MULTIPLE ELECTRON CAPTURE

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A. Niehaus

To cite this version:

A. Niehaus. MULTIPLE ELECTRON CAPTURE. Journal de Physique Colloques, 1987, 48 (C9),

pp.C9-137-C9-146. �10.1051/jphyscol:1987923�. �jpa-00227341�

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JOURNAL D E PHYSIQUE

Colloque C9, supplement au n012, Tome 48, decembre 1987

MULTIPLE ELECTRON CAPTURE

A. NIEHAUS

Fysisch Laboratorium, Rijksuniversiteit Utrecht, Princetonplein 5, NL-3584 CC Utrecht, The Netherlands

Abstract: The present state of knowledge on multiple capture processes is illus- trated by discussing a selection of recently published experimental results in the framework of the "molecular classical overbarrier model (MCBM)". For this discussion the model is extended to allow the calculation of angular differential cross sections for well defined capture processes. Finally, several points of interest regarding the spectroscopy of multiply excited states populated by two-electron capture are discussed using recently published or original data from electron spectroscopy.

1. INTRODUCTION

We will limit the discussion in this paper to processes involving more than one

"active electron". Single capture processes have been recently reviewed [I], and extensive information on the recent development of the field of multiple capture can best be obtained from the proceedings of three conferences 12-41 devoted to this subject. Here we only summarize the most important steps in the development during the last years in order to have a basis for the following somewhat more detailed outline of our present understanding of the physics of multiple capture processes.

Multiple capture processes may be indicated as:

whereby, in the low velocity region, the (r+s-q) electrons may be thought of as being "spontaneously" emitted,-either by one of the collision partners after the collision, or by the quasimolecule during the collision. For this kind of ionization the term "transfer ionization (TI)" is commonly used [5]. Except for results from some rather early work [6,71 on reactions of type (1) for ions with low q-values, as available from normal ion sources, nothing was known, as recent as ca 1975, for the more highly charged ions, where the potential energy of ~ q + is high enough to lead, in principle, to the ionization of several target electrons.

The first step towards a better understanding for the case of high q-values was made by carrying out systematic measurements of absolute capture cross sections, a

,

for a large range of q- and r-values and for different col ision v locities [8:9f.

It was found that these cross sections are very large (10- la

-

^10-l' ^{cm2) and}

-

^for

given values of q and r

-

are virtually independent of collision velocity. The aq were further found to increase nearly linearly with q, and to decrease systematicai- ly with the number (q-r) of captured electrons. An interpretation of these data was hampered by the fact that processes characterized by the value-pair (q,r) are not well defined: the same final projectile state (r) can arise for processes leading to different target charge states (s), and, even for a final state defined by the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987923

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triple of values (q,r,s), the final state can, in general, be reached via different intermediate states of the collision system. In this situation, the logical second step was, to carry out measurements of cross sections for the formation of defined charge states of target

and

projectile. Such coincidence measurements of cross sections as were performed in several laboratories [lo, 11,121. It turned out that, in general?'rto each (r)-value there belongs a distribution of s values (s 2 q-r), proving that one or more electrons are emitted in the process. The s-distribution was further found to increase in width with q and with the number (q-r) of captured electrons, indicating that the potential energy set free by binding (q-r) electrons in the highly charged ion is somehow responsible for the emission of the (r+s-q) electrons. These results led to the formulation of a statistical model 1131 which was based on the assumption that the potential energy available in a collision system is equipartitioned among the target electrons. On the one hand, this model explained the measured charge state distributions for larger q- and (q-r)-values rather well, on the other hand, however, it did of course not explain 'where the electrons come from'

-

projectile, target, or quasimolecule

-

and, also, was apparently in contradiction with other experimental data that proved the processes to occur in a very "unstatistical" way. Such data were obtained by the methods of

"translation spectroscopy (TS)" [14,15,161 and electron spectroscopy (ES) of the autoionization electrons [17,18,19]. By(TS) it was shown that a final projectile charge state r=q-1 arises from two or three different processes, characterized by distinct energy gains (Q) in the energy of relative motion. These processes are, single capture, double capture followed by projectile autoionization and

-

^{in some}

cases

-

three electron capture followed by the spontaneous emission of two electrons by the projectile. From the values of the corresponding energy gains (Q) in the case of double capture it was further evident that the electrons were very selectively captured into states lying in a rather narrow region of binding energies. The position and the width of this "population window" was further found to depend in a systematic way on the charge state q and on the binding energies of the target electrons. (ES)-measurements, which became feasible with the advent of efficient sources for highly charged ions [20,21] confirmed these conclusions for two electron capture and proved that, quite generally, also in case of multiple electron capture from multielectron target atoms, electron emission by the projectile is dominant [22,23]. In addition, these (ES)-measurements yielded a wealth of new spectroscopic information on multiply excited few electron ions. This information will be further outlined in the last section of this paper. Regarding the capture process itself, it thus became obvious that, instead of scheme (I), a more detailed scheme may be used, namely,

Aq+

+

B + A(P-s)+

+

BS+

L A *

+

^(r

-

^(q-s))e-

.

⁽²⁾

This decomposition of the overall process into two successive steps simplifies its description considerably. The first step is a simple (multiple) charge exchange process which, in principle, can be described by established methods such as the Landau-Zener approximation [24]. In practice, however, such a description, which requires the evaluation of transition probabilities at all crossings of the potential curves of the quasimolecule, can only be applied in the most simple cases, because there exist, in general, infinitely many such crossings. It was therefore desirable to find a simpler model that would be able to describe the processes at least approximately, and to evaluate the large amount of available experimental data in terms of physical quantities. For single electron capture such a simple model had already previously been formulated 1251, and had been found to be very successfull.

This model is based on the so called "overbarrier criterion"

-

first applied to the description of resonant charge exchange 1261

-

which says that an electron will be transferred from B to Aq+ at a critical distance Rc at which the t y of the potential barrier separating the Coulpmb wells, caused by B+ and by Aq

,

^{has an}

energy equal to the level occupied by the electron when bound to B. Recently, BBrBny et a1 [27] have formulated a model for the description of multiple electron capture which is based on the same criterion. This extended model allows one to calculate upper limits of multiple capture cross sections without the use of any free

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parameter. However, it does not include in its formulation the possiblity to make predictions regarding the final states the electrons occupy on A and B after the collision. A formulation not having this limitation was later proposed by the present author 1281. In this latter version the overbarrier criterion is

-

for each electron

-

applied twice, on the incoming part of the trajectory, and on the out- going part. Also, the problem of screening of the nuclear charges by the "active"

electrons is treated differently, and some "dynamics" is included by incorporating the time-energy uncertainty relation into the otherwise classical formulation. The model in this form, which we call the "molecular classical overbarier model (MCBM)", will be used for the discussion in the next chapter.

At last, a very recent development regarding the experimental side should be mentioned, namely, the performance of angular differential cross section measurements for which the final projectile

-

and target charge states are determined by the coincidence method [29,30]. These studies provide very detailed information regarding the mechanism of reaction (1).

2. THE PRESENT STATE OF UNDERSTANDING OF MULTIPLE ELECTRON CAPTURE

In this chapter we will discuss a selection of recently published, and of original experimental data in the framework of the "molecular classical overbarrier model (MCBM)" [28]. The aim of this discussion is to illustrate the present state of our understanding of the rather complicated multielectron processes (11, for a rigorous description of which there exists up to now no practical concept.

The (MCBM) has been described in detail elsewhere [28]. In that description it is not explicitly shown how angular differential cross sections can be obtained. Since recently measurements of angular differential cross sections have been performed f29,30,31], which have not yet been confronted with predictions of the (MCBM), we give here a simple prescription for calculating angular differential cross sections within the (MCBM).

In the (MCBM) the electrons of the target atom B become successively molecular electrons as the nuclei ~ q + and B approach, whereby the first electron passing the potential barrier is more loosely bound than the second one, the second one more loosely than the third one, etc. When the nuclei separate again, and the barrier rises above the respective binding energies of the molecular electrons, these electrons become successively again atomic electrons on A or on B. In this way it can be distinguished "which electrons" a e ound to A or B after the collision. For example, the final states populated in A&-'?+ when the "first two" electrons

-

^i.e.

those which became first and second molecular

-

are captured by ~,'q will in general be different from those populated when the first and, say, the third electron are captured by ~ q + . To distinguish such processes, in the (MCBM) certain strin s (j) are assigned that indicate which of the active electrons are captured by Aq', and which remain on the target atom. For example (j) = (110000) indicates a process in which the first two electrons are captured by ~ q + , while the other four of the six electrons considered to participate remain on B. The cross section for a process of given string is given by

with R: the critical0 distances for electrons of label (t) on the incoming part of the trajectory. Formula (3) implies the assumption of straight line trajectories and simply means that thy jjross section is composed of ring shaped areas that contribute with probabilities P to the process. The repulsive Coulomb forces at each point of a trajectory are known within the mfdel. These forces change in strength each t time an ele on becomes molecular at Rt, and each time an electron becomes atomic again at R O ~ ~ . The scattering angle for a trajectory with impact parameter (b) may therefore be calculated as a sum gf deflection angles, caused by the forces between two critical distances, Rk and R, say. If we use the small angle approximation, which is certainly appropri"ate hers, the corresponding deflection angle is simply

8 = -

k 2Eb ( 4 )

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when the Coulomb potential is given by Ck/R in the region Rk<R< Pk

.

The scattering angle for the whole trajectory is then

where the sum is taken over the appropriate pieces of the trajectory. An expression for the differential cross section at the same "level of crudeness" as

(3) for the cross section, is now obtained by p r ~ w t i n g the co t ibutions A

P

3 s onto the angular range between scattering angles 8 (b=Rt) and Ot+l(b=Rt+l): t' t

t

w(~)(B) = A .~(j)/(~n.sine. lO(j)

-

^8(j)

1)

^for ^O ⁾

<

^{0 8} ⁽⁶⁾

t t t t t+l t

The differential cross section for the process (j) thus becomes

w(J)(e)

= N

e

^w^:^j⁾⁽^e⁾ ( 7 )

t=t

Expressions (4-7) are tsed, together with the relevant expressions given in ref.

1281, if experimental data are compared with predictions of the (MCBM).

Absolute cross sections: Experimental absolute cross sections os belong, in general, to several distinguishable processes. In order to com8.zre the model predictions with such phenomenological cross sections, the evolution of the system from the initially formed state to the measured final state must be known. Although the model predicts the binding energy of all electrons, there is still some uncertainty regarding the decay of the multiply excited atoms formed initially.

Especially, in the case of doubly excited states there may be stabilization of autoionizing states by radiative transitions, and in the case of multiply excited states it is not yet known whether such states predominantly decay by Auger-cascades or rather by emission of fewer high energy electrons. Comparisons which have been made under the assumption that autoionization does occur when energetically possible, have lead to a surprisingly good agreement between model predictions and measured cross sections for the system A$+/A~ 1281. In this system cascades should not be important because, due to the low value of q, no double autoionization is energetically pofsibl~ In Tab 1 the comparison is shown for three experimental cross sections o

5,3* O5

4'

^aⁿ^- In all three cases the final states are reached by autoionization of prbjectile i~f'or target (B), as indicated. The numbers nl(A,B) and n2(A,B) are the quantum numbers of the two highest excited electrons on A or B, respectively, as predicted by the model. Based on these numbers it can be judged

final Oth

(j) nl( n2( 1 Autoion. state (r,s)

[AZ]

00110 3.6(B) 3.6(B) Target (B) 3 ~ 3 1.26

00101 3.6(B) 3.6(B) II 0.95

00011 3.6(B) 3.6(B) II 11 0.99

11100 3.6(A) 3.6(A) Projectile(A)

"

3.62

11010 3.6(A) 3.6(A) ¹¹ ^,I 1.26

11001 3.6(A) 3.6(A) 11 ¹¹ 0.95

sum: 9.03 8.4 11000 4.1(A) 3.9(A) Projectile(A) 4.2 9.16 7.8 00111 4.1(B) 3.9(B) Target(B) 2.4 0.99 0.9

Table 1: Comparison of experimental cross sections for processes ~ r

+

~Ar + ~ r ~ + +

+

ArS+ (r+s+-s)e- (last column; ref. 28), with the sum of model cross sections (last but one column) that' correspond to processes defined by the strings (j) (first column). Also indicated the principle quantum numbers nl(~,~), n2(A,~) of the two most highly excited electrons on A or B, and the final charge states (r,s).

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whether or not autoionization of the initially formed ions occurs. Although it is seen that projectile ionizaton dominates, some target autoionization is also predicted. Recently extensive comparisons for systems ~rq+/Ar with q ranging from 6 to 13 have been carried out 1311. Also here it is found that the agreement is surprisingly good in view of the crudeness of the model and the complexity of the process.

Population windows: The (MCBM) predicts in its static form a fixed value for the binding energy of each of the electrons participating in a process of type (1). This fixed value is replaced by a, Gaussian distribution after incorporating the time- energy uncertainty into the model. If more than one electron are transferred, there arises for the multiply excited state the problem as to which extent the electrons may be treated as independent. In our previous work [18,32,33] we have combined the Gaussian distributions of the one electron binding energies quadratically to one Gaussian of the total binding energy. In this way one obtains a "population window"

for the multiply excited state. For a large number of collision systems A ~ + / H ~ , H ~

KV18063 the position and the width of this

"o'+ (

96

keV "predicted window" was compared to the

actual probability distribution of the 31n'l' -21"

-

binding energies of the doubly excited

states formed by two electron capture [19,32,33]. This comparison was made on the basis of the measured autoionization electron spectra. In case of autoionization into one final state the intensity distribution of the observed lines directly reflects the probability ... distribution. Good qualitative agreement was found in almost all cases. For new electron spectra arising from collisions of the ,bare ions 08+ with He and H2 the comparison is shown in Fig. 1. In both cases states belonging to configurations (31n1l') and (41n'11) are populated. For He the population window in electron energy is shown for decay of the populated states into the (211&1"')- continuum. For H2 the calculated window is shown for decay into (211'&1"')- and

EfilTTER FRRtiE ENERGYlEVl (31"~l"')-continuum. It is seen that

the rather different population FIGURE CAPTIONS distributions observed in the experiment, Fig. 1: Electron spectra arising from are qualitatively well reproduced by the the autoionization~of doubly excited model. This qualitative agreement also states populated by double capture from includes the "height" of the calculated the two electron argets He and H2 into windows, as is found quite generally, the bare ion The spectra are i.e.. the same normalization of the transmission corrected, and given in Gaussian relative to the spectra leads to the frame of the emitting particle. similar heights of the measured peaks

relative to the Gaussian.

The spectrum for H2 exhibits an interesting feature which is also found in other systems: although, according to the calculated window, the intensity of the lines belonging to the states (3111'1') should increase with n', actually a decrease of the intensity is found. This suggests that there is some constraint regarding the energy exchange between the two captured electrons, favouring those two-electron states which arise from the one electron states predicted for sequential single capture.

For the present case, the most probable one electron states are predicted to have quantum numbers nl = 4.6 and n2 = 3.9, and the half widths of both n-distributions is approximately only An = 1. One therefore might say that, according to the (MCBM) an extra mechanism is required to realize the population of states like (nl = 3, n2

= 9). The situation just discussed is probably the same as the one encountered in

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several other systems

-

for instance N5+, 06+/H2

-

where the population of Rydberg series 2pnfl' is observed [34,35]. Also in those cases the height of the corresponding autoionization lines, due to decay to the 2s-continuum are considerably lower than predicted by the (MCBM)-window. As an explanation for the occurrence of these lines electron-electron correlation effects have been proposed 1341.

3. SPECTROSCOPIC INFORMATION

Differential cross sections: Recently the first measurements of differential cross sections for well defined final states were reported [29,30,31]. Due to the fact that large impact parameter collisions contribute dominantly to the capture processes, differential cross sections peak at rather low values of E.O (Collison energy x scattering angle

-

1-10 keV.deg). But because of the same reason, these measurements are very sensitive to details regarding the changes the "electron cloud" undergoes during the collision. For the system 08+/He it was found [291 that the peak in the differential cross section at E.O

-

4 [keV.deg] for capture of two electrons into states (nl = 3, n2 = 4) is consistent with the assumption of

"sequential capture"

-

the mechanism also assumed in the (MCBM)

-

and inconsistent with a one-step two-electron capture mechanism. In addition it was found that, in the case of multiple capture studied for N ~ + / A ~ , the assumptions made in (MCBM) regarding the screening of the projectile charge by the "molecular" electrons is more realistic than the assumptions made in the model of BBrBny et a1 [27]. In cases of multiple capture followed by multiple ionziation, a comparison of measured differential cross sections with predictions of the (MCBM) are complicated because it is not always clear which intermediate states

-

characterized by the above defined strings (j)

-

contribute to the observed fin 1 state. In Fig. 2 we show such a comparison for the differential cross section og

2

of the system Ar9+/Ar. The experimental curve is adapted from ref [31]. The theotetical curve is obtained using the extended (MCBM)-model as described

In connection with atomic spectroscopy, one interesting aspect is that electron capture into highly charged ions is a rather selective process, which in addition is well enough understood for predictions to be made as to which states are mainly above. The contributions of the following strings are taken into account: one string (111100000) with the innermost "1" at position to = 4, four strings (....10000) with to = 5,

-

^L 2

~ r ~ ' / ~ r 16 2 keV

- ⁵^{= 4}

$ .2

y

5 -

0

3

' -

- 3

-

0

ten strings with to = 6, and twenty strings with to = 7. The sum of all these contributions is finally smoothed with a Gaussian of .15" width. In the figure it is indicated where the contributions belonging to a certain to peak. It should be emphasized that both, experiment and calculation are absolute. The quoted angular resolution of the experiment is

--.

^15'

.

^The

1'.

0' 0.5' overall agreement regarding, absolute

SCATTERING ANGLE 9 value, angle position, and width of the

two differential cross sections is very good. The absence of the shoulder in Fig. 2: Comparison of the ezperimental dif- the experimental curve indicates that ferential cross section a (0) for the the contributions belonging to to = 6 process *r9+

+

^Ar ^-+ ^~ ^r ^~ ^Ar4+⁺ ^~

+

^~ 2e- probably do not autoionize twiceq and ⁴

[ref. 311, with the prediction based on the therefore do not ontribute to a

(MCBM) (see text).

t

9 7 '

but rather to Ug

.

The processes belonging to string's with to = 4,5 lead to the highest excitation of the captured electron and therefore should be responsible for the measured cross section, because emission of two electrons is most probable. This seems to be confirmed by the measurement.

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populated In certain collision systems A~+/B. In this way it is not only possible to choose a suitable collision system in order to study certain states, but also to control the population of states to a certain extent

-

for instance by using different target atoms with a given ~ q + , or by using A(~-I)+ and Aq+ to populate the same states after capture. Such methods may yield additional information needed to identify states observed. In this connection it is important to emphasize that double electron capture has been shown to conserve electron spln for light ions and two electron targets [36]. Therefore the possible multiplicity of the states populated is known, and can be controlled by choosing appropriate systems.

Since multiple electron capture leads in general to multiply excited states that usually autoionize faster than radiate, the method of optical spectroscopy of states formed by capture processes has been llmited to single capture [37,38]. The main spectroscopic information that can, in principle, be obtained using multiple electron capture, will certainly have to come from electron spectroscopy. In the case of states formed in two-electron capture from two-electron targets the application of this method is straight forward and can presently be performed with an accuracy comparable to the accuracy achieved for optical spectroscopy in the X- ray region (Ac -.lev)

.

In the case of multiply excited states formed by capture from multielectron targets electron spectroscopy will have to be combined with the coincident detection of

-

^{at least}

-

the charge state of the target, in order separate out the dominant contribution to the electra spectra from decay of states formed by double capture. Such measurements have not yet been performed. We will summarize here some recent results concerning states formed by double capture from two-electron targets.

One rule which has been confirmed quite generally [17,18,19] concerns the decay of doubly excited states by electron emission: the decay occurs with very strong preference into the nearest continuum. An e mple for this behaviour is also the o8+/Ii2 spectrum shorn in Fig.. The states OE(41n'l') that lie above the (31-1')- limit decay completely to (311'~1"'), and not to (21"~l"') as they do below this limit. No exception to this rule has been found for continua that differ in principle quantum number. For the branching to continua (. .2scl) and (. .2pel) from states such as (..31n'11) one finds typically a ratio of

-

⁵in favour of the (2pcl)-continuum [18].

Another rule, which seems to hold fo the light ion-systems studied so far, concerns the fluorescence yield for Li-like-'L-configurations of the type (ls21n'l'), which are forbidden to autoionize because of the spin selection rule: the fluorescence yield for the allowed, optical transitions within the quartet system is close to 100% 1361. Only the lowest quartet 4 ~ 0 and 4 ~ e , which are not allowed to decay radiatively, at least partially decay by (forbidden) autoionization, as evidenced by the existence of the corresponding K-LL-Auger lines [36].

15252 Fig. 3: Comparison of

2s wavelengths of the dielectronic satellite

1 I

^cnen⁽¹⁹⁸⁶⁾

1

^lines ^evaluated ^from

electron spectra [ref.

/

^8ely-^Dubau^et^a1¹¹⁹⁸¹⁾

I

391, with results from optical spectrosco~

(Nicolosi/~ondello(l977):

(

a e n / a n a I

I

^ref. ⁴⁰⁾ ^and ^with

theoretical results (Vainshteinlsafranova (1978): ref. 42; Bely- Dubau et al. (1981): ref.

THIS WORK 43; Chen (1986): ref.

44).

21,8 22.0 22.2 2.4 22.6 22.8 23.0 A

'I Wavelength

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The energy positions of many doubly- and triply excited levels in He-like, Li-like, and Be-like ions have been measured by electron spectroscopy with an accuracy of ca .lev [18,19,35,39]. In some cases they have been assigned and compared to theoretical calculations. An example for such a comparison is shown in Fig. 3 for Li-like OVI ions of the configuration (1~2121'). Instead of level-energies we show wavelengths corres onding to optical transitions from the doublet states to the ground state (1s 2s12S, and first excited state ( 1 ~ ~ 2 p ) ~ P ~ .

2P

These so called

"dielectronic satellite lines" have also been measured by optical spectrosco y 1401.

i

From our electron energies, arising from autoionizing transitions to (Is

'

)2~, we have obtained the wavelength using the center of gravity energies for the final states [41]. The resulting wavelengths are listed in Tab. 2.

Transition Wavelength

[A]

lower state upper state

Table 2: Wavelengths of the dielectronic satellite lines as obtained from electron spectra due to autoionization of the upper states indicated.

In Fig.3 the width of the heavy vertical lines indicate the quoted uncertainty, which for our data ranges from 0.005 to 0.001

A.

The comparison with recent calculations [42,43,44] demonstrates that accurate experimental data for doubly excited Li-like ions are still needed.

A case of special spectroscopic interest are the doubly excited He-like ions in states of configurations with two equivalent electrons, because for these states electron correlation is very important [e.g. 451. We have measured elec ron spectra arising from autoionization of states of the (31311)-configurations of CL and 0''

[46]. Autoionization occurs into (2s,p). The measured spectrum is shown in Fig.4. It consists of a superposition of lines which are partially broadened because, due to a rather short lifetime, autoionization occurs when the doubly charged target is still at a distance of V.T (V E relative velocity, z E lifetime), which leads to a (PC1)- shift and -broadening of the line. The PCI-shift is given by [47]

q~ v qT 5 target charge

A € =

-

_2.v.T _{{ I - +}

IV -

^ve

+ I I

v ⁺ ^Eelectron velocity ⁽⁷⁾ The level energies and lifetimes z for the (3131') states of

c4+

have also been calculated [48,49,50]. In Fig.4 we have indicated, by vertical lines, the positions obtained when the theoretical energy positions are shifted according to relation (7) using the theoretical T-values. One notices that, within the accuracy of the measurement the theoretical peak positions agree very well with the experimenal ones. This suggests that both, theoretical energy positions and lifetimes of the states are correct. A more detailed bvaluaton of the measured spectra in terms of the known line-shapes [47] will lead to a more stringent test [51].

Finally, we would like to point out that, in principle, spectroscopic information of the types outlined above for states populated by capture of two electrons, can also

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Fi

.

^4:PCI-broadened and -shifted electron 1 3 ~ 6 + ( 6 ~ ~ 4 + ( 3 1 3 1 . ) + ~ 5 i ( 2 1 . ) sp:ctra arising from collisions of the bare

'" F"""""""

^uv18060 ions

cs

with H,. The part correspond in^ to decay of the do;bly excited states- (3131;) + (21"~l"') is shown. The vertical bars indicate theoretical positions shifted by the PCI-shift that corresponds to the theoretical lifetime of the respective states (see text).

be obtained for states populated by capture of three and more electrons. Of especial interest would be states belonging to configurations with three equivalent electrons. Spectra obtained for c6+/xe show features which indicate that such states are in fact populated [51]. To study such spectra in detail it is necessary to carry out the measurements in coincidence with the detection of xe3+.

ACKNOWLEDGEMENT

I would like to acknowledge many fruitful discussions with M. Mack. This work was performed as part of the research program of the "Stichting voor Fundamenteel Onderzoek der Materielt (FOM) with financial support from the "Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek" (ZWO).

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