- Email: [email protected]
Two-center electron-electron interactions in collisions of fast Ne7+ and Ne6+ ions with gas atoms
s.--
Nuclear Instruments and Methods in Physics Research B 98 (1995) 262-265
Kl g
NOMB
Beam Interactions with Materials 8 Atoms
ELSEVIER
Two-center electron-electron interactions in collisions of fast Ne7+ and Ne6+ ions with gas atoms B. Sulik a,
*,S. Ritz
‘, I. Kid& a, G. Xiao b, G. Schiwietz b, K. Sommer b, R. Kiihrbriick b, M. Grether b, N. Stolterfoht b
AInstitute of Nuclear Research of ’ Hahn-Meitner
the Hungarim
of Sciences, POB 51, H-4001 Dehrecm,
Academy
Institute, Glienicker
Str. 100. D-14109
Hungar)
Berlitz, Germany
Abstract Experimental and theoretical studies of the two-center electron-electron interaction occurring during energetic ion-atom collisions are presented. Experiments were performed using the accelerator facility VICKSI at HMI, Berlin. Electron spectra from Auger and Coster-Kronig transitions following the excitation of a highly charged neon projectile have been studied by zero-degree electron spectroscopy. Various target atoms with atomic numbers ranging from 1-18 were used as exciting partners. We applied both impact parameter treatments and the plane wave Born approximation to describe screening effects and dielectronic two-center processes (“antiscreening”). We found that the ls-21 excitation of the Ne” projectile at 8.5 MeV/u impact energy is mainly due to the screened target nucleus. In contrary, two-center processes are likely to be dominant in the 2s-nI excitation of the 6 MeV/u Neh’ projectile. The 2s-nl cross sections are roughly proportional to the number of electrons per target atom. This fact suggests that, in disagreement with first order theories, the 2s-nl excitation is significantly governed by the two center electron-electron interaction.
Collisional two-center electron-electron interaction comes into play when both partners carry electrons into an atomic collision. The Coulomb field of the nuclei may strongly be screened if the electrons remain in their ground state during the collision. Screening effects can reduce significantly the cross section of inelastic processes. In specific cases. inelastic processes are enhanced by the mutual collision of projectile and target electrons, i.e., when the repulsion between the electrons changes their states during the collision. This latter process is referred to as dielectronic process [l]. It has often been denoted as antiscreening in literature [2]. Both collisional screening effects and dielectronic two-center processes are manifestations of the two-center electron-electron interaction [3]. They were treated first by Bates and Griffing [4] for H + H collisions within the framework of the plane wave Born approximation (PWBA). Similar studies have been performed by several authors (e.g. Refs. [2,5-S]). Contrary to the early theoretical studies [4], the detailed experimental investigations of dielectronic two-center processes have been performed only recently. In high-energy atomic collisions, evidence for dielectronic two-center processes has been provided by Zouros et al. [9] and HiilskGtter et al. [IO]. Recently, it has been demonstrated that dielec-
* Corresponding 0168-583X/95/$09.50
author. 0
SSDI 0168-583X(9.5)00121-2
tronic processes yield a large contribution to the electron loss [ll-131 and to the excitation [13] of the projectile in many collision systems, in accordance with the theory. DuBois and Manson [14] studied the ionization of the target by neutral H and He projectiles. They found that the production of low energy electrons emitted from the target outer shells is mainly due to dielectronic two-center processes. In the present work, we compare the results of two studies performed on two different collision systems. In the first study [15], the method of 0” Auger spectroscopy was applied to measure state-selective K-shell excitation in Li-like Ne’+ incident on Hz, He, CH,, Ne and Ar with 8.5 MeV/u impact energy. For details see Ref. [15]. A separate analysis of the states ZP (dominant component: ls(2s2p3P)‘P) and ZP (dominant component: ls(2Qp ‘P)‘P) was performed. The intensity ratio of the two lines significantly depends on the target atomic number. This dependence was interpreted as a result of time ordering, interference and dealignment effects in the process of single excitation. In the calculations, the semiclassical approximation was used up to second order. For the screening effect we utilized the method of Ritz et al. [16]. For the dielectronic process, the closure approximation for the semiclassical approximation was applied (see e.g. Refs. [17,18]). Good agreement was found with the experimental data. It supports that the calculated contributions to the cross sections should be realistic. Those for the emission
1995 Elsevier Science B.V. All rights reserved
B. Sulik et al. / Nucl. Instr. and Meth. in Phys. Res. B 98 (I 995) 262-265
of the :P line at 0” are displayed in Fig. 1. They can be considered as indirectly verified by the experiments. Fig. 1 shows that the screening contribution to the ls-2p excitation is roughly equal to, or higher than the dielectronic contribution in the investigated target atomic number region. In the present work, the second study [19] is treated in more details. Our aim was to find a collision system where the role of dielectronic two-center processes is dominant. The possible dominance of dielectronic two-center processes is apparent with an intuitive picture emerging from the analysis given by Briggs and Taulbjerg within the PWBA framework [5]. Their analysis has shown that twocenter dielectronic processes become dominant for excitations associated with small energy and momentum transfer, i.e., for distant and fast collisions. In distant collisions the nucleus of a neutral target atom is almost completely screened and target electrons enter as the most effective agents in exciting or ionizing the projectile. For the second study, we selected an excitation process with significantly smaller energy and momentum transfer values than those characterizing the K-shell excitation of the neon projectile in the first study. We measured the 2s-nI excitation of the metastable Neh+ ls’2s2p “PO projectile followed by a Coster-Kronig (C-K) transition: Nehf ls22s2p 3Po + ls22pnI(
n > 6)
+ ls’2s + e-(C-K). The energy transfer value for the ls-2p transition of Ne’+ is 895 eV, while it is 204 eV for the 2s-71 transition of the Ne ” ion [20]. In the experiments, different target gases (H,, He, CH,, N1, Ne, Ar) in a gas cell were bombarded by 120 MeV Ne ‘+ ions at a beam line of the VICKSI accelerator facility in Hahn-Meitner-Institute, Berlin. The ejected electron spectra were acquired by a tandem elec-
10-19
170 MeV Ne’+ 1s -> 2p
I.1 100
1
10’ Target Atomic Number Z,
Fig. 1. Differential Auger emission cross section and its contributions for the I P line. Labeled lines: theory (semiclassical approximation). The cross section belonging to the bare target nuclei is
also displayed for reference.
263
1IZO-MeV NeGC+ H,, He I
00
10'1
2.8
3.0
3.2
3.4
3.6
:8
Electron Energy (keV) at zero degree in 120 MeV Neht +H, and Ne’+ +He collisions with the same target pressure (5.3X lo-’ mbar) in the gas cell. The mean quantum numbers arc indicated at the different Coster-Kronig groups. Fig. 2. Electron
spectra
measured
tron spectrometer at zero degrees relative to the beam direction. The experimental arrangement was the same as that given in Ref. [21], so that only a few details shall be given here. The metastable fraction of the beam was close to 50% [22]. The absolute target pressure in the gas cell, i.e., the number-density of the scattering centers was directly measured in the gas cell by means of a membranetype Baratron pressure sensor. It was kept constant by a regulated valve. Therefore the relative cross sections for different targets could be determined. Fig. 2 displays the electron spectra obtained with Hz and He targets. The Coster-Kronig peak groups are located on the two wings of the electron loss (EL) peak. The intensities of the groups are proportional to the cross sections of 2s-nl excitations summed over the orbital angular momentum quantum number 1. We note that for the H, target electron intensities are larger than that for He target at the same target cell pressure. This is true not only for the Coster-Kronig peaks but for the whole region of the electron loss peak. This experimental finding is in agreement with the above mentioned intuitive picture, which suggests that both the hydrogen and helium nuclei are almost completely screened, and the excitation of the projectile is mostly due to dielectronic two-center processes. In this case, the two loosely bound electrons of the HZ molecule should be more effective exciting agents than the more tightly bound electrons of He. Hence, it gives a clear evidence for the importance of dielectronic two-center processes for the investigated collision system. In the present work, our attention is focused on the relative cross sections for producing the n = 7 final state. The line group intensities have been evaluated after transforming the spectra into the projectile frame of reference and subtracting the background. In this way, we obtained
3.2. COLLISIONS WITH HEAVY PARTICLES
B. Sulik et al. / Nucl. Instr. and Meth. in Phys. Rex B 98 (1995) 262-265
264
relative yields for electron emission in the projectile frame at 0” which are proportional to the corresponding differential cross sections. These are the quantities to be compared with the theory. A more detailed analysis of the data is to be published [23]. Calculations have been performed for n = 7, within the PWBA framework. The screening and dielectronic contributions were calculated separately, according to the formulas of Ref. [8]. The 2s-nlm projectile form factors were determined by the help of the rotation matrix method [24]. The differential cross section was calculated within the LS coupling scheme, supposing that only the final states with M = 0 will contribute to the Coster-Kronig emission at 0”. We used screened hydrogenic wave functions for both the projectile and the target with Slater screening constants [25]. More precise calculations appeared to be not necessary, since we analyzed cross section ratios rather than absolute cross sections. The calculations are also not sensitive to the choice of the coupling scheme. It was found that the angular distribution of the Coster-Kronig emission, calculated within the framework of the LS coupling scheme, is not far from isotropy. In order to compare experiment and theory, the molecular targets were treated as a group of neutral atoms. Hence, we reduced the measured cross sections to individual target atoms. For carbon, e.g., we subtracted the measured Ha cross section twice from the CH, cross section. This rough model provides data for the molecular targets which look consistent with those for the noble gases. The measured cross sections were normalized to the theory at the hydrogen atom. The comparison of theory and experiment is presented in Fig. 3. There is an excellent agreement between experiment and theory (solid curve, labeled by “total”) when
120 MeV Ne6+
2s -> 7
, ’
I
I
I
100
I Acknowledgement
10’
Target
Atomic Number
going from H, to He. For heavier targets, the agreement breaks down. PWBA predicts a steeper increase of the cross sections with the target atomic number Z, than that of the experimental data. This behavior originates from the calculated screening contribution. The Z-r-dependence of the dielectronic contribution is very similar to that of the experimental data for heavier targets. An important finding is that the measured single differential Coster-Kronig emission cross sections are nearly proportional to the number of the target electrons. The experimental cross section ratios (cross section divided by the cross section for the hydrogen atom) are 1.7 ) 0.1 for He, 5.9 f 0.6 for C, 6.5 +_0.5 for N, 9.5 f 0.7 for Ne and 14.5 & 1.8 for Ar. This regular behavior appears to agree well with the intuitive picture that the studied excitation process is dominated by the projectile electron - target electron interactions. Surprisingly, it is also true for heavier targets, contrary to the PWBA results. When comparing the calculated curves in Figs. 1 and 3, one may realize that the behavior of the different contributions is very similar in the two cases. The most important difference is that the dielectronic contribution becomes dominant for light targets in the 2s-7 excitation case. The breakdown of the theory for heavy targets in the same case may be attributed to a significant difference of the two collision systems. In the case of the ls-2p excitation, it can be justified to restrict considerations to the n < 2 manifold in the first or second order calculation. One may argue that the n = 2 shell of the Ne’+ ion is sufficiently separated from higher-lying shells. In the case of the 2s-nl excitations, however, there are many states close to each other. First order calculations may be out of their region of applicability for heavier targets, and a realistic higher-order calculation would need an enormous size for the basis set. It should also be noted that the polarization of the target by the highly charged projectile ion is neglected within the framework of the present first order theories. For the case of the Ne6+ 2s-nl excitations by Hz and He targets, it can be concluded that the measured cross section ratios provide evidence for an inelastic atomic collision process which is dominated by the target electron-projectile electron interactions. The surprising fact is that the significance of two-center electron-electron interactions is likely to be true for heavier, many-electron targets. This finding suggests to study the process in a wider range of targets and impact velocities, and treat the present collision system beyond first order theories.
Z,
Fig. 3. Differential Coster-Kronig emission cross section and its contributions for n = 7. Labeled lines: theory (PWBA), symbols: present experiment (normalized to theory at the hydrogen The cross section belonging to the bare target nuclei displayed for reference.
target). is also
This work was supported by the German-Hungarian Collaboration in Science and Technology (Project No. 751, by the Hungarian Academic Research Fund (AKA, No. 1-300-2-91-O-790) and by the Hungarian National Science Fund (OTKA, No. 3011).
B. Sulik et al. /Nucl. Instr. and Meth. in Phys. Res. B 98 (1995) 262-265
References
[ 131 T.J.M. Zouros, D.H. Lee, J.M. Sanders and P. Richard, Nucl. Instr. and Meth. B 79 (1993) 166.
[l] N. Stolterfoht,
Nucl. Ins&. and Meth. B 53 (1991) 477.
[2] J.H. MC&ire, N. Stolterfoht and P.R. Simony, Phys. Rev. A 24 (1981) 97. [31 N. Stolterfoht, in Spectroscopy and Collisons of Few Electron Ions, eds. M. Ivascu, V. Florescu and V. Zoran (World Scientific, Singapore, 1989) p. 342. 141 D.R. Bates and G. Griffing, Proc. Phys. Sot. (London) Sect. A 66 (1953) 961; Proc. Phys. Sot. (London) Sect. A 67 (1954) 663. [51 J.S. Briggs and K. Taulbjerg, in Structure and Collisions of Ions and Atoms, ed. I.A. Sellin (Springer, Berlin, 1978) p. 105. [61K.L. Bell, V. Dose and A.E. Kingston. J. Phys. B 2 (1969) 831. [71 R. Anholt, Phys. Lett. A 114 (1986) 126. k31E.C. Montenegro and W.E. Meyerhof, Phys Rev. A 43 (1991) 2289. [91 T.J.M. Zouros, D.H. Lee and P. Richard, Phys. Rev. Lett. 62 (1989) 2261. [lOI H.P. Hilskiitter, W.E. Meyerhof, E.D. Dillard and S.T. Guardola, Phys. Rev. L&t. 63 (1989) 1938. [ill H.-P. HiilskBtter, B. Feinberg, W.E. Meyerhof, A. Belkacem, J.R. Alonso, L. Blumenfeld, E.A. Dillard, H. Gould, N. Guardala, G.F. Krebs, M.A. McMahan, M.E. RhoadesBrown, B.S. Rudde, J. Schweppe, D.W. Spooner, K. Street, P. Thieberger and H.E. Wegner, Phys. Rev. A 44 (1991) 1712.
WI D.H. Lee, T.J.M. Zouros, Anthony,
265
Y.D. Wang
J.M. Sanders, and J.H. McGuire,
P. Richard, J.M. Phys. Rev. A 46
(141 R.D. DuBois and Steven. T. Manson, Nucl. Instr. and Meth. B 86 (1994) 161. [15] N. Stolterfoht, A. Mattis, D. Schneider, G. Schiwietz, B. Skogvall, B. Sulik and S. Ritz, Phys. Rev. A 48 (1993) 2986. [16] S. Ritz, B. Sulik, I. Kid& and N. Stolterfoht, Phys. Rev. A 47 (1993) 1930. [17] E.C. Montenegro and W.E. Meyerhof, Phys. Rev. A 46 (1992) 5506. [18] N.M. Kabachnik, J. Phys. B 26 (1993) 3803. [19] B. Sulik, N. Stolterfoht, S. Ritz, 1. KBdBr, G. Xiao, G. Schiwietz, P. Grande, R. Kijhrbriick, K. Sommer and M. Grether, in Abstract of Contributed Papers of the XVIII ICPEAC, eds. T. Andersen, B. Fastrup, I? Folkmann and H. Knudsen (University of Aarhus, Denmark, 1993) p. 528. ~201R.J. Maurer and R.L. Watson, At. Data and Nucl. Data Tables 34 (1986) 185. ml A. Itoh, D. Schneider, T. Schneider, T.J.M. Zouros, G. Nolte, G. Schiwietz, W. Zeitz and N. Stolterfoht, Phys. Rev. A 31 (1985) 684. La N. Stolterfoht, Phys. Rep. 146 (1987) p. 401. [231 B. Sulik, S. Ritz, I. Khdlr, G. Xiao, G. Schiwietz, K. Sommer, P. Grande, R. Kiihrbriick, M. Grether and N. Stolterfoht, submitted to Phys. Rev. A. [24] M.R.C. McDowell and J.P. Coleman, Introduction to the Theory of Ion-Atom Collisions (North-Holland, Amsterdam-London, 1970) p. 325 and p. 317. 1251J.C. Slater, Phys. Rev. 36 (1930) 57.
(1992) 1374.
3.2. COLLISIONS
WITH HEAVY PARTICLES
Nuclear Instruments and Methods in Physics Research B 98 (1995) 262-265
Kl g
NOMB
Beam Interactions with Materials 8 Atoms
ELSEVIER
Two-center electron-electron interactions in collisions of fast Ne7+ and Ne6+ ions with gas atoms B. Sulik a,
*,S. Ritz
‘, I. Kid& a, G. Xiao b, G. Schiwietz b, K. Sommer b, R. Kiihrbriick b, M. Grether b, N. Stolterfoht b
AInstitute of Nuclear Research of ’ Hahn-Meitner
the Hungarim
of Sciences, POB 51, H-4001 Dehrecm,
Academy
Institute, Glienicker
Str. 100. D-14109
Hungar)
Berlitz, Germany
Abstract Experimental and theoretical studies of the two-center electron-electron interaction occurring during energetic ion-atom collisions are presented. Experiments were performed using the accelerator facility VICKSI at HMI, Berlin. Electron spectra from Auger and Coster-Kronig transitions following the excitation of a highly charged neon projectile have been studied by zero-degree electron spectroscopy. Various target atoms with atomic numbers ranging from 1-18 were used as exciting partners. We applied both impact parameter treatments and the plane wave Born approximation to describe screening effects and dielectronic two-center processes (“antiscreening”). We found that the ls-21 excitation of the Ne” projectile at 8.5 MeV/u impact energy is mainly due to the screened target nucleus. In contrary, two-center processes are likely to be dominant in the 2s-nI excitation of the 6 MeV/u Neh’ projectile. The 2s-nl cross sections are roughly proportional to the number of electrons per target atom. This fact suggests that, in disagreement with first order theories, the 2s-nl excitation is significantly governed by the two center electron-electron interaction.
Collisional two-center electron-electron interaction comes into play when both partners carry electrons into an atomic collision. The Coulomb field of the nuclei may strongly be screened if the electrons remain in their ground state during the collision. Screening effects can reduce significantly the cross section of inelastic processes. In specific cases. inelastic processes are enhanced by the mutual collision of projectile and target electrons, i.e., when the repulsion between the electrons changes their states during the collision. This latter process is referred to as dielectronic process [l]. It has often been denoted as antiscreening in literature [2]. Both collisional screening effects and dielectronic two-center processes are manifestations of the two-center electron-electron interaction [3]. They were treated first by Bates and Griffing [4] for H + H collisions within the framework of the plane wave Born approximation (PWBA). Similar studies have been performed by several authors (e.g. Refs. [2,5-S]). Contrary to the early theoretical studies [4], the detailed experimental investigations of dielectronic two-center processes have been performed only recently. In high-energy atomic collisions, evidence for dielectronic two-center processes has been provided by Zouros et al. [9] and HiilskGtter et al. [IO]. Recently, it has been demonstrated that dielec-
* Corresponding 0168-583X/95/$09.50
author. 0
SSDI 0168-583X(9.5)00121-2
tronic processes yield a large contribution to the electron loss [ll-131 and to the excitation [13] of the projectile in many collision systems, in accordance with the theory. DuBois and Manson [14] studied the ionization of the target by neutral H and He projectiles. They found that the production of low energy electrons emitted from the target outer shells is mainly due to dielectronic two-center processes. In the present work, we compare the results of two studies performed on two different collision systems. In the first study [15], the method of 0” Auger spectroscopy was applied to measure state-selective K-shell excitation in Li-like Ne’+ incident on Hz, He, CH,, Ne and Ar with 8.5 MeV/u impact energy. For details see Ref. [15]. A separate analysis of the states ZP (dominant component: ls(2s2p3P)‘P) and ZP (dominant component: ls(2Qp ‘P)‘P) was performed. The intensity ratio of the two lines significantly depends on the target atomic number. This dependence was interpreted as a result of time ordering, interference and dealignment effects in the process of single excitation. In the calculations, the semiclassical approximation was used up to second order. For the screening effect we utilized the method of Ritz et al. [16]. For the dielectronic process, the closure approximation for the semiclassical approximation was applied (see e.g. Refs. [17,18]). Good agreement was found with the experimental data. It supports that the calculated contributions to the cross sections should be realistic. Those for the emission
1995 Elsevier Science B.V. All rights reserved
B. Sulik et al. / Nucl. Instr. and Meth. in Phys. Res. B 98 (I 995) 262-265
of the :P line at 0” are displayed in Fig. 1. They can be considered as indirectly verified by the experiments. Fig. 1 shows that the screening contribution to the ls-2p excitation is roughly equal to, or higher than the dielectronic contribution in the investigated target atomic number region. In the present work, the second study [19] is treated in more details. Our aim was to find a collision system where the role of dielectronic two-center processes is dominant. The possible dominance of dielectronic two-center processes is apparent with an intuitive picture emerging from the analysis given by Briggs and Taulbjerg within the PWBA framework [5]. Their analysis has shown that twocenter dielectronic processes become dominant for excitations associated with small energy and momentum transfer, i.e., for distant and fast collisions. In distant collisions the nucleus of a neutral target atom is almost completely screened and target electrons enter as the most effective agents in exciting or ionizing the projectile. For the second study, we selected an excitation process with significantly smaller energy and momentum transfer values than those characterizing the K-shell excitation of the neon projectile in the first study. We measured the 2s-nI excitation of the metastable Neh+ ls’2s2p “PO projectile followed by a Coster-Kronig (C-K) transition: Nehf ls22s2p 3Po + ls22pnI(
n > 6)
+ ls’2s + e-(C-K). The energy transfer value for the ls-2p transition of Ne’+ is 895 eV, while it is 204 eV for the 2s-71 transition of the Ne ” ion [20]. In the experiments, different target gases (H,, He, CH,, N1, Ne, Ar) in a gas cell were bombarded by 120 MeV Ne ‘+ ions at a beam line of the VICKSI accelerator facility in Hahn-Meitner-Institute, Berlin. The ejected electron spectra were acquired by a tandem elec-
10-19
170 MeV Ne’+ 1s -> 2p
I.1 100
1
10’ Target Atomic Number Z,
Fig. 1. Differential Auger emission cross section and its contributions for the I P line. Labeled lines: theory (semiclassical approximation). The cross section belonging to the bare target nuclei is
also displayed for reference.
263
1IZO-MeV NeGC+ H,, He I
00
10'1
2.8
3.0
3.2
3.4
3.6
:8
Electron Energy (keV) at zero degree in 120 MeV Neht +H, and Ne’+ +He collisions with the same target pressure (5.3X lo-’ mbar) in the gas cell. The mean quantum numbers arc indicated at the different Coster-Kronig groups. Fig. 2. Electron
spectra
measured
tron spectrometer at zero degrees relative to the beam direction. The experimental arrangement was the same as that given in Ref. [21], so that only a few details shall be given here. The metastable fraction of the beam was close to 50% [22]. The absolute target pressure in the gas cell, i.e., the number-density of the scattering centers was directly measured in the gas cell by means of a membranetype Baratron pressure sensor. It was kept constant by a regulated valve. Therefore the relative cross sections for different targets could be determined. Fig. 2 displays the electron spectra obtained with Hz and He targets. The Coster-Kronig peak groups are located on the two wings of the electron loss (EL) peak. The intensities of the groups are proportional to the cross sections of 2s-nl excitations summed over the orbital angular momentum quantum number 1. We note that for the H, target electron intensities are larger than that for He target at the same target cell pressure. This is true not only for the Coster-Kronig peaks but for the whole region of the electron loss peak. This experimental finding is in agreement with the above mentioned intuitive picture, which suggests that both the hydrogen and helium nuclei are almost completely screened, and the excitation of the projectile is mostly due to dielectronic two-center processes. In this case, the two loosely bound electrons of the HZ molecule should be more effective exciting agents than the more tightly bound electrons of He. Hence, it gives a clear evidence for the importance of dielectronic two-center processes for the investigated collision system. In the present work, our attention is focused on the relative cross sections for producing the n = 7 final state. The line group intensities have been evaluated after transforming the spectra into the projectile frame of reference and subtracting the background. In this way, we obtained
3.2. COLLISIONS WITH HEAVY PARTICLES
B. Sulik et al. / Nucl. Instr. and Meth. in Phys. Rex B 98 (1995) 262-265
264
relative yields for electron emission in the projectile frame at 0” which are proportional to the corresponding differential cross sections. These are the quantities to be compared with the theory. A more detailed analysis of the data is to be published [23]. Calculations have been performed for n = 7, within the PWBA framework. The screening and dielectronic contributions were calculated separately, according to the formulas of Ref. [8]. The 2s-nlm projectile form factors were determined by the help of the rotation matrix method [24]. The differential cross section was calculated within the LS coupling scheme, supposing that only the final states with M = 0 will contribute to the Coster-Kronig emission at 0”. We used screened hydrogenic wave functions for both the projectile and the target with Slater screening constants [25]. More precise calculations appeared to be not necessary, since we analyzed cross section ratios rather than absolute cross sections. The calculations are also not sensitive to the choice of the coupling scheme. It was found that the angular distribution of the Coster-Kronig emission, calculated within the framework of the LS coupling scheme, is not far from isotropy. In order to compare experiment and theory, the molecular targets were treated as a group of neutral atoms. Hence, we reduced the measured cross sections to individual target atoms. For carbon, e.g., we subtracted the measured Ha cross section twice from the CH, cross section. This rough model provides data for the molecular targets which look consistent with those for the noble gases. The measured cross sections were normalized to the theory at the hydrogen atom. The comparison of theory and experiment is presented in Fig. 3. There is an excellent agreement between experiment and theory (solid curve, labeled by “total”) when
120 MeV Ne6+
2s -> 7
, ’
I
I
I
100
I Acknowledgement
10’
Target
Atomic Number
going from H, to He. For heavier targets, the agreement breaks down. PWBA predicts a steeper increase of the cross sections with the target atomic number Z, than that of the experimental data. This behavior originates from the calculated screening contribution. The Z-r-dependence of the dielectronic contribution is very similar to that of the experimental data for heavier targets. An important finding is that the measured single differential Coster-Kronig emission cross sections are nearly proportional to the number of the target electrons. The experimental cross section ratios (cross section divided by the cross section for the hydrogen atom) are 1.7 ) 0.1 for He, 5.9 f 0.6 for C, 6.5 +_0.5 for N, 9.5 f 0.7 for Ne and 14.5 & 1.8 for Ar. This regular behavior appears to agree well with the intuitive picture that the studied excitation process is dominated by the projectile electron - target electron interactions. Surprisingly, it is also true for heavier targets, contrary to the PWBA results. When comparing the calculated curves in Figs. 1 and 3, one may realize that the behavior of the different contributions is very similar in the two cases. The most important difference is that the dielectronic contribution becomes dominant for light targets in the 2s-7 excitation case. The breakdown of the theory for heavy targets in the same case may be attributed to a significant difference of the two collision systems. In the case of the ls-2p excitation, it can be justified to restrict considerations to the n < 2 manifold in the first or second order calculation. One may argue that the n = 2 shell of the Ne’+ ion is sufficiently separated from higher-lying shells. In the case of the 2s-nl excitations, however, there are many states close to each other. First order calculations may be out of their region of applicability for heavier targets, and a realistic higher-order calculation would need an enormous size for the basis set. It should also be noted that the polarization of the target by the highly charged projectile ion is neglected within the framework of the present first order theories. For the case of the Ne6+ 2s-nl excitations by Hz and He targets, it can be concluded that the measured cross section ratios provide evidence for an inelastic atomic collision process which is dominated by the target electron-projectile electron interactions. The surprising fact is that the significance of two-center electron-electron interactions is likely to be true for heavier, many-electron targets. This finding suggests to study the process in a wider range of targets and impact velocities, and treat the present collision system beyond first order theories.
Z,
Fig. 3. Differential Coster-Kronig emission cross section and its contributions for n = 7. Labeled lines: theory (PWBA), symbols: present experiment (normalized to theory at the hydrogen The cross section belonging to the bare target nuclei displayed for reference.
target). is also
This work was supported by the German-Hungarian Collaboration in Science and Technology (Project No. 751, by the Hungarian Academic Research Fund (AKA, No. 1-300-2-91-O-790) and by the Hungarian National Science Fund (OTKA, No. 3011).
B. Sulik et al. /Nucl. Instr. and Meth. in Phys. Res. B 98 (1995) 262-265
References
[ 131 T.J.M. Zouros, D.H. Lee, J.M. Sanders and P. Richard, Nucl. Instr. and Meth. B 79 (1993) 166.
[l] N. Stolterfoht,
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(1992) 1374.
3.2. COLLISIONS
WITH HEAVY PARTICLES