INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS

J. Phys. B: At. Mol. Opt. Phys. 34 (2001) 3751–3761 PII: S0953-4075(01)23652-9

Experimental and theoretical investigations ofsingle-electron capture and loss in He+–Ar collisions

E R Marquina1, A Amaya-Tapia2, R Hernandez-Lamoneda3 andH Martınez2

1 Facultad de Ciencias, UAEM, AP 396-3, Cuernavaca, Mor., Mexico2 Centro de Ciencias Fısicas, UNAM, AP 48-3, 62250 Cuernavaca, Mor., Mexico3 Centro de Investigaciones Quımicas, UAEM, AP396-3, Cuernavaca, Mor., Mexico

E-mail: hm@fis.unam.mx

Received 29 March 2001, in final form 26 June 2001Published 24 September 2001Online at stacks.iop.org/JPhysB/34/3751

AbstractExperimental and theoretical investigation of single-electron capture andadditional experimental studies of single-electron loss cross sections in He+–Arcollisions at impact energies of 1.5–5.0 keV for experimental studies and from10 to 4000 keV for the theoretical calculations are presented. Comparisons aremade with other experimental results, for single-electron capture the presentmeasurements confirm the behaviour observed by previous measurements inthe energy range 1.5–5.0 keV, except with the data of Eisele and Nagy (1977J. Chem. Phys. 66 883–5), and for single-electron loss an extrapolation of thehigh-energy results to low energies shows good agreement with the presentdata, giving the general shape of the cross section curve. Our theoreticalcalculations are in good agreement with the experimental data and reproducethe main features of the cross section energy dependence. We present the mostimportant contributions to the total cross sections from the partial capture crosssection to the He(1s) and He(n = 2) states, with the former as the dominantchannel over the energy region considered.

1. Introduction

Single-electron capture and loss are some of the dominant processes in collisions between ionsand neutral particles over a wide range of energy, therefore these processes play a central role inthe charge and energy balances of different types of plasmas, e.g. aeronomy (Siscoe 1995) andastrophysical plasmas (Kaastra 1998, Uberoi 2000). The single-electron capture and loss crosssections between He+ and Ar atoms have been the subject of numerous extensive experimentalstudies (Stedeford and Hasted 1955, Fedorenko et al 1956, Moran and Conrads 1973, Eiseleand Nagy 1977, Rudd et al 1985, Pivovar et al 1962, Barnett and Stier 1958, Atan et al 1991,De Castro Faria et al 1988, Jones et al 1959, Nikolaev et al 1961, Gilbody et al 1971, DuBois

0953-4075/01/193751+11$30.00 © 2001 IOP Publishing Ltd Printed in the UK 3751

3752 E R Marquina et al

1989, DeHeer et al 1966 for single-electron capture and Pivovar et al 1962, Dimitriev et al1962, Atan et al 1991, De Castro Faria et al 1988, Knudsen et al 1982, Jones et al 1959,Shah and Gilbody 1975, Rudd et al 1985, Shinpaugh et al 1995, Sant’Anna et al 1995 forsingle-electron loss). For single-electron capture there is a strong disagreement between someof them in the energy range 1.5–5.0 keV and for the loss process there are no data in this energyrange. More recently, renewed interest has arisen in energy-transfer reactions between rare-gas metastable atoms and rare-gas ions because of their application to the pumping of rare-gasion lasers, where electron capture processes were found to be important (Tsuji et al 1993).However, no theoretical calculation of the cross sections for charge-exchange collisions fromheavy target atoms by He+ ions is available in the literature to the best of our knowledge. Forsingle-electron loss there is only the calculation at high energies (1000–4000 keV) of Grandeet al (1996). For these reasons it is worthwhile to determine the relevant cross sections bothexperimentally and theoretically.

In this work we present absolute measurements of the differential and total cross sectionsfor single-electron capture and loss in He+ collisions with Ar atoms, defined by

He+ + Ar → He0 + · · · single-electron capture

→ He2+ + · · · single-electron loss.

The energy range covered by the present experimental study is 1.5–5.0 keV. Details of theexperimental arrangement are described in section 2. Also we have calculated single-electroncapture total cross sections by 10–4000 keV He+ ions in Ar by using two-centre atomic orbitalclose-coupling expansions (TCAO). We report formation cross sections to low-lying heliumexcited states. The semiclassical model applied to study the capture from each M subshell ofAr is described in section 3.

2. Experiment

Details of the experimental arrangement have been given previously (Martınez et al 1997,1998), so only a brief description of the experimental set-up will be given here. He+ ions wereformed in an arc discharge source containing He gas (99.99% purity) at ion source pressuresof 0.07–0.09 mTorr. Ions were extracted and accelerated in the energy range 1.5–5.0 keV. TheHe+ beam is passed through an einzel-type lens and directed to a Wien velocity filter in orderto obtain an analysed beam at the desired velocity. Next, the He+ ions are passed betweencylindrical electrostatic deflection plates which were used both to steer the beam and to bendit by 10◦ to prevent photons in the ion source from reaching the detection system. Then, thecollimated He+ beam entered the scattering chamber, which housed a gas target cell where lossand capture phenomena to form He2+ and He0 took place. The gas target cell was a cylinder oflength 2.54 cm and diameter 2.54 cm in which the target gas pressure (typically 0.4 mTorr) wasmeasured with a calibrated MKS capacitance manometer (model 270C). The entrance aperturewas 1 mm in diameter and the exit aperture was 2 mm wide and 6 mm long. This geometrypermitted the measurements of the He0 and He2+, the directions of which make an angle of upto ±7◦ with respect to the incoming beam direction. Path lengths and apertures gave an overallangular resolutions of the system of 0.1◦. All apertures and slits have knife edges. The celltarget was located at the centre of a rotatable, computer-controlled vacuum chamber that movedthe whole detector assembly, which was located 47 cm away from the target cell. A precisionstepping motor ensured high repeatability in the positioning of the chamber over a large seriesof measurements. The detector assembly consisted of a Harrower-type parallel-plate analyserwith a 0.36 mm entrance aperture and two- channel electron multiplier (CEM) attached to itsexit end. The beam entered the uniform electric field of the analyser at an angle of 45◦. The

Experimental and theoretical investigations of single-electron capture and loss in He+–Ar collisions 3753

neutral beam (He0) passed straight through the analyser through a 1 cm orifice on its rear plateand impinged on a CEM so that the neutral counting rate could be measured. Separation ofcharged particles occurred inside the analyser, which was set to detect the He2+ ions with thelateral CEM. The multiplier counting efficiencies for He2+ and for He0 were assumed to be thesame as H+ at the same energy (Crandall et al 1975). A retractable Faraday cup was located33 cm away from the target cell, allowing the measurement of the incoming He+ ion-beamcurrent. A Keithley Instruments Electrometer model 610C was used to measure the beamcurrent entering the Faraday cup. Vacuum base pressures in the system were 2.0 × 10−7 Torrwithout gas in the cell and 1.0 × 10−6 Torr with gas.

Under the thin target conditions used in this experiment, the differential cross sections forthe formation of He0 and He2+ were evaluated from the measured quantities by the expression

dσ

d�= I (θ)

nLI0(1)

where I0 is the number He+ ions incident per second on the target; n is the number of Aratoms per unit volume; L is the length of the scattering chamber and I (θ) is the number ofHe0 (or He2+) particles per unit solid angle per second detected at a laboratory angle θ withrespect to the incident beam direction. The total cross section for the production of the He0

and He2+ particles was obtained by the integration of dσ/d� over all measured angles; thatis

σ = 2π∫ θmax

0

dσ

d�sin(θ) dθ. (2)

For θ > θmax the differential cross sections drop below the experimental detection limit.Extreme care was taken when the absolute differential cross section was measured. The

reported value of the angular distribution was obtained by measuring it with and without gasin the target cell with the same steady beam. Then point-to-point subtraction of both angulardistribution was carried out to eliminate the counting rate due to neutralization of the He+

beam on the slits and those arising from background distributions. The He+ beam intensitywas measured before and after each angular scan. Measurements not agreeing to within 5%were discarded. Angular distributions were measured on both sides of the forward direction toassure they were symmetric. The estimated RMS error is 15%, while the cross sections werereproducible to within 15% from day to day.

Several runs were made at different gas pressures and dσ/d� was determined for eachrun. These were compared in order to estimate the reproducibility of the experimental resultsas well as to determine the limits of the ‘single-collision regime’ since the differential and totalcross sections reported are absolute.

In this paper changes were not observed in the absolute values with respect to the ionsource conditions. Also, no variation in the distributions were detected over a target pressurerange of 0.2–0.6 mTorr.

2.1. Errors

Several sources of errors are present. Possible sources of systematic errors are the following:(a) the effective length of the gas cell (7%); (b) density determination (9%); (c) themeasurements of the target gas pressure (4%); (d) the measurements of the incident ion current(5%); (e) the angular resolution (0.1◦) and (f) the detector calibration (3%).

With the assumption of molecular flow, Toburen et al (1968) derived a simple way toestimate the effective path length, which is longer than the physical length because of gas

3754 E R Marquina et al

streaming from the apertures. This effective increase in path length was estimated to beapproximately 3% and then the effective path length was assumed to be equal to the geometricallength of the cell 2.54 cm. The error of the path length from this assumption was estimatedto be no more than 7%. The largest source of error in the present measurements arose fromthe determination of the Ar density. The target density n is determined from the target gaspressure and temperature. The total uncertainty was estimated to be of the order of 9%. TheHe+ beam intensity was measured before and after each scan. Measurements not agreeing towithin 5% were discarded, and a total uncertainty of 5% was estimated. The CEMs couldbe calibrated in situ with low-intensity He0 and He2+ beams, which could be measured as acurrent in a Faraday cup by a sensitive electrometer. The uncertainty in the detector calibrationwas estimated to be less than 3.5% on each side. Although data were corrected to account formost of these uncertainties, the absolute error of the reported cross sections is believed to beless than ±15%. This estimate represents both random and systematic errors. The relativeaccuracy or reproducibility is found to be better than 15%.

3. The semiclassical close-coupling model

Since we are mainly interested in ion–atom collisions at intermediate energies, we consideredclassical straight lines traversed at constant velocity V = V0 for the nuclear motion, while theTCAO close-coupling expansion was employed in solving the time-dependent Schrodingerequation for the dynamics of one active electron (Kuang and Lin 1996). The interactionpotential is assumed as the sum of two effective potentials centred at each nucleus, each withthe form

V (r) = −Z0

r+ (Z1 + Z2r)

e−Z3r

r(3)

where the parameters Z0, Z1, Z2 and Z3 are determined so that the energy levels of interestcan be well represented by the eigenvalues obtained on diagonalizing the Hamiltonian of anatom (He + e−) or (Ar + e−) with the selected parameters (see table 1). The potentials havethe expected asymptotic behaviour for small and large r for the He and Ar cases and closelyfollows the potentials found by Szydlik and Green (1974).

Within the semiclassical impact parameter approximation, the time-dependentwavefunction �(r, t) was expanded in terms of bound atomic orbitals with the plane-waveelectronic translational factors PHe,Ar(t) at each of the two atomic centres, i.e.

� = PHe(t)∑i

aHei (b, t)�He

i (rHe) + PAr(t)∑i

aAri (b, t)�Ar

i (rAr) (4)

where b is the impact parameter. The atomic states �He,Ari used for the TCAO close-coupling

method were then expanded in terms of a set of even-tempered basis functions

�He,Ari (r) =

∑k

CHe,Arnk Nl(τk)e

−τkr r lϒlm(r) (5)

where i = {n, l,m}, Nl(τk) is a normalization constant, and the exponential parameters τk aretaken to form a geometric sequence τk = αβk , k = 1, 2, . . . , kmax, where the two parameters αand β are determined by reproducing the energy levels of interest. The coupled equations forthe coefficients ai were integrated up to internuclear separations of 100 au where all couplingshad essentially vanished. The calculated orbital energies compared with experimental valuesand the parameters that we used are shown in table 1. The basis used for the calculationsconsists of all n = 1–4 He orbitals at the He centre, as well as all n = 3–4 Ar orbitals at the

Experimental and theoretical investigations of single-electron capture and loss in He+–Ar collisions 3755

Table 1. Potential and wavefunctions parameters with the orbital energies. (Experimental valuesfrom Moore (1949).)

Potential parameters

Z0 Z1 Z2 Z3

He 1.0 −1.0 −0.65 2.7Ar 1.0 −17.0 −3.0 2.15

Wavefunction parameters

He Ar

S P D F S P D Fα 0.05 0.19 0.19 0.19 0.08 0.08 0.03 0.08β 1.7 1.13 1.13 1.13 2.45 3.33 2.4 1.9

Helium orbital energies

1s 2s 2p 3s 3p 3d 4s 4p 4d 4fCalculated −0.902 −0.157 −0.125 −0.064 −0.056 −0.056 −0.034 −0.031 −0.031 −0.031Experimental −0.904 −0.146 −0.124 −0.061 −0.058 −0.056 −0.034 −0.032 −0.031 −0.031

Argon orbital energies

3s 3p 3d 4s 4p 4d 4fCalculated −1.089 −0.570 −0.056 −0.146 −0.087 −0.032 −0.031Experimental −1.067 −0.579 −0.070 −0.155 −0.104 −0.032 −0.031

Ar centre. The initial states considered for the Ar centre were 3s0, 3p0 and 3p1. From theasymptotic ai values one can obtain state-selected probabilities and partial cross sections. Thetotal electron capture cross sections were obtained by summing the cross sections for each Msubshell and multiplying by 2, in order to take into account the number of equivalent targetelectrons available for capture in each subshell (Amaya-Tapia et al 2000).

4. Results and discussion

Measurements of differential cross sections have been performed at laboratory angles of−3.9◦ < θ < +3.9◦ for single-electron capture (−2.6◦ < θ < +2.6◦ for single-electronloss) and collision energies of 1.5 � Elab � 5.0 keV. The measured angular distributions forsingle-electron capture and single-electron loss of He+ in Ar are shown in figures 1 and 2,respectively, as a function of the projectile energy (the estimated error is of the size of thedata point). The cross sections for the loss process are four orders of magnitude lower thanfor the capture process. All curves plotted in figures 1 and 2 show an overall decrease in thedifferential cross section with increasing angle. The rate of decrease is much bigger in thecapture process than in the loss process and in both there is an increase in the differential crosssections of about one order of magnitude between 1.5 and 5.0 keV. The measured differentialcross sections for single-electron capture have been integrated over the observed angular range,and are shown in figure 3. Our cross sections are found to be of the order of magnitude of10−16 cm2. The error bars are a measure of the reproducibility of the data (15%). We haveincluded data from different groups to compare with our results (Stedeford and Hasted 1955,Fedorenko et al 1956, Moran and Conrads 1973, Eisele and Nagy 1977, Rudd et al 1985). Theshape and magnitude, within the experimental error of the present cross sections for single-electron capture, are in good agreement with those measured by Stedeford and Hasted (1955)and Fedorenko et al (1956) and merge smoothly with the data of Rudd et al (1985), but a strong

3756 E R Marquina et al

Figure 1. Measured absolute differential cross sections for single-electron capture of He+ ions inAr.

discrepancy was found with the behaviour of the data of Eisele and Nagy (1977). Above 2 keVthe present cross section agree well with the data of Moran and Conrads (1973) and belowthere is a discrepancy between them.

In figure 4 we plot the total cross sections for single-electron loss obtained by integrationof the angular distributions as a function of the impact energy. The error bars are a measureof the reproducibility of the data (15%). The σ12 cross sections have been underestimatedbecause the H0 signal for our maximum incident current (I0) drops below our experimentaldetection limit for angles higher than 2.6◦. We estimate this contribution to be within 6% ofthe reported value. Our cross sections are found to be of the order of magnitude of 10−21 cm2.Figure 4 shows a comparison between the present data and the results at high energies (Pivovaret al 1962, Dimitriev et al 1962, Atan et al 1991, De Castro Faria et al 1988, Knudsen et al1982, Jones et al 1959, Shah and Gilbody 1975, Rudd et al 1985, DuBois 1989, Shinpaughet al 1995, Sant’Anna et al 1995, Grande et al 1996). An extrapolation of the high-energyresults to low energies shows good agreement with the present data, with the exception of thedata of Shinpaugh et al (1995) which has been described as preliminary results. The shape ofthe total cross section shows a monotonically increasing behaviour as a function of the incidentenergy.

Experimental and theoretical investigations of single-electron capture and loss in He+–Ar collisions 3757

Figure 2. Measured absolute differential cross sections for single-electron loss of He+ ions in Ar.

Our calculated total capture cross sections are shown and compared to a variety ofexperimental results in figure 5. The theoretical calculations are in good agreement withthe experimental data comprising the energy region from 40 to 4000 keV, reproducing themain features of the cross section energy dependence. Best agreement is obtained for energiesaround 200 keV where the model is above the experimental values but within a factor oftwo. For higher energies it is well known that leaving out the continuum channels from thecoupled-channel calculation leads to an overestimation of the capture probabilities and thusthe discrepancy in this region rises to a factor of six. For energies below 40 keV one expectsimportant molecular orbital effects such as adiabatic rearrangement of all electrons as a functionof the time which clearly cannot be reproduced by our simple one-electron potential and ourmodel ceases to be meaningful. These limitations have been discussed in our previous work(Amaya-Tapia et al 2000, 2001).

The most important contributions to the total cross section comes from the partial capturecross section to the He(1s) and He(n = 2) states which are displayed in figure 6. Clearly,capture to the He(1s) state dominates over the energy region considered, but the contributionfrom He(n = 2) is substantial particularly at low energies.

By examining the behaviour of the capture probabilities P(b) as a function of impactparameter b, as is done in figure 7, we can see that the highest probability for an electrontransfer occur between 1.1 and 2.4 au. At small impact parameter we also observed that a

3758 E R Marquina et al

Figure 3. Total cross sections for single-electron capture of He+ ions in Ar.

Figure 4. Total cross sections for single-electron loss of He+ ions in Ar.

smooth behaviour at high energies changes to an oscillatory pattern as the energy decreases.Such oscillatory behaviour is typical of charge transfer reactions. This oscillations at smallvelocity reflect the oscillation of the electron between the target and the projectile when theorbiting velocity of the electron is faster than the collision velocity.

In summary, we have reported experimental measurements of the absolute differential andtotal cross sections for single-electron capture and loss of He+in Ar at impact energies between1.5 and 5.0 keV. The total cross section for single-electron capture is compared with otheravailable measurements while for single-electron loss, an extrapolation of the high-energy

Experimental and theoretical investigations of single-electron capture and loss in He+–Ar collisions 3759

Figure 5. Total cross sections for single-electron capture of He+ ions in Ar.

Figure 6. Calculated M subshell cross sections for single-electron capture.

3760 E R Marquina et al

Figure 7. Total single-electron capture probability as a function of the impact parameter at acollision energy of 100 keV.

results for the electron loss process to low energies show good agreement with the presentdata. We have calculated single-electron capture cross sections for the He+ + Ar collisionsystem, in the impact energy range 10–4000 keV. The resulting total cross sections are in goodagreement with previous experimental data comprising the energy region from 40 to 4000 keV,reproducing the main features of the cross section energy dependence. The most importantcontributions to the total cross sections comes from the partial capture cross sections to theHe(1s) and He(n = 2) states, being the former, the contribution which dominates over theenergy region considered.

Acknowledgments

The authors would like to thank Professor C D Lin for letting us use the close-coupling codedeveloped by his group. We are grateful to F Castillo and PG Reyes for helpful suggestion andcomments, and thank Jose Rangel and A Gonzalez for their technical assistance. This workwas supported by DGAPA IN-100392 and CONACyT 32175-E.

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