ELECTRON CAPTURE AND IONIZATION IN ION-ION COLLISIONS

(1)

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ELECTRON CAPTURE AND IONIZATION IN

ION-ION COLLISIONS

E. Salzborn

To cite this version:

(2)

JOURNAL DE PHYSIQUE

Colloque C1, suppl6ment au nol, Tome 50, janvier 1989

ELECTRON CAPTURE AND IONIZATION IN ION-ION COLLISIONS

E. SALZBORN

Institut fiir Kernphysik, Strahlenzentrum, Universitdt Giessen. 0-6300 Giessen, F.R.G.

RCsumC

-

Nous prgsentons une revue des 6tudes rgcentes en faisceaux croisCs des phCnombnes de capture et d'ionisation dans des collisions ion-ion. Nous nous intgressons plus particuliGrement aux systbmes les

+

plus simples de collisions H+

+

He et He

+

He

,

mettant enjeu respec- tivement un ou deux electrons. Dans la mesure des donnCes disponibles, nous discutons aussi les collisions impliguant des ions multicharg6s.

Abstract

-

A report is given of recent crossed-beams studies of electron capture and ionization in ion-ion collisions. Special attention is

+

drawn to the simplest collision systems H

+

He and ~ e +

+

He involving only one and two electrons, respectively. Collisions involving multiply-charged ions are discussed, where they are available.

1

-

INTRODUCTION

Compared to ion-atom collisions, the study of ion-ion collisions is a relatively young field of physics. Experimental techniques based on the use of crossed or merged ion beams have been successfully developed in the past two decades, however, only since 1977 have reliable experimental data on electron capture and ionization in ion-ion collisions become available.

Information about ion-ion collisions is needed for astrophysical applications and an understanding of laboratory discharges. In recent years, investigations of ion-ion collision processes have been strongly stimulated by research on thermonuclear fusion using either inertial or magnetic confine- ment.

For example, for the use of high current heavy ion beams, as proposed for ig- niting a DT pellet, a detailed knowledge of possible sources of beam losses is of vital interest. One major loss mechanism is due to charge changing interactions between ions within the beam bunches in the storage rings. Such ion-ion collisions occur at low relative energies of less than 1 keV/u due to the longitudinal and transverse energy spread of the beam. In the heavy ion

+

fusion scenario HIBALL I1 /1/ intense beams of 10 GeV Bi ions are proposed as the ignitor. In order to assess the beam intensity losses the cross sections both for

+

electron capture: ~ i +

+

Bi + B ~ O

+

Bi 2

+

and for

+

ionization: Bi+

+

Bi -+ Bi

+

~ i

+

~e +

have to be known as a function of collision energy. It should be noted that, for instance, a 1% beam intensity loss in the HIBALL I1 storage rings gives rise to a peak power deposition of 1.25 MW to the walls.

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Cl-208 JOURNAL. DE PHYSIQUE

In magnetic fusion, on the other hand, there is presently much interest in plasma neutralizers /2/ which offer considerably higher neutralization ef- ficie~icies than gas targets (85% vs 60%) for conversion of multi-megawatt H- beams into neutral HO beams needed for auxiliary heating of next generation

fusiori plasmas. Further, the use of a plasma neutralizer based on multiply- charged ions has the advantage of a substantially reduced optimum line density /3/ due to the larger electron removal cross sections. Howeve'r, design studies of plasma neutralizers suffer from the lack of experimental cross sections for the single electron removal

and the double electron removal reaction

The latter reaction directly degrades the efficiency of a plasma neutralizer. There are numerous further practical applications, but ion-ion collisions are particularly important also because they test collision theory at the most fundamental level, e.g. in collisions between protons and the hydrogenic ions

+ 2+ 3+

He , Li , Be ,

... .

This short report will be confined almost exclusively to very recent experiments with intersecting beams. Special attention is given to the simplest

+

collision systems H* + H+ and He + He involving only one and two electrons, respectively. Collisions involving multiply-charged ions are also included in this article, where they are available.

For partly more comprehensive reviews of ion-ion collisions the reader is referred to valuable articles by Gilbody /4/, Dolder /5-7/, Dolder and Peart / 8 , 9 / , and Dunn /lo/.

2

-

EXPERIMENTAL METHODS

The experimental data discussed here have been obtained by means of the intersecting-beam technique. The general features of this method have been excell.ently reviewed by Brouillard and Claeys /11/ and only an outline of the experi.men-tal approach will be given.

Two. well-collimated and momentum-analyzed ion beams of variable energies are arranged to intersect at some angle in an ultra-high vacuum region. The energy transferred in electron capture or ionization reactions is much less than the beam energies, so the reaction products remain within their parent beams until they are separated by electric or magnetic fields and detected. Although this method, in principle, appears to be straightforward, inherent difficulties arise from the small target thickness provided by the ion beams. Even at ultra-high vacuum (10-lo mbar) in the interaction region the residual gas density exceeds the ion densities within the beams, which are limited by space charge effects. These conditions not only result in 'comparatively low signal. count rates (typically between 1 and 100 s-'1, but also in poor signal-to-background ratios (typically 1 0 - ~ t o lo-')

.

Theref ore, signal-recovery techniques have to be employed in order to separate required signal from background events which arise from the interaction of both beams with residual gas particles. Furthermore, the small fractions of ion-ion reaction products have to be separated from their parent ion beams of much higher -11 intensities. Here, typically, the intensity ratios are of the order of 10

(4)

are required to ensure that slit scattered or secondary particles cannot reach the single-particle detectors for the reaction products. Therefore, major concern in designing intersecting-beam experiments has to be directed to the problem of how to minimize the background count rates.

In spite of these difficulties and the need for complex experimental arrange- ments, intersecting-beam techniques have been successfully developed in a few laboratories. Accurate data have been obtained for interaction energies rang- ing from 0.1 eV to several hundreds of keV. The attainable energies and the energy resolution depend greatly upon the angle 8 chosen for beam intersection. The beams may cross perpendicularly (8=90°: Belfast), or obliquely (8=8.5O, 160°: Newcastle; 8=45O: Giessen), or they may be merged (8=0°: Louvain-la- Neuve). Merged beams provide access to very low center-of-mass energies and offer enhanced energy resolution even for conveniently energetic beams of keV energies. This can be readily seen from the equation

where Ecm is the interaction energy in the center-of-mass frame and MI, _El

and M2, E2 denote the masses and laboratory energies, respectively, of the ions of the two beams. Inclined beams are usually easier to set up than merged beams. Moreover, measurements of the spatial overlap of the beams become less elaborate since the collision geometry is well defined.

It can be easily seen from eq. ( 5 ) that a given center-of-mass energy E

cm can be obtained with various combinations of beam laboratory energies El and E2. Verification that the cross section depends only upon Ecm and not upon El and E provides a very important experimental consistency check.

2

In a crossed-beams configuration the cross section is obtained from the relation

e2

s

vlv2 sin 8

a = - F (6)

1112 (v:+v;- 2v1v2 cos 8) 1/2

where S denotes the signal count rate after allowing for the measured efficiency of detection. _11,12, vl and v2 are the currents and velocities of the

-

respective beams, and e is the elementary charge. The form factor F takes account of the spatial overlap of the non-uniform current densities within the beams and is given by

where i,(z) and i,(z) are the respective beam currents flowing in elements of

I *

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C1-210 JOURNAL DE PHYSIQUE

Fig.1 illustrates the essential features of the crossed-beams apparatus used

+

in Giessen /12/. A slow beam A (5-20 keV) and a fast beam B+ or H- (5-150 keV) are arranged to intersect at 8 = 45O in an ultra-high vacuum region with a base pressure of about 2.10-l1 mbar. In order to reduce the background, both ions beams (which are collimated to about 2 mm x 2 mm) are cleaned, shortly before intersection, by electrostatic deflectors El, E2 from particles in other charge states which result from charge-changing collisions in the residual gas. The charge states of the collision products formed in both beams are analyzed a short distance downstream from the interaction region.

+

An electrostatic deflector E3 separates B0 atoms from the parent B ion beam. In case of an H- ion beam both reaction products H0 and H+ are identified.

+

A2+ ions formed in the slower beam are separated from the parent A beam by a two-stage electrostatic analyzer system consisting of an ion-optical mirror E4 followed by a 180° spherical analyzer E5. The product A0 atoms pass undeflected through the mirror E4. The parent ion beams are recorded by biased Faraday cups Fl,F2, whilst the reaction products are counted by channeltron- based single-particle detectors *DI,D2,D3. In order to avoid degradation of the ultra-high vacuum in the intersection region, the beam dumps F1, F2 are installed in a separately pumped vacuum region.

With this experimental arrangement the following processes have been studied: Electron capture: A+

+

B+ -, 112+

+

go (8

Ionization: A+

+

B+ -+ A ~ +

+

B+

+

e (9) Mutual neutralization: H+ + H- -P H0

+

HO (10)

+

0

+

Transfer ionization: H~ + H; -, H~ + H~ + e (11)

Because of lack of space the latter two reactions are not discussed in this artic:le.

L+(HI

(6)

Experimentally, the cross section oi for ionization (9) cannot be obtained 2

+

directly. The measurements only provide cross sections o(A for the produc- 2 +

tion of A ions from the combined processes of electron capture (8) and ionization (9). With a knowledge of the cross section a for electron cap-

C

ture, the ionization cross section is obtained from the difference Oi = a (li2+i -aC.

Of all the quantities in eq. (6) the true signal count rate S is the most difficult to determine since it is completely masked by background counts which are normally some orders of magnitude more frequent. In order to dis- criminate signal from background events a coincidence technique is employed in measuring the reactions ( 8 1 , (10) and (11). Since the reaction products are formed simultaneously and since their flight times from the beam intersection to the detectors are fixed, the corresponding output pulses of the two ion/atom-detectors show a fixed time delay in case of true signals, whereas there is no time correlation between pulses from'background events. Thus, in a time spectrum the signals resulting from ion-ion collisions form a well defined peak on top of a flat background due to random coincidences

(Fig.2).

0

0 200 400 600 800 1000

CHANNEL NUMBER

2+

Fig.2

-

Coincidence spectrum of H0 and He particles from the reaction

+

0 2+

H+ + He + H + He measured at Ecm = 40.3 keV /la/. 2 +

In measuring the A formation from combined reactions (8) and (9) only detector D2 of Fig.1 is operated. In this case a beam modulation technique is employed for signal recovery. Both ion beams are chopped by fast electrostatic deflection and the actual time spectrum of thq A2+ detector counts is recorded. Each pulse cycle of 2.46 ms length, which is repeated at 407 Hz, con- sists of four sections. In section I (see Fig. 3 ) both beams are switched off and the A ~ + detector records only background events which are not caused by the ion beams. In .section I1 and I11 only the slow and fast ion beams, respectively, are switched on. The detector records additional background due to the pertinent beams. In section IV, finally, both ion beams are on and, in addition to all the background contributions, the signal is recorded. Thus,

2

+

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JOURNAL DE PHYSIQUE

2+

Fig.3

-

Time spectrum of the Hea detector count rate from the reaction

1 2

+

Het

+

Heb +

+

. .

.

at ECM = 54.7 keV, with pulsed ion beams /13/.

a ioooo 6000 _I W Z Z a 6000 1 U

.

E'

z 4000 3 0 U 2000 0 .

I) COLtLISIONS INVOLVING PROTONS

+

Collisions between H and He ions represent the simplest ion-ion collision

system to study. Since only a single electron is involved, the reactions

100 200 CHANNEL NUMBER

- _I _I

+-

I - - n +-III-+ IV-

HO + He 2

+

f l electron capture (ac (12a)

HS'

+

He 2 + H+

+

He

+

e ionization (oil (12b) . -

-

provide the ideal testing ground for theories of charge-changing collisions between ions. As the wavefunctions are known exactly, the accuracy of the calculated cross sections directly reflects the quality of the approximations used in the different theoretical models.

-t

-Measurements of oC and =(He2+) have been reported by the groups in Belfast /14-17/, Newcastle/l8,19/, and Giessen /12,20/. Fig.4 illustrates that the

+

cross sections o for electron capture in H _C + He collisions measured by the

3 grou.ps are now in excellent agreement.

I

,

0

In Fig.5 the experimental data for oc is represented by a solid line and compared with theoretical predictions. In particular, calculations based on coupled-state approaches are in excellent agreement with experiment. Basis sets of atomic wavefunctions have been used by Fritsch and Lin /21/, Winter /22,23/ and Bransden et a1/24/. These calculations are all in very good accord with experiment over the entire energy range. In the lower energy range the data are also well reproduced by the molecular-state results of Winter et a1 /25/, Kimura and Thorson /26/ (not shown), and Errea et a1 /27/. The 'one- and-a-half-center' expansion by Reading et a1 /28/ is in agreement with experiment above the cross section maximum. Whereas the results of the Coulomb-Born approximation by Sinha and Sil /29/ systematically underestimate the cross section, the predictions of the continuum-distorted-wave approxima-

(8)

vt,l C108 crn I s I 2 3 4 5 6

10 50 100 E c m CkeVl

Fig.4

-

Cross sections a for electron capture (into all bound HO states) in

C

H+

+

~ e + collisions: o Peart et a1 /19/; l Rinn et a1 /12/; v Watts et a1

/17/, this data revises earlier data (not shown) by Angel et a1 /16/. The error bars represent the 90% (o,e) and 68% (v), respectively, confidence limit of statistical error.

v,,~ CIOa

cmlsl

2 3 4 5 6 30 20 10 5 2 1 10 50 100

E,

,

CkeVl

+

Fig.5

-

Cross sections ac for electron capture in H

+

He collisions:

-combined experimental data of Fig.4; Calculations: l Fritsch and Lin /21/;

v Winter / 2 2 / ; 8 Winter /23/; o Bransden et a1 /24/; O Winter et a1 /25/;

v Errea et a1 /27/; n Reading et a1 /28/;

+

Sinha and Sil /29/; A ~elkic! et

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Cl-214 JOURNAL DE PHYSIQUE

calculations by Olson /31/, overestimate the measured cross section. More recent calculations by Datta et a1 /32/ in the framework of the continuum- intermediate-state approximation lie above the measurements for their lowest energy of 50 keV. However, the discrepancy seems to become smaller with increasing collision energy.

In conclusion, for electron capture in the simplest ion-ion collision system,

+

H+

+

He , there is excellent accord between experimental data from 3 groups and a number of theoretical approaches.

+

Ionization in H + He collisions is much less understood than electron capture, Experimentally, the cross sections ai for ionization are obtained from

2 + 2

+

the difference ai = a (He )-aC, where a (He ) is the total cross section for ~ e formation from combined reactions (12a) and (12b). Fig. 6 illustrates ~ +

2 +

this procedure for a(He ) /20/ and ac /12/ measurements by Rinn et al. It is 2+

pleasing to note that the u(He and ac data,although involving completely different methods of signal recovery in the experiment (beam-pulsing technique and coincidence technique, respectively), merge towards lower energies where ionization decreases. As a result, however, the error bars on the oi values obtained by subtraction become increasingly larger.

+

2 +

(10)

In Fig.7 the experimental cross sections o obtained by the groups in Belfast i

/15,17/, Newcastle /19/ and Giessen /20/ are compared with theoretical predictions. First, the agreement among the experimental results is not as excellent as for the oc data. Though within combined error bars at the lower impact energies, the results from Giessen are somewhat larger in absolute magnitude than the data from Belfast and Newcastle. This must be due to

2

+

enhanced cross sections a(He 1 , since the experimental ac data all agree very well.

Three theoretical predictions clearly overestimate the ionization cross section at lower impact energies. These are the continuum distorted-wave approximation (CDW) by

elk id

/33/, a modification of this (MCDW) by Miraglia /34/ and Salin's /35/ approximation (S). The 'one-and-a-half-center' expansion (POHCE) by Reading et a1 /28/ predicts a rather weak energy dependence overestimating the cross section at both low and high energies. The large experimental uncertainties do not permit an accurate assessment of the remain- ing theoretical approaches. These are a calculation by Bates and Griffing /36/ based on the first-order Born approximation (Bl), a classical-trajectory Monte-Carlo calculation (open circles) by Olson /31/, a close-coupling calculation (full circles) by Fritsch and Lin /39/ with basis sets of 20-23 pseudostates at each center, two versions of a multiple-scattering approximation (MSI and MSF) by Garibotti and Miraglia /37/ and Miraglia /38/, respectively, and a very recent elaborate triple-center calculation (crosses) by Winter /23/.

+

In conclusion, compared to electron capture in H

+

He collisions, ionization in this fundamental system is much less understood, both experimentally and theoretically. V , , (10~crnls) 2 3 5 7 9

+

Fig.7: Cross sections oi for ionization in H+

+

He collisions. Experimental

-

results: N

-

smoothed measurements by Peart et a1 /19/; v measurements by Watts et a1 /17/ which revise earlier data (not shown) by Angel et a1 /16/; A o(Iie2+) data by Angel et a1 /15/ at energies whkre a,

=

a(Iie2+); I measure-

L

ments with fit curve of Fig. 6 by Rinn et a1 /20/. Theoretical results: CDW ~elki; /33/; MCDW Miraglia /34/; S Salin /35/; B1 Bates and Griffing /36/; POHCE Reading et a1 /28/; MSI Garibotti and Miraglia /37/; MSF Miraglia /38/;

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C1-216 JOURNAL DE PHYSIQUE

In an extension to reactions (12a,b), electron capture and ionization in col- 2+ lisions between protons and the least multiply-charged hydrogenic ions Li ,

3

+

Be , B4+, and

c5+

have been theoretically studied by Winter /40/ within a coupled

-

Sturmian

-

pseudostate

-

approach. The results (Fig.8) show simple, recurring forms: Each of the electron-capture cross sections has a single maximum, which becomes progressively lower, and occurs at a higher proton energy as the target nuclear charge ZT increases. The same is true of the ionization cross sections. The decline of the cross sections with increasing ZT is more rapid for electron capture than for ionization, so that whereas

+

electron capture substantially dominates ionization for He targets over most 5+

of the energy range studied, for C targets the reverse is true.

7

-

4

When scalea cross sections

oc

= o .Z and o. = oieZT for electron capture and c T

ionization, respectively, are plotted versus scaled proton energy 2

E/(25.ZT) = (v/ZT12, where v/ZT is the proton speed in units of the Bohr velocity of the target ion, the curves for each process agree closely with one another. The scaled electron capture cross sections peak at the scaled energy (v/ZT)

=

0.5, whereas the scaled ionization cross sections show a broad maximum at about (v/ZT)

=

1.1.

Experimental cross sections for these processes are not available for

+

hydrogenic ions beyond He

.

-51;

I t 1 1 1 1 1 1 1 I I f 1

100

PROTON ENERGY (keV)

Fig.8

-

Calculated cross sections versus proton energy (relative to the target ion) for electron capture into all states of HO (solid curves) and for ionization (dashed curves) in collisions between protons and the ground-state

+

(12)

+

For proton impact ionization of many-electron ions A a simple classical scaling relation has been given by Watts et a1 /41/. The scaled ionization cross section

zi

is expressed as

where u is the ionization energy of the electrons in the ith subshell and ni i

is the number of such electrons; R is the Rydberg constant and Z is the pro- P

jectile charge. This expression modifies a scaling relation given by Vriens /42/ to allow for inner-shell contributions to measured values of oi. In Pig.9 values of

zi

obtained from eq. (13) for HI colliding with

,

'

c

,'N 11'.

+

Ga , In

,

and T1 ions are plotted against scaled energy = E /Au where E is

P P

the projectile energy and A is the projectile mass expressed in units of

+

electron mass. Experimental data /43/ for H

+

H0 collisions are also included for comparison. At the higher energies, the scaled values of

gi

can be seen to be in agreement to within about a factor of 2. This simple scaling relation may therefore be useful for obtaining rough estimates of cross sections for proton impact ionization of other many-electron ions at high velocities.

Scaled e n e r g y

Fig.9

-

Scaled ionization cross sections

zi

versus scaled energy (see text)

+

for H collisions with H0 ( o ) ; c+(+); N+ (x); ~ l + (I); Ga ( m ) ; I ~ + ( A ) ; and

TI+ ( r )

.

From Ref. /44/.

+

For a discussion of electron capture by protons from many-electron ions A

+

the reader is ~eferred to ~ e f .

/&/

(Li ) , Ref ./44/ ( c + , N ) , and Ref ./41/

+

(Il', Ga , In and T1 1 . For a few other target ions-, e.g. ~ ~ + / 4 6 / and Ti ,

+

2+

(13)

11) COLLISIONS BETWEEN ~ e + IONS

+

Collisions between two He ions represent the simplest system of homonuclear

+

ions. Apart from their direct relevance to fusion, He + He collisions are also of fundamental theoretical interest because of the two-electron interaction. Theoretical approaches, for which difficulties are considerably enhanced due to the second electron present in the collision system, became available only recently.

Cross sections oc for electron capture (into all bound lie0 states) in collisions

have been measured by Peart et a1 / 4 7 / and Melchert et a1 / 4 8 / . Fig. 10 illustrates that the experimental data from both groups are in excellent agreement.

Fig.10

-

Cross sections o for electron capture (into all bound H ~ O states)

C

+

in He + He collisions : o Peart et a1 / 4 7 / ; Melchert et a1 / 4 8 / . The error bars represent the 90% confidence limit of statistical error.

Note that in a crossed-beams experiment (Fig.1) the reaction products , H ~ O

2+

+

(14)

In Fig. 11 the experimental results are compared with theoretical predictions. In order to facilitate comparison the combined data of Fig.10 are represented by a solid line obtained again by a 4-parameter best fit. Willis et a1 /49/ have performed classical-trajectory Monte-Carlo calculations using three distinct types of model potentials. Only the results labelled CTMCA appear to be quite good, but the authors confess that 'the reasons for this are not clear'. The approaches CTMCB (obtained by switching potentials during the collision) and CTMCC (obtained using pure Coulomb potentials) clearly overestimate the cross section. Classical-trajectory ~onte-carlo' calculations inherently depend on the proper choice of a model potential in order to treat the two-electron problem as an effective one-electron problem. The results of a time-dependent Hartree-Fock approach by Henne et a1 /50/ systematically overestimate the cross section.

A simple two-state coupling MO calculation /48/ shows that the capture into the ground state of IieO is approximately only 50% of the total capture cross section at energies below the cross section maximum. This is supported by the good agreement with the scaled inverse reaction

He2+

+

He(ls2) -+ He+(ls)

+

He+(ls) (15)

which has been studied experimentally and theoretically by Afrosimov et a1 /51/ and Harel and Salin /52/, respectively.

+

Fig.11

-

Cross sections oc for electron capture in He

+

He collisions:

-

combined experimental results of Fig.10;

---

scaled experimental and theoretical data by Afrosimov et a1 /51/ and Harel and Salin /52/. resvec-

2

+

tively, for the inverse reaction He2+ + He (1s + ~e+(ls) + He (Is) ;

(15)

Very recently, coupled-state calculations with larger basis sets of molecular /53,54/ or atomic /55/ wave-functions became available. These results are all in very good accord with experiment below the cross section maximum. However, Fritsch and L i n / 5 5 / as well as Kimura /54/ point out that close agreement with data is obtained only when capture both into spin-singlet and spin- triplet states of H ~ O is taken into account. Thus, the good agreement of the

MO results by Allan /53/ is not clear, since his calculations include only the singlet contributions. At and beyond the cross section maximum the calculations overestimate the data. This is due to the onset of ionization which is neglected in the theoretical approaches.

+

In conclusion, electron capture in low-energy He + He collisions has been understood only very recently.

2+

In Fig. 12 are shown cross sections o(He ) /47,13/ and ac /48/ for ~ e + + ~ e + collisions, from which the cross sections oi for ionization are obtained by subtraction. Again, experimental results from the groups at Newcastle and Giessen are in excellent agreement. The ai data, represented by a fit curve

(solid line), are compared with theoretical predictions in Fig. 13.

5

10

20

50

100

200 E,,

( k e V )

+

Fig. 12 - Cross sections for He + He collisions:

o(~e'+): x Peart et a1 /47/,

.

Melchert et a1 /13/; oc: o Melchert et a1 2+

/48/; ai calculated from ai = o(He )-ac: O deduced from the work of Peart et a1 /47/, 1 Melchert et a1 /48/. The error bars represent the 90% confidence limit of statistical errors. Both cross sections ac and ai are fitted by a

2 +

(16)

First of all we note that there are no theoretical results available based on quantum calculations. The only theoretical approach with which the oi data

- can be compared directly are classical-trajectory Monte-Carlo calculations by Willis et a1 / 4 9 / using three different types of model potentials. Only the results labelled CTMCB (upright triangles) appear to be quite good at the higher impact energies. However, this model potential predicts electron capture cross sections a, which clearly overestimate the measurements (see

-

Fig. 11)

.

On the other hand, the CTMCA approach (inverted triangles) , which reasonably reproduces the oc values in Fig.11, fails completely in predicting the energy dependence of the ionization cross section oi. Finally, the CTMCC approach (crosses) reproduces neither the oc nor the oi data. For comparison also included in Fig. 13 (broken curve) are experimental cross sections / 2 0 /

+

for ionization in H

-

He collisions at the same relative velocities. Both ionization cross sections show practically the same dependence on relative

+

velocity; however, ionization of He by H+ is about a factor of 2.3 smaller

+

than by He impact.

In conclusion we note that, in contrast to electron capture, ionization in He+

+

~ e + collisions is not understood as yet.

V,,

(

108cm/s

I

E,, (keV1

+

Fig. 13

-

Cross sections oi for ionization in He

+

He+ collisions: -

-

combined experimental results of Fig. 12; v CTMCA, A CTMCB, X CTMCC calculations by Willis et a1 / 4 9 / with exemplary error bars representing the 68% con£ idence limit;

---

experimental cross section / 2 0 / for ionization in

+

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111) COLLISIONS BETWEEN HEAVY IONS

+

Co1l:ision experiments with ions both heavier than He have been performed solely with identical ion pairs. Measurements have been reported for the

+

collision systems ~ i + + Li /56,57/; ~ a + + Na /58/; ~ r +

+

Ar /59/; K+

+

K+,

+

~ b +

+

~ b + /58/; ~ e +

+

~ e + /59/; CS+

+

Cs /60-63/; and TI+

+

~1+/64/. In all 2 +

these experiments only total A production cross sections from combined processes of electron capture (ac) and ionization (oi) have been measured. For heavy ion fusion applications, however, the cross sections ac and ai need

- -

be known separately since the total beam loss cross section aL is given by

+

For t:he closed-shell systems Li + Li /65,66/ and CS+

+

Cs /67/ it has been shown theoretically that collisions will be dominated by ionization rather than electron capture. This is consistent with an experimental estimate of a

C

+

for C:s

+

csf collisions /68/.

In measurements with heavy ions a further experimental difficulty is involved which results from enhanced scattering in the collision due to lower relative velocities of the collidants. Care must be taken to ensure that the angular acceptances of the analyzers and detectors are large enough to collect all

+

scattered reaction products. A discrepancy in the CS+ + Cs data measured by the groups in Belfast /60,62/ and Newcastle /61/ is possibly explained by incomplete collection of all the cs2+ ions formed at lower impact energies.

Only very recently, the first separate measurements of cross sections ac and

+

o became available for the heavy systems Xe

+

Xe and ~ i +

+

Bi /69/. The i

results for the latter ions are shown in Fig. 14. In the energy range inves- tigated electron capture cleary dominates ionization, in contrast to the fin-

+

dings for the closed-shell ion Cs

.

From this data total loss cross sections aL can be obtained which enable an assessment of beam intensity losses in the storage rings of the heavy ion fusion scenario HIBALL I1 / I / . A simple esti-

mate /70/ shows that beam losses up to 1.7 % are to be expected which give rise to a peak power deposition of more than 2 MW to the ring walls. The high energy particle flux to the walls, particularly concentrated behind bending magnets, will require special precautions with respect to, e.g. too high a specific power deposition, wall material activation and vacuum instabilities due to released wall partic1e.s.

+

(18)

+

Fig.14 -

-

Cross sections for ~ i +

+

Bi collisions /69/:

2 + o electron capture ac; x ionization ai; A total si2+ production a(Bi = a

+

ai; total beam loss cross section uL = 2(2uC + oi).

C

IV) COLLISIONS INVOLVING MULTIPLY-CHARGED IONS This field is almost completely unexplored.

Resonant electron capture in the one-electron collision system

has been studied in two pioneering experiments. Jognaux et a1 /71/ used the merged-beam technique for measurements in the CM energy range 0.01

-

1.7 keV whereas Peart and Dolder /72/ employed inclined beams for CM energies 0.1

-

20 keV. Unfortunately, both measurements suffered from incomplete collection of the reaction products. Since the collidants repel each other both in the incoming and outgoing reaction channel, sufficient angular acceptance of analyzers and detectors becomes a crucial experimental difficulty, especially at the low collision energies accessible in a merged-beam experiment. The experimentalists were well aware of this fact and assigned limits to the angular acceptance of their apparatus. Cross sections for reaction (17) have been calculated by Bates and Boyd /73/, Dickinson and Hardie /74/, and Zhdanov /75/ using semi-classical two-state approximations. When the theoretical results are modified, by considering the differential cross sections, to cor- respond to the limited experimental collection efficiencies, agreement with the measurements is obtained within rather broad limits of error. Clearly, improved experiments are needed for this uniquely simple collision process. Of course, experimentalists dream of studying electron capture and ionization processes in collisions between two multiply-charged ions

(19)

C1-224 JOURNAL DE PHYSIQUE

Up to now, however, there are no experimental investigations of reactions (18) or (19) available. One reason may be that nobody could afford so far two powerful ECR ion sources most suited for providing intense beams of multiply-charged ions for a crossed-beams experiment. Additionally, increased experimental difficulties are to be expected in such measurements due to enhanced background from residual gas interactions and increased angular scattering of the reaction products resulting from the stronger Coulomb repulsion between the collidants. Therefore, theoretical calculations like the ones shown in Fig. 15 by Janev and Belic /76/ for quasi-resonant electron capture in collisions N3+ +

c2+

and F ~ +

+

04+, respectively, could not be verified so far experimentally, even though the cross sections predicted are quite large.

Fig. 15

-

Cross sections for ground-state to ground-state electron capture in the quasi-resonant reactions

N3+ +

c2+

+ N2+

+

c3+

-

0.44 eV F ~ + + 04+ + F ~ +

+

05+

+

0.34 eV, calculated by Janev and Belic /76/.

The only experimental attempt to study ion-ion collisions with multiply- charged ions has recently been performed by Kim and Janev /77/ by use of a folded-beam ion-ion collider. A collimated beam of 30 keV

x3+

ions (X = Ar and Kr) is made to fold into itself by reflection in an electrostatic mirror (Fig. 16). On the way back to the analyzing magnet, reflected

x3'

ions may

3+

lose one electron in collisions with incident X ions either by an ionization or by an electron capture process. The product

x4+

ions are separated by the analyzing magnet and individually detected, whilst the reflected beam of

x3+

ions is recorded by a Faraday cup. The cross sections for electron loss from combined processes of electron capture and ionization in ~ r

+

~~ +r and ~ +

3+

~ r + ~Kr + collisions, obtained at a fixed center-of-mass energy Ecm=60 keV, are (6.1 ?: 1.7).10-~~ cm2 and (2.9 0.8) -10-l6 cm2, respectively. These cross sections are surprisingly large, however, they have been found consistent with theoretical estimates based on the Fano-Lichten electron promotion and the molecular inner-shell-vacancy decay models. Because of the long interaction length provided by the field-free drift region between mirror and magnet, a relatively strong ion-ion signal has been obtained on top of a smooth background due to ion-residual gas interaction so that a special method for signal recovery has not been utilized in this experiment. On the other hand, the accurate evaluation of the spatial overlap of the beams becomes a difficult experimental problem. The enhanced stripping of a

3+ .

(20)

C E M DETECTOR B E A M ' SCANNER ~r 5 x IO-''T

-

7

MIRROR

-

-Jo+v

Fig. 16 - Schematic view of the folded-beam ion-ion collision experiment by Kim and Janev /77/.

4

-

CONCLUSIONS

Although the realization of experiments with intersecting ion beams is quite complicated, experimental techniques have now reached maturity in a few laboratories. In the last decade a bulk of reliable data for electron capture and ionization in ion-ion collisions has become available. Only recently, however, theoretical approaches could successfully describe the electron-capture

+

process in the simplest collision systems H + ~ e + and He

+

~ e + involving only one and two electrons, respectively. The process of ionization in these

+

collision systems is much less understood; for He

+

He collisions theoretical approaches based on quantum physics are not available at all. For complex multi-electron systems separate measurements of electron capture and ionization are still scarce. Here, much remains to be done, both experimentally and theoretically.

Further innovative experiments may aim at the determination of the final states of the collision products or at differential cross section measurements. Another challenge to experimentalists is the unexplored field of collisions between multiply-charged ions.

Acknowledgements

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JOURNAL DE PHYSIQUE

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