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Electron capture in collisions of O8+ with H: Absolute line emission cross sections
Volume 124, number 1,2
PHYSICS LETTERS A
14 September 1987
E L E C T R O N C A P T U R E I N C O L L I S I O N S O F 0 8+ W I T H H: ABSOLUTE LINE EMISSION CROSS SECTIONS R. H O E K S T R A a,b, D. C I R I C c, F.J. DE H E E R b and R. M O R G E N S T E R N a a Kernfysisch Versneller lnstituut, Rijksuniversiteit Groningen, 9747AA Groningen, The Netherlands b FOM-InstituteforAtomic andMolecularPhysics, 1098 SJAmsterdam, The Netherlands c Boris Kidric Institute, Belgrade, Yugoslavia
Received 23 June 1987; revised manuscript received 24 July 1987;accepted for publication 27 July 1987 Communicated by B. Fricke
We present the first experimental determination of absolute line emission cross sections, resulting from charge changing collisions of bare oxygen ions with atomic hydrogen. The O VIII lines resulting from the dominantly populated n= 5 level confirm to a large extent the almost coinciding theoretical data obtained with an MO approach by Shipsey et al. and with an AO + approach by Fritsch and Lin. Emission from the non-dominantly populated n = 6 level is found to be stronger than predicted by theory and favours the MO data.
Electron capture processes in collisions of bare ions with atomic hydrogen are of fundamental interest [ 1,2] and play an important role in the diagnostics of fusion plasmas, e.g. in connection with the injection o f atomic hydrogen beams [3,4]. The most detailed information on these processes can be obtained by measuring the cross sections for line emission from the excited states formed by electron capture. In our program to measure such lines, so far the collision systems He 2+, C 6÷ and N 7+ o n H have been investigated [5,6]. We now succeeded to measure emission cross sections for the O 8+ + H system, which is especially interesting for plasma physics applications, and which could not be investigated before, owing to small O 8÷ beam intensities. Our measurements are performed in an accelerator range between 10 and 18 kV and are confined to the O VIII lines 6--.3, 5 ~ 4 , 5 ~ 3 , 4 ~ 3 and 3 ~ 2 in the VUV range, with the numbers referring to the main quantum numbers n involved in the transition. A measurement o f visible lines which would be especially interesting from an applied point of view is still impossible with the presently available ion beam and has to be postponed to future investigations. The most extensive calculations o f partial cross sections for O 7÷ (n, l) population during O 8÷ colli-
sions on H have been performed by Shipsey et al. [ 1 ] using a molecular orbital ( M O ) expansion, and by Fritsch and Lin [2] using an extended atomic orbital ( A O + ) expansion o f the electronic wavefunctions involved. We will compare our measurements with their results. Up to now these calculations as well as other ones by Salin [ 7 ], Bendahman et al. [8] and Kimura and Lane [9] could only be tested by comparison with experiments in which total charge exchange cross sections were determined. The most extensive measurements of this kind were performed by Meyer et al. [10] between 0.1 and 10 keV/amu, yielding a generally good agreement with theory. However these experimental data are not sensitive to the relative distribution o f partial cross sections for capture into certain nl-states. As opposed to this line emision cross sections measured in our experiments are dependent on partial cross sections, although the fine structure of lines originating from different/-levels on one n-shell cannot be resolved due to the quasi/-degeneracy in hydrogenic systems (see further on for more details). The experimental set up, described before [ 11 ] will briefly be summarized. A beam of O 8÷ was produced by an electron-cyclotron-resonance ( E C R ) source of the M I N I M A F I O S type [ 12,13 ]. The ~80 isotope was
0375-9601/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
73
Volume 124, number 1,2
PHYSICS LETTERS A
used to avoid beam c o n t a m i n a t i o n s of H ] or He-" ~. At kinetic energies between 80 and 160 keV beam currents of 5 to 10 nA (electric) have been obtained at beam diameters of ca 3 mm. H2 was dissociated by a Slevin-type radio-frequency (rf) discharge source [14], yielding a dissociation fraction of ca 65%. The absolute density profiles of H a n d H2 in the collision region were d e t e r m i n e d by observing visible light from the two target constituents induced by electron impact, and by exploiting the knowledge of ratios of cross sections for the corresponding processes [ 16 ]. UV light emitted from the 0 7~ ions was observed by a grazing incidence m o n o c h r o m a t o r which is equipped with a position sensitive microchannelplate detector a n d which is absolutely calibrated on its wavelength d e p e n d e n t sensitivity using various electron and ion impact processes with known cross sections [11]. All light m e a s u r e m e n t s were performed with a purely molecular H2 target on the one hand, and - with the rf-discharge on - with a mixed H and H2 target on the other hand. The error in the experimental results is due to a relative and systematical absolute error. The relative error is given by the quadratical sum of the statistical error ( 5 - 2 5 % ) a n d the fluctuation in target density due to different overlaps of ion and target beams (5%).
14 September 1987
When s u m m e d quadratically the uncertainties in the absolute target density (15%) and absolute spectrometer calibration give rise to an absolute error of 20 to 35% depending on the wavelength of the radiation. A possible error due to polarization of the emitted light has been omitted because it will be certainly smaller than 15% (see the more detailed discussion of Dijkkamp et al. [ 17 ]). We estimate the total error to be 25%. For a comparison of our experimental results with theory we have calculated line emission cross sections from the capture cross sections given by Shipsey et al. [ 1 ] and by Fritsch and Lin [ 2 ]. Only states with main q u a n t u m n u m b e r s n = 4, 5 and 6 have to be considered since population of other states occurs to a negligible a m o u n t . Lifetimes and partial transition probabilities in the hydrogen like 0 7 ~ ion can easily be calculated using the formulas given by Bethe and Salpeter [ 15 ]. All lifetimes involved turn out to be below 1 ns. This means that a complete cascading occurs within the viewing range of the monochromator and consequently has to be taken into account in calculating the emission cross sections. In table 1 we give the fractions of substate populations with m a i n q u a n t u m n u m b e r s n = 4, 5 and 6, contributing to the various lines observed in our experiments.
Table 1 Calculated fractions of nl-state populations (in %), which contribute to n ' ~ n" line emission by direct or cascade decay. Measured transitions
n
F/' --~ n "
74
n,/-contributions (%) /=0
1
2
3
4
5
6-3 (2=lT.lnm)
6
27.14
4.22
22.37
51.49
5-3 0.=20.0 nm)
6 5
0.6l 31.87
0.41 4.25
0.52 23.63
4.10 63.74
28.43 0
0
5-4 (2=63.3 nm
6 5
0.32 22.73
0.27 2.20
0.29 10.70
2.13 36.26
16.18 100
100 -
4-3 (2=29.3 nm
6 5 4
0.23 0.95 41.59
0.87 0.84 4.20
0.77 0.79 25.44
8.27 9.23 100
59.5 100 -
100 -
3-2 (,i= 10.3 nm)
6 5 4
4.64 4.73 4.92
4.38 4.35 4.20
3.87 3.58 3.01
53.32 64.83 100
84.31 100 -
100
0
0
Volume 124, number 1,2
PHYSICS LETTERS A
F r o m this table one finds e.g. the cross section for 5-3 emission to be
08÷+ H
*2
A 60
,
,
i
i
14 September 1987
i
I
a ( 5 ~ 3 ) = 0.006 l a ( 6 s ) + 0.0041 a ( 6 p )
50
z,O + 0 . 0 0 5 2 a ( 6 d ) + 0.0410tr(6f) + 0.2843tr(6g) 30
+ 0.3187tr(5s) + 0.0425tr(5p)
0 ~ I 3 ~ 2 : 10.2 nm 20
I
I
i
I
I
L~O
f
+ 0.2363a(5d) + 0.6374tr(5f).
T
I 3o ~ 20 0"~ZI][ ~---3:29-3 nm I
I
I
i
I
i
30
20 0"~2~15 ~/+ : 63.3 nm I
I
I
I
I
0.2
0.3
0.4
0 I5
Ol6
V
#
,
,
I
I
f
0.2
o13
o14
I
I
0.7 al ul
~'-
Oa*+ H ,
,
,
16 12 10 8 6
O~Z[~ 5 ~ 3 : 20.Onto I
I
o.s
0.6
I
o.7 a~.
V
Fig. 1. Emission cross sections for various 07 + (n--, n') lines after 08+ collisions on H as function of the collision velocity. Solid error bars indicate statistical errors, dotted error bars indicate the range of systematic uncertainties. The dotted and solid lines represent theoretical emission cross sections as obtained by Shipsey et al. [ 1] and by Fritsch and Lin [2] respectively.
Emission cross sections o b t a i n e d in this way from theoretical M O and AO + d a t a are c o m p a r e d with m e a s u r e d ones in fig. 1. Generally we find good agreement between theory and experiment. The largest differences between M O and A O + theory are found for the (relatively weak) 6 - , 3 line. F o r this line the experimental points lie above theoretical curves, but indicate a preference for the M O data, which yield higher n = 6 capture cross sections. It should be p o i n t e d out that also in the C 6- + H collision system the capture cross sections for the nond o m i n a n t l y p o p u l a t e d higher states seem to be larger than predicted by theory [16], a n d also to favour MO-calculations. In view o f the general agreement between theory a n d experiment one can ask in how much detail theory is really tested. O f course there are m o r e sublevel cross sections than measured lines, a n d no d o u b t there are other sets o f capture cross section d a t a which would yield a comparable agreement. We tried e.g. a set o f data in which the a(n) cross sections were taken from theory, but where t h e / - p o p u l a t i o n s were assumed to be distributed according to statistical weights. The resulting agreement with e x p e r i m e n t a l data was by no means worse than that shown in fig. 1. On the other hand, an equal p o p u l a t i o n o f all lsublevels within one n-shell yielded a considerably poorer agreement, the theoretical emission cross sections being significantly too low. It one assumes that the theoretical d a t a are by a n d large correct, one finds on closer inspection o f these d a t a together with table l, that the observed lines are m a i n l y due to populations o f only 3 or 4 sublevels: 5g, 5f, 6h and 6g. This is d e m o n s t r a t e d in table 2 for the example o f a collision velocity o f 0.47 a.u. starting with the theoretical d a t a o f Shipsey et al. In view o f the fact that the 6--,3 emission line is relatively weak one can state that these four levels are respon75
Volume 124, number 1,2
PHYSICS LETTERS A
14 September 1987
Table 2 Contributions (in A 2 ) of the most important sublevels to the various emission lines, as calculated from the data of Shipsey et al. [ 1 ]. The last column indicates the fraction o f the total line cross section, represented by these contributions.
Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support by the Stichting voor Zuiver-Wetenschappelijk Onderzoek (ZWO).
Lines
References
Contributions (in A 2) from levels
Fraction of total
5-3 5-4 4-3 3-2
5d
5f
5g
6g
2.2 1.0 0.1 0.3
10.5 6.0 1.5 10.7
13.4 13.4 13.4
1.4 0.8 2.9 4.1
6h
7.2 7.2 7.2
95.2% 98.4% 94.1°/o 93.4%
sible for~90% of the light observed in our experiment. In conclusion we can state that the obtained agreement between calculated and measured emission cross sections is a strong support for the calculated capture cross sections, especially for the dominantly populated levels.
The authors would like to thank J. Sijbring for his excellent technical support without which the experiments could not have been performed within the allotted time. One of us (DC) is grateful to the KVI, University of Groningen, for kind hospitality during the measurements and to the FOM-Institute in Amsterdam for the possibility to take part as a guest scientist. This is part of the research program of the
76
[ 1 ] E.J. Shipsey, T.A. Green and J.C. Browne, Phys. Rev. A 27 (1983) 821. [2] W. Fritsch and C.D. Lin, Phys. Rev. A 29 (1984) 3039. [3] R.J. Fonk, D.S. Darrow and K.P. Jachnig, Phys. Rev. A 29 (1984) 3288. [4] J. Spence and H.P. Summers, J. Phys. B 19 (1986) 3749. [5] D. Dijkkamp, D. Cirid and F.J. de Heer, Phys. Rev. Lett. 54 (1985) 1004. [6] D. Cirid, D. Dijkkamp, E. Vlieg and F.J. de Heer, J. Phys. B 18 (1985) 4745. [7] A. Salin, J. Phys. (Paris) 45 (1984) 671. [81 M. Bendahman, S. Bliman. S. Dousson, D. Hitz, R. Gayet, J. Hanssen, C. Hard and A. Satin, J. Phys. (Paris) 46 (1985) 56l. [9] M. Kimura and N.F. Lane, Phys. Rev. A 35 {1987) 70. [10] F.W. Meyer, A.M. Howald, C.C. Havener and R.A. Phaneuf, Phys. Rev. A 32 (1985) 3310. [ 11 ] D. Dijkkamp, D. CiriC E. Vlieg, A. de Boer and F.J. de Heer, J. Phys. B 18 (1985) 4763. [12] R. Geller and B. Jacquot, Nucl. lnstrum. Methods 202 (1982) 399. [13] A.G. Drentje, Nucl. lnstrum. Methods B 9 (1985) 526. [ 14] J. Stevin and W. Stifling, Rev. Sci. lnstrum. 52 (1981) 1780. [ 15 ] H.A. Bethe and E.E. Salpeter, Q u a n t u m mechanics of oneand two-electron atoms (Springer, Berlin, 1957). [16] R. Hoekstra, D. Cirid, Yu.S. Gordeev, A.N. Zinoviev. F.J. de Heer and R. Morgenstern, to be published.
PHYSICS LETTERS A
14 September 1987
E L E C T R O N C A P T U R E I N C O L L I S I O N S O F 0 8+ W I T H H: ABSOLUTE LINE EMISSION CROSS SECTIONS R. H O E K S T R A a,b, D. C I R I C c, F.J. DE H E E R b and R. M O R G E N S T E R N a a Kernfysisch Versneller lnstituut, Rijksuniversiteit Groningen, 9747AA Groningen, The Netherlands b FOM-InstituteforAtomic andMolecularPhysics, 1098 SJAmsterdam, The Netherlands c Boris Kidric Institute, Belgrade, Yugoslavia
Received 23 June 1987; revised manuscript received 24 July 1987;accepted for publication 27 July 1987 Communicated by B. Fricke
We present the first experimental determination of absolute line emission cross sections, resulting from charge changing collisions of bare oxygen ions with atomic hydrogen. The O VIII lines resulting from the dominantly populated n= 5 level confirm to a large extent the almost coinciding theoretical data obtained with an MO approach by Shipsey et al. and with an AO + approach by Fritsch and Lin. Emission from the non-dominantly populated n = 6 level is found to be stronger than predicted by theory and favours the MO data.
Electron capture processes in collisions of bare ions with atomic hydrogen are of fundamental interest [ 1,2] and play an important role in the diagnostics of fusion plasmas, e.g. in connection with the injection o f atomic hydrogen beams [3,4]. The most detailed information on these processes can be obtained by measuring the cross sections for line emission from the excited states formed by electron capture. In our program to measure such lines, so far the collision systems He 2+, C 6÷ and N 7+ o n H have been investigated [5,6]. We now succeeded to measure emission cross sections for the O 8+ + H system, which is especially interesting for plasma physics applications, and which could not be investigated before, owing to small O 8÷ beam intensities. Our measurements are performed in an accelerator range between 10 and 18 kV and are confined to the O VIII lines 6--.3, 5 ~ 4 , 5 ~ 3 , 4 ~ 3 and 3 ~ 2 in the VUV range, with the numbers referring to the main quantum numbers n involved in the transition. A measurement o f visible lines which would be especially interesting from an applied point of view is still impossible with the presently available ion beam and has to be postponed to future investigations. The most extensive calculations o f partial cross sections for O 7÷ (n, l) population during O 8÷ colli-
sions on H have been performed by Shipsey et al. [ 1 ] using a molecular orbital ( M O ) expansion, and by Fritsch and Lin [2] using an extended atomic orbital ( A O + ) expansion o f the electronic wavefunctions involved. We will compare our measurements with their results. Up to now these calculations as well as other ones by Salin [ 7 ], Bendahman et al. [8] and Kimura and Lane [9] could only be tested by comparison with experiments in which total charge exchange cross sections were determined. The most extensive measurements of this kind were performed by Meyer et al. [10] between 0.1 and 10 keV/amu, yielding a generally good agreement with theory. However these experimental data are not sensitive to the relative distribution o f partial cross sections for capture into certain nl-states. As opposed to this line emision cross sections measured in our experiments are dependent on partial cross sections, although the fine structure of lines originating from different/-levels on one n-shell cannot be resolved due to the quasi/-degeneracy in hydrogenic systems (see further on for more details). The experimental set up, described before [ 11 ] will briefly be summarized. A beam of O 8÷ was produced by an electron-cyclotron-resonance ( E C R ) source of the M I N I M A F I O S type [ 12,13 ]. The ~80 isotope was
0375-9601/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
73
Volume 124, number 1,2
PHYSICS LETTERS A
used to avoid beam c o n t a m i n a t i o n s of H ] or He-" ~. At kinetic energies between 80 and 160 keV beam currents of 5 to 10 nA (electric) have been obtained at beam diameters of ca 3 mm. H2 was dissociated by a Slevin-type radio-frequency (rf) discharge source [14], yielding a dissociation fraction of ca 65%. The absolute density profiles of H a n d H2 in the collision region were d e t e r m i n e d by observing visible light from the two target constituents induced by electron impact, and by exploiting the knowledge of ratios of cross sections for the corresponding processes [ 16 ]. UV light emitted from the 0 7~ ions was observed by a grazing incidence m o n o c h r o m a t o r which is equipped with a position sensitive microchannelplate detector a n d which is absolutely calibrated on its wavelength d e p e n d e n t sensitivity using various electron and ion impact processes with known cross sections [11]. All light m e a s u r e m e n t s were performed with a purely molecular H2 target on the one hand, and - with the rf-discharge on - with a mixed H and H2 target on the other hand. The error in the experimental results is due to a relative and systematical absolute error. The relative error is given by the quadratical sum of the statistical error ( 5 - 2 5 % ) a n d the fluctuation in target density due to different overlaps of ion and target beams (5%).
14 September 1987
When s u m m e d quadratically the uncertainties in the absolute target density (15%) and absolute spectrometer calibration give rise to an absolute error of 20 to 35% depending on the wavelength of the radiation. A possible error due to polarization of the emitted light has been omitted because it will be certainly smaller than 15% (see the more detailed discussion of Dijkkamp et al. [ 17 ]). We estimate the total error to be 25%. For a comparison of our experimental results with theory we have calculated line emission cross sections from the capture cross sections given by Shipsey et al. [ 1 ] and by Fritsch and Lin [ 2 ]. Only states with main q u a n t u m n u m b e r s n = 4, 5 and 6 have to be considered since population of other states occurs to a negligible a m o u n t . Lifetimes and partial transition probabilities in the hydrogen like 0 7 ~ ion can easily be calculated using the formulas given by Bethe and Salpeter [ 15 ]. All lifetimes involved turn out to be below 1 ns. This means that a complete cascading occurs within the viewing range of the monochromator and consequently has to be taken into account in calculating the emission cross sections. In table 1 we give the fractions of substate populations with m a i n q u a n t u m n u m b e r s n = 4, 5 and 6, contributing to the various lines observed in our experiments.
Table 1 Calculated fractions of nl-state populations (in %), which contribute to n ' ~ n" line emission by direct or cascade decay. Measured transitions
n
F/' --~ n "
74
n,/-contributions (%) /=0
1
2
3
4
5
6-3 (2=lT.lnm)
6
27.14
4.22
22.37
51.49
5-3 0.=20.0 nm)
6 5
0.6l 31.87
0.41 4.25
0.52 23.63
4.10 63.74
28.43 0
0
5-4 (2=63.3 nm
6 5
0.32 22.73
0.27 2.20
0.29 10.70
2.13 36.26
16.18 100
100 -
4-3 (2=29.3 nm
6 5 4
0.23 0.95 41.59
0.87 0.84 4.20
0.77 0.79 25.44
8.27 9.23 100
59.5 100 -
100 -
3-2 (,i= 10.3 nm)
6 5 4
4.64 4.73 4.92
4.38 4.35 4.20
3.87 3.58 3.01
53.32 64.83 100
84.31 100 -
100
0
0
Volume 124, number 1,2
PHYSICS LETTERS A
F r o m this table one finds e.g. the cross section for 5-3 emission to be
08÷+ H
*2
A 60
,
,
i
i
14 September 1987
i
I
a ( 5 ~ 3 ) = 0.006 l a ( 6 s ) + 0.0041 a ( 6 p )
50
z,O + 0 . 0 0 5 2 a ( 6 d ) + 0.0410tr(6f) + 0.2843tr(6g) 30
+ 0.3187tr(5s) + 0.0425tr(5p)
0 ~ I 3 ~ 2 : 10.2 nm 20
I
I
i
I
I
L~O
f
+ 0.2363a(5d) + 0.6374tr(5f).
T
I 3o ~ 20 0"~ZI][ ~---3:29-3 nm I
I
I
i
I
i
30
20 0"~2~15 ~/+ : 63.3 nm I
I
I
I
I
0.2
0.3
0.4
0 I5
Ol6
V
#
,
,
I
I
f
0.2
o13
o14
I
I
0.7 al ul
~'-
Oa*+ H ,
,
,
16 12 10 8 6
O~Z[~ 5 ~ 3 : 20.Onto I
I
o.s
0.6
I
o.7 a~.
V
Fig. 1. Emission cross sections for various 07 + (n--, n') lines after 08+ collisions on H as function of the collision velocity. Solid error bars indicate statistical errors, dotted error bars indicate the range of systematic uncertainties. The dotted and solid lines represent theoretical emission cross sections as obtained by Shipsey et al. [ 1] and by Fritsch and Lin [2] respectively.
Emission cross sections o b t a i n e d in this way from theoretical M O and AO + d a t a are c o m p a r e d with m e a s u r e d ones in fig. 1. Generally we find good agreement between theory and experiment. The largest differences between M O and A O + theory are found for the (relatively weak) 6 - , 3 line. F o r this line the experimental points lie above theoretical curves, but indicate a preference for the M O data, which yield higher n = 6 capture cross sections. It should be p o i n t e d out that also in the C 6- + H collision system the capture cross sections for the nond o m i n a n t l y p o p u l a t e d higher states seem to be larger than predicted by theory [16], a n d also to favour MO-calculations. In view o f the general agreement between theory a n d experiment one can ask in how much detail theory is really tested. O f course there are m o r e sublevel cross sections than measured lines, a n d no d o u b t there are other sets o f capture cross section d a t a which would yield a comparable agreement. We tried e.g. a set o f data in which the a(n) cross sections were taken from theory, but where t h e / - p o p u l a t i o n s were assumed to be distributed according to statistical weights. The resulting agreement with e x p e r i m e n t a l data was by no means worse than that shown in fig. 1. On the other hand, an equal p o p u l a t i o n o f all lsublevels within one n-shell yielded a considerably poorer agreement, the theoretical emission cross sections being significantly too low. It one assumes that the theoretical d a t a are by a n d large correct, one finds on closer inspection o f these d a t a together with table l, that the observed lines are m a i n l y due to populations o f only 3 or 4 sublevels: 5g, 5f, 6h and 6g. This is d e m o n s t r a t e d in table 2 for the example o f a collision velocity o f 0.47 a.u. starting with the theoretical d a t a o f Shipsey et al. In view o f the fact that the 6--,3 emission line is relatively weak one can state that these four levels are respon75
Volume 124, number 1,2
PHYSICS LETTERS A
14 September 1987
Table 2 Contributions (in A 2 ) of the most important sublevels to the various emission lines, as calculated from the data of Shipsey et al. [ 1 ]. The last column indicates the fraction o f the total line cross section, represented by these contributions.
Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support by the Stichting voor Zuiver-Wetenschappelijk Onderzoek (ZWO).
Lines
References
Contributions (in A 2) from levels
Fraction of total
5-3 5-4 4-3 3-2
5d
5f
5g
6g
2.2 1.0 0.1 0.3
10.5 6.0 1.5 10.7
13.4 13.4 13.4
1.4 0.8 2.9 4.1
6h
7.2 7.2 7.2
95.2% 98.4% 94.1°/o 93.4%
sible for~90% of the light observed in our experiment. In conclusion we can state that the obtained agreement between calculated and measured emission cross sections is a strong support for the calculated capture cross sections, especially for the dominantly populated levels.
The authors would like to thank J. Sijbring for his excellent technical support without which the experiments could not have been performed within the allotted time. One of us (DC) is grateful to the KVI, University of Groningen, for kind hospitality during the measurements and to the FOM-Institute in Amsterdam for the possibility to take part as a guest scientist. This is part of the research program of the
76
[ 1 ] E.J. Shipsey, T.A. Green and J.C. Browne, Phys. Rev. A 27 (1983) 821. [2] W. Fritsch and C.D. Lin, Phys. Rev. A 29 (1984) 3039. [3] R.J. Fonk, D.S. Darrow and K.P. Jachnig, Phys. Rev. A 29 (1984) 3288. [4] J. Spence and H.P. Summers, J. Phys. B 19 (1986) 3749. [5] D. Dijkkamp, D. Cirid and F.J. de Heer, Phys. Rev. Lett. 54 (1985) 1004. [6] D. Cirid, D. Dijkkamp, E. Vlieg and F.J. de Heer, J. Phys. B 18 (1985) 4745. [7] A. Salin, J. Phys. (Paris) 45 (1984) 671. [81 M. Bendahman, S. Bliman. S. Dousson, D. Hitz, R. Gayet, J. Hanssen, C. Hard and A. Satin, J. Phys. (Paris) 46 (1985) 56l. [9] M. Kimura and N.F. Lane, Phys. Rev. A 35 {1987) 70. [10] F.W. Meyer, A.M. Howald, C.C. Havener and R.A. Phaneuf, Phys. Rev. A 32 (1985) 3310. [ 11 ] D. Dijkkamp, D. CiriC E. Vlieg, A. de Boer and F.J. de Heer, J. Phys. B 18 (1985) 4763. [12] R. Geller and B. Jacquot, Nucl. lnstrum. Methods 202 (1982) 399. [13] A.G. Drentje, Nucl. lnstrum. Methods B 9 (1985) 526. [ 14] J. Stevin and W. Stifling, Rev. Sci. lnstrum. 52 (1981) 1780. [ 15 ] H.A. Bethe and E.E. Salpeter, Q u a n t u m mechanics of oneand two-electron atoms (Springer, Berlin, 1957). [16] R. Hoekstra, D. Cirid, Yu.S. Gordeev, A.N. Zinoviev. F.J. de Heer and R. Morgenstern, to be published.