The single ionization cross sections for He and H-2 by positron impact have been measured in the first few eV above threshold and found to exhibit a different energy dependence from the corresponding electron results. If the data, between 1 and 3 eV above threshold, are fitted by a power law, exponents of 1.99 +/- 0.19 and 1.70 +/- 0.11 are obtained for He and H-2, respectively. This agrees qualitatively with extensions of the Wannier theory in that the exponent is larger than for electron impact. The quantitative disagreement with the predicted value of 2.65 might indicate that the range of validity of this theory is smaller than expected

Ashley, P

Laricchia, G

Moxom, J

UCL Discovery

VOLUME 77, NUMBER 7 P HY S I CA L REV I EW LE T T ER S 12 AUGUST 19961250Near-Threshold Ionization of He and H2 by Positron ImpactP. Ashley, J. Moxom, and G. LaricchiaDepartment of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom(Received 6 November 1995)The single ionization cross sections for He and H2 by positron impact have been measured in thefirst few eV above threshold and found to exhibit a different energy dependence from the correspondingelectron results. If the data, between 1 and 3 eV above threshold, are fitted by a power law, exponentsof 1.99 6 0.19 and 1.70 6 0.11 are obtained for He and H2, respectively. This agrees qualitativelywith extensions of the Wannier theory in that the exponent is larger than for electron impact. Thequantitative disagreement with the predicted value of 2.65 might indicate that the range of validity ofthis theory is smaller than expected. [S0031-9007(96)00865-4]PACS numbers: 34.80.DpThe study of the near-threshold behavior of two-electron escape from a positive ion continues to attractexperimental and theoretical interest [1]. Some recentresults [2,3] have cast doubts on the validity of the “ridgestate” characterization of the correlated e2 pair. In thismodel the e2 are approximately equidistant from theion and escape from it almost collinearly and with auniform energy distribution, as described by Wannier [4].Theoretically, the problem has also been considered inthe case of positron impact ionization [5–12]. In thiscase, the two outgoing particles are likely to be closertogether than for e2 impact ionization, and the theoreticaldescription of the process is expected to be very sensitiveto the details of the approximation employed. Thisprocess is also interesting because of the absence of theexchange interaction and the possibility of the formationof the electron-positron bound-state, positronium (Ps),with a threshold energy 6.8 eV below the threshold fordirect ionization sEid. Experimental data had suggestedthat positron and electron impact might result in the samenear-threshold energy dependence of the single ionizationcross sections [13,14]. However, the accuracy of thesedata was rather poor. Experimental investigations ofnear-threshold direct ionization by positron impact arehindered by the comparatively low beam intensities andpoor energy resolutions. Ps formation, which dominatesion production near Ei , may introduce an additionalcomplication. In the present work, the cross sectionsfor single direct ionization by positron impact have beeninvestigated in detail within the first few eV abovethreshold for the first time and, in contrast to previoussurmises, significant differences are observed from theelectron impact case. The measurements have been madewith an energy resolution of around 0.5 eV and themean beam energy has been calibrated by determiningthe thresholds for Ps formation in different gases. Thebackground contributions to the ion signal, arising, forexample, from Ps formation, have been measured directlyand subtracted from the data.By considering collision processes which result in twoparticles in the final state, Wigner [15] showed that the0031-9007y96y77(7)y1250(4)$10.00near-threshold energy dependence of the associated crosssection is dominated by the long range interaction of theproduct particles. Wannier [4] extended these ideas to thecase of three quasistationary charged particles, as mightarise near the threshold for electron impact ionization ordouble photodetachment. He argued that for impact ener-gies sEd just above Ei , the energy dependence of the crosssection for double e2 escape from a singly charged posi-tive ion is purely dependent on the asymptotic configu-ration of the final state and, using classical arguments,derived the following expression for the cross sectionsQ2i d for single ionization by e2 impact of a neutral atom:Q2i ~ sE0dn, (1)where E0 ­ E 2 Ei and n ­ 1.127.Considerable experimental and theoretical effort in thestudy of this phenomenon has ensued [16]. Much ex-perimental support, e.g. [17,18], has been found for thepower law expressed by Eq. (1) which has also been rede-rived semiclassically and quantum mechanically [19–21].However, recent experiments with spin-tagged electronsincident on atomic hydrogen [22] and a reexamination ofphotodetachment cross sections [23] have produced evi-dence of structure in Q2i which is inconsistent with theWannier theory. An alternative model has been proposedby Temkin [9–11]. Unlike in the Wannier description,here the electrons are not equidistant from the ion and theescape is determined, at threshold, by events in which theinner electron sees the charge of the ion directly, whilethe other sees the Coulomb dipole (CD) potential pro-duced by the ion and the inner electron. Both theWannier-type and CD descriptions have been applied in the case ofpositron and electron projectiles and these and other theo-retical results are given in Table I.In the present work, a 100 mCi 58Co b1 emitter wasused in conjunction with a W-mesh moderator and aretarding field anlayzer to produce a beam of around 5 3103 e1 s21 with a measured longitudinal energy spread,in the magnetic field used to confine the beam, of 0.5 eVFWHM. This energy spread is an upper limit on thetrue energy spread due to the angular divergence of the© 1996 The American Physical SocietyVOLUME 77, NUMBER 7 P HY S I CA L REV I EW LE T T ER S 12 AUGUST 1996TABLE I. Some of the available theoretical results for thenear-threshold energy dependence of the e6 impact ionizationcross sections. C and a are quantities related to the dipolemoment created by the ion and the ejected electron; m is aconstant of integration. These quantities are discussed in detailin [10].Theory PredictionWannier [4] Q2i sE0d ~ sE0d1.127Peterkop [19,20]Rau [21]Klar [5,6] Q1i sE0d ~ sE0d2.651Temkin [9–11] Q6i sE0d ~ E0slnE0d223 f1 1 C sinsa lnE0 1 mdgGeltman [12] Q2i sE0d ~ E0Q1i sE0d ~RE00 expf2ps2yxd1y2g dxbeam and instrumental resolution. The apparatus in andaround the interaction region is presented schematicallyin Fig. 1. The e1 beam was crossed with a gas jetand a pulsed electric field was used to extract the ionsfrom the interaction region. The ion-extraction fieldwas triggered by the detection of e1 at the end ofthe flight path and was pulsed on, therefore, after theassociated collisions. In this way, perturbations during acollision were minimized. Ions of the desired charge-to-mass ratio were selected by measuring their flight times.The mean beam energy sEd was augmented in 0.5 eVsteps by means of a ramp generator which supplied, insynchronism, the advance pulse to a multichannel scaler(MCS) storing the number of positron-ion coincidences.If this number is divided, after background subtraction, bythe incident beam intensity (also measured versus E), anion yield is obtained as a function of the incident energy.This yield is directly proportional to the single ionizationcross section by e1 impact sQ1i d.An investigation of the near-threshold behavior of Q1iin this manner requires (i) the accurate determination ofthe background on the ion coincidence signal, (ii) the ef-ficiencies for ion detection and scattered e1 transport tobe energy independent, and (iii) a careful calibration ofthe projectile incident energy. By measuring ion-e1 coin-cidences, ions resulting from Ps formation (the dominantionization process near Ei) are largely undetected. How-ever, random coincidences between ions and uncorrelatede1 result in a background which can be measured by pre-venting the e1 which have produced an ion (and havehence lost Ei which is 24.58 and 15.45 eV for He and H2,respectively) from reaching the detector. This was doneby applying a retarding potential sVretd to the grids g1 andg2, just sufficient to prevent all e1 that have created an ionfrom reaching the MCP. These grids were grounded formeasurements of the gross signal. A slight disparity be-tween e1 count rates for each retarder state arose from thefailure to detect those e1 which are scattered (either elas-tically or after target excitation) at angles such that theirlongitudinal velocity is insufficient to overcome the poten-tial barrier set by Vret. Since the background was propor-tional to the ion extractor pulse rate, this disparity led to aslight underestimate of the true background and was cor-rected by normalizing the background to the ratio betweenthe pulse rates for each retarder state. Elastically scatterede1 repelled by Vret could conceivably traverse the interac-tion region a second time and create an ion, leading to anoverestimate of the background. However, even assumingisotropic elastic scattering, the probability of such an eventis estimated to be ,0.1%. Grids g1yg2 were switchedbetween 0 V and Vret states at the end of each pass of theMCS. Thus signal and background were measured alter-nately, reducing the effects of instrumental drift and sourcedecay, hence allowing long data acquisition times.The 26 mm diameter MCP was large enough to ensurethat, for the impact energies studied here, all scatterede1 could impinge on its active area so that the scatterede1 detection efficiency was not dependent on energy inthe range of interest here. An energy independent iondetection efficiency relies on detecting all e1 before anion can drift out of the volume from which it can beextracted and detected. By definition, in near-thresholdionization, the e1 of interest survive with little kineticenergy and may also be backscattered. With the aid ofcomputer simulations of the e1 trajectories in the system,a weak electrostatic field penetrating the interaction regionwas devised to accelerate the quasistationary e1 whileintroducing a negligible perturbation to the incident beamenergy [24]. This field was generated by the retarding fieldanalyzer and the e1 accelerator tube R2, shown in Fig. 1.Considerable effort has been expended in trying toverify the effect of such a penetration field experimentally.The ion yield was measured as a function of voltage onR2 and it was found that, at an incident energy 3 eVabove Ei , applying 2200 and 2300 V to R2 resulted ina 2.0 6 1.0 factor increase in the yield over the field-freecase, while the single ion rates remained independent ofthis voltage. With higher potentials applied to R2, beamfocusing effects were observed and so measurements wereperformed with R2 at 2300 V .The incident e1 energy was determined by measuringthe onset of the positronium formation cross section sQPsdfor a selection of gases by randomly triggering the ionextractor with a pulse generator. Below Ei , all ionizationis the result of Ps formation and so, in this case, theion yield is proportional to QPs. It has been shown [25]FIG. 1. A schematic diagram of the apparatus around theinteraction region (not to scale).1251VOLUME 77, NUMBER 7 P HY S I CA L REV I EW LE T T ER S 12 AUGUST 1996that for Ne, Ar, Kr, and Xe, QPs has a predominantly s-wave energy dependence for a few eV above threshold.Therefore the Ps yields for Ar, Kr, and Xe determinedwith the present system have been fitted by this form,using a shift on the apparent incident energy, arisingfrom the e1 work function of the moderator and contactpotential effects, as one of the fitting parameters. Thisallowed the determination of E to within 0.1 eV.The present values of Q1i for He and H2 are shownin Figs. 2(a) and 2(b), respectively, along with thoseobtained by other workers [13,14,26,27]. Also shown arethe values of Q2i for theses gases [28,29]. The ion yieldswere converted into absolute cross sections using a targetdependent normalization constant, obtained by fitting ionyields to Q2i [30] over the range of energies from 600 to1000 eV. At these energies the ion yields were found tohave almost the same energy dependencies as Q2i , and itwas assumed that the cross sections had merged.For He the present values of Q1i are, at all energiespresented here, smaller than those obtained by KnudsenFIG. 2. (a) Q1i for He: filled circles, the present data; opencircles [13]; open squares [26], open upward pointing triangles[14]; open downward pointing triangles [30]. Q2i for He [28],solid line. (b) Q1i for H2: filled circles, the present data; opencircles [13]; open squares [26], open triangles [31]. Q2i for H2[27], solid line.1252et al. [13] (e.g., by 25% at 32 eV), Fromme et al. [26](by 50% at 31 eV), and Sueoka et al. [14] (by 70% at30.6 eV), but are larger than those obtained by Jacobsenet al. [30] (by around 27% at 30 eV). For H2, the presentdata are in fair accord with those of Refs. [13,14] above20 eV but, as in the case of He, approach zero fasterwith decreasing impact energy. The present results for H2are, however, around 50% greater than those obtained byJacobsen et al. [31] at 28.2 eV. In both gases the presentvalues of Q1i are significantly smaller than Q2i at lowenergies where Q1i and Q2i have significantly differentenergy dependencies. This may be due to the importanceof Ps formation in this energy range. In the case ofinner shell ionization [32], differences observed in themagnitude of near-threshold cross sections for e2 and e1impact have been attributed primarily to the accelerationor deceleration effects on each projectile in the Coulombfield of the nucleus.In Figs. 3(a) and 3(b) the cross sections are plottedagainst E0 on logarithmic axes. The data have beenFIG. 3 (a) The present data for He, filled circles. Leastsquares fits to the data (see text) with n ­ 1.99, solid line;n ­ 2.27, long dashed line; and n ­ 2.65, short dashed line.Q2i [17], solid squares. (b) The present data for H2, filledcircles. Least squares fits to the data (see text) with n ­ 1.70,solid line; n ­ 2.65, dashed line. Q2i [27], solid squares.VOLUME 77, NUMBER 7 P HY S I CA L REV I EW LE T T ER S 12 AUGUST 1996least squares fitted by Eq. (1) over two energy ranges:(i) from 1 , E0 , 3 eV, the near threshold region, wherethe Wannier theory is expected to be valid [5]; and(ii) for E0 . 3 eV, where the data may be qualitativelycompared with the predictions of a CTMC calculation[33] for H. The points below 1 eV were not used inthe near threshold fit because of the effects of the finitebeam energy spread on the measured energy dependenceof Q1i . To investigate the possibility of a residualbackground on the data, the mean value of the data belowthreshold was calculated and found to be zero withinstatistical uncertainties. By performing a least squaresfit to the near threshold data, the values obtained for nin Eq. (1) are 1.99 6 0.19 and 1.70 6 0.11 for He andH2, respectively. The uncertainties are those arising fromthe fitting procedure and the error in the beam energycalibration. Within the errors these values are the same,and qualitatively agree with the extension of the Wanniertheory to e1 impact [5–8] in that n is larger than fore2, but quantitatively disagree with the expected valueof 2.65. The discrepancy may indicate that the range ofvalidity of Eq. (1) is smaller than expected.Marchand et al. [17] found that for single ionizationby e2 impact the exponent in Eq. (1) decreased from1.16 6 0.03 for 0.2 , E0 , 0.8 eV to 1.02 if the fit wasextended up to E0 ­ 12 eV. Physically, this is believedto arise from a weakening of the e2-e2 correlation in thefinal state. When the fit to the present data is performedfor higher energies, the exponent values obtained are2.27 6 0.08 and 1.71 6 0.03 for He and H2, respectively.The value obtained for H2 is the same as for the nearthreshold fit, however, for He the value is slightly higher.A CTMC calculation [33] predicts that Q1i follows apower law energy dependence up to 9 eV above thresholdand the fact that the data can be fitted by a power lawreasonably well in a similar energy range is in qualitativeagreement with this calculation, although the value ofn was expected to be 3–4, for single ionization of H0.No comparison is made here with the Coulomb-dipoletheory [9–11] since its range of validity is expected tobe confined to a much smaller range of energies sE0 ,0.1 eVd [11] than investigated in the present work.In conclusion, the cross sections for direct ionizationof He and H2 by e1 impact have been measured inthe first few eV above threshold for the first time.The results show that Q1i increases from threshold lessrapidly than Q2i and reveal a difference in the energydependencies of Q2i and Q1i . The results contradictprevious tentative experimental conclusions [13,14] thatthe two cross sections may exhibit a similar energydependence close to threshold and qualitatively agree withWannier-type theories which predict a larger exponent inthe case of e1. Work is continuing to probe in greaterdetail the first few eV above threshold.The authors wish to thank M. Charlton, W. Raith,and J.M. Rost for useful discussions, I. Rangue, E. J. C.Oldfield, and P. Aggerholm for technical assistance, andthe Engineering and Physical Sciences Research Councilfor support under Grant No. GR/K56322. G. L. alsowishes to thank the Nuffield Foundation for the award ofa Science Research Fellowship.[1] See, e.g., G. Dawber et al., J. Phys. B 28, L271 (1995);D. S. F. Crothers, J. Phys. B 19, 463 (1986); J. S. Briggs,in The Physics of Electronic and Atomic Collisions (AIP,New York, 1993), p. 221, and references therein.[2] J. R. Friedman et al., Phys. Rev. A 46, 652 (1992); X. Q.Gou and M. S. Lubell, J. Phys. B 26, 1221 (1993).[3] A. Huetz et al., J. Phys. B 27, L13 (1994).[4] G. H. Wannier, Phys. Rev. 90, 817 (1953).[5] H. Klar, J. Phys. B 14, 4165 (1981).[6] H. Klar, in Electronic and Atomic Collisions, editedby J. Eichler, I. V. Hertel, and N. Stolterfoht (Elsevier,Amsterdam, 1984), p. 767.[7] P. Grujic, J. Phys. B 15, 1913 (1994).[8] J.M. Rost and E. J. Heller, Phys. Rev. A 49, R4289(1994).[9] A. Temkin, J. Phys. B 15, L301 (1982).[10] A. Temkin, Phys. Rev. Lett. 49, 365 (1982).[11] A. Temkin, Phys. Rev. A 30, 2737 (1984).[12] S. Geltman, J. Phys. B 16, L528 (1983).[13] H. Knudsen et al., J. Phys. B 23, 3955 (1990).[14] O. Sueoka, B. Jin, and A. Hamada, Appl. Surf. Sci. 85, 59(1995).[15] E. P. Wigner, Phys. Rev. 73, 1002 (1948).[16] See e.g., F. H. Read, in Electron Impact Ionization, editedby T.D. Märk and G.H. Dunn (Springer-Verlag, Wien,1985), p. 42, and references therein.[17] P. Marchand, C. Paquet, and P. Marmet, Phys. Rev. 180,123 (1969).[18] S. Cvejanovic and F. Read, J. Phys. B 7, 1841 (1974);J. B. Donahue et al., Phys. Rev. Lett. 48, 1538 (1982);R. Hippler et al., J. Phys. B 16, L617 (1983).[19] R. Peterkop, J. Phys. B 4, 513 (1971).[20] R. Peterkop, in Theory of Ionization of Atoms by ElectronImpact, edited by D.G. Hummer (Colorado UniversityPress, Boulder, 1977).[21] A. R. P. Rau, Phys. Rev. A 4, 207 (1971).[22] D.M. Crowe et al., J. Phys. B 23, L325 (1990).[23] J. R. Friedman et al., Phys. Rev. A 46, 652 (1992).[24] P. Ashley et al., Hyperfine Interact. 89, 389 (1994).[25] J. Moxom et al., Phys. Rev. A 50, 3195 (1994).[26] D. Fromme et al., Phys. Rev. Lett. 57, 3031 (1986).[27] F.M. Jacobsen et al., J. Phys. B 28, 4691 (1995).[28] D. Rapp and P. Englander-Golden, J. Chem. Phys. 43,1464 (1965).[29] E. Krishnakumar and S. K. Srivastava, J. Phys. B 21, 1055(1988).[30] J. Moxom, P. Ashley, and G. Laricchia, Can. J. Phys. (tobe published).[31] F.M. Jacobsen et al., J. Phys. B 28, 4675 (1995).[32] H. Schneider et al., Phys. Rev. Lett. 71, 2707 (1993);W.N. Lennard et al., Phys. Rev. Lett. 61, 2428 (1988).[33] A. E. Wetmore and R. E. Olson, Phys. Rev. A 34, 2822(1986).1253

Near-threshold ionization of He and H-2 by positron impact

P. Ashley

J. Moxom

G. Laricchia

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Physical Review Letters

Near-Threshold Ionization of He and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>by Positron Impact

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Near-threshold ionization of He and H-2 by positron impact

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