

σelas =2π

k2

∞∑

l=0

(2l + 1)[chµl(k) −

− cos2λl(k)]exp−2µl(k). (5)

For the numerical solution of the differentialequation (2) the modified version of the com-puter program [9] was used.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

10 100

To

tal E

last

ic C

ross

Sec

tio

ns

[π a

2 0]

Energy [eV]

e+ + He(1s2) → e+ + He(1s2)

Hylleraas

Campbell et al. [1]

Hewitt et al. [10]

Figure 1. Elastic integral cross sections for e+-Hescattering.

Figure 1 shows a comparison of calcu-lated elastic cross sections as a function of thepositron energy with the previous results ob-tained by Campbell et al. [1] and Hewitt et al.

[10]. We found that the computed cross sectionis sensitive to the wave function chosen for theapproximate description of the ground state ofHe atom. The obtained values of the COPM-H and COPM-HF cross sections are in a rea-sonable agreement with the results of the pre-vious quantum mechanical calculations, whilethe CTMC data overestimates these by a fac-tor of 5. Improvement of the CTMC calcula-tions is planned in the future. The relativelybetter agreement between the COPM-CI andthe multi-state close-coupling data shows thatCOPM-CI model gives a good account of theelastic scattering process.Acknowledgements

This work was supported by the Hun-garian Scientific Research Found: OTKANos.T031833, T032306, the Grant ”Bolyai”from the Hungarian Academy of Sciences, TeTA-19/2001, the Austrian Fonds zur Forderungder wissenschaftlichen Forschung, FWF (Aus-tria), and EU under contract No. HPRI-CT-2001-50036.

a) Max Planck Institute for the Physics of ComplexSystems, Noethnitzer Str. 38, 01187 Dresden,Germany

[1] C. P. Campbell et al. Nucl. Instr. and Meth. inPhys. Res. B143 (1998) 41.

[2] O. Sueko and S. Mori, J. Phys. B: At. Mol. Opt.Phys. 27 (1994) 5083.

[3] P. Aslhley, J. Moxom, G. Lariccia, Phys. Rev. Lett.77 (1996) 1250.

[4] F. A. Gianturco and D. De Fazio, Phys. Rev. A50(1994) 4819.

[5] F. A. Gianturco and R. Melissa, Nucl. Instr. andMeth. in Phys. Res. B143 (1998) 81.

[6] R. H. Garvey, C. H. Jackman, A. E. S. Green,Phys. Rev. A12 (1975) 1144.

[7] A. K. Bhatia and R. J. Drachman, J. Phys. B: At.Mol. Opt. Phys. 27 (1994) 1299.

[8] B. H. Bransden, Atomic Collision Theory,The Benjamin Cummings Publishing Company,Durham, England, (1983).

[9] A. C. Allison, Comput. Phys. Commun. 3 (1972)173.

[10] R. N. Hewitt, C. J. Noble and B. H. Bransden, J.

Phys. B25 (1992) 557.

55