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Radiative double electron capture in heavy-ion atom collisions
m
Nuclear Instruments and Methods in Physics Research B 98 (1995) 303-306
__ __
MIMI
B
Beam Interactions with Materials & Atoms
@
EISEVIER
Radiative double electron capture in heavy-ion atom collisions
’
*,
A. Warczak aY M. Kucharski a, Z. Stachura b, H. Geissel ‘, H. Irnich ‘, T. Kandler ‘, C. Kozhuharov ‘, P.H. Mokler ‘, G. Miinzenberg ‘, F. Nickel ‘, C. Scheidenberger ‘, Th. Stijhlker ‘, T. Suzuki ‘, P. Rymuza d a Uniwersytet Jagiellohki,
Instytut Fizyki, 30-059 Krakch, Poland b Instytut Fizyki Jqdrowej, 31-342 Kratiw, Poland ’ Gesellschafijiir Schwerionenforschung, 64220 Darmstadt, Germany d Instytat Problem6w Jpdrowych, 05-400 iwierk, Poland
Abstract Total cross sections for radiative double electron capture (RDEC) in collisions of fast highly charged ions with light target atoms were estimated. The applied method is based on the principle of detailed balance using the cross sections for the double photoionization process. Preliminary results of a dedicated RDEC experiment aiming at the observation of photons with twice the single REC photon energy, associated with double charge exchange, are discussed. Additionally, results of complementary measurements of double capture (without photon registration) by fully stripped U ions in collisions with C atoms at 295 MeV/u are presented. Here, a surprisingly enhanced cross section for double electron capture is found in accordance with observations reported in the literature.
1. Introduction Radiative electron capture (REC) was observed for the first time in fast heavy-ion atom collisions in the early seventies [I]. Within the impulse approximation, where the active target electron is treated as a quasi-free particle, REC can be considered as the time-reversed photoionization. It allows, by using the principle of detailed balance, to calculate REC cross sections directly from photoionization cross sections [2,3]. Among charge-exchange processes the leading role of single REC in fast collisions of fully stripped ions with light atoms is established. Moreover, theory [2,3] as well as experiments [4] clearly show that single REC into the projectile K-shell (K REC) is the dominant REC channel. Double radiative electron capture (DREC) has been addressed only theoretically [5]. Here, if the independent electron model (IEM) is assumed, the filling of both K-shell vacancies in one collision via electrons from a multi-electron target-atom can be discussed as two independent transitions followed by the emission of two single REC photons with energy ho = E, + E, (Fig. la). Going beyond the IEM, a certain fraction of the transitions of two
* This work was supported in part by the State Committee for Scientific Research (Poland) under research grant No. 201779101. * Corresponding author.
target electrons into the projectile K-shell should occur with the emission of one photon with twice the energy of single REC photons (Fig. lb). Hence, by taking into account the electron-electron interaction, an exotic double charge-exchange process can be discussed - radiative double electron capture (RDEC).
2. Cross section estimation for RDEC We estimate the ratio of the RDEC cross section (U aDEC) with respect to single REC cross section (ma& in three different ways: (1) by using the relationship of RDEC to two-electron one-photon transitions (K,, transitions [6]), (ii) by using the relationship of RDEC to the double photoionization process, (iii) by applying the twoelectron model (TEM) where the two active electrons are considered as one quasiparticle. Two-electron one-photon transitions are forbidden within the IEM in which the same central field is adopted for the initial and final states. However, they become possible if one allows for a change in the atomic field due to the change in the atomic configuration between the initial and the final state. This property of electronic transitions has been already applied in order to calculate the branching ratio R [7] between the K,, transition rates and the hypersatellite (K,,) transition rates. Similarly, it has been used in calculations of cross sections for double photoionization [8]. The first guess for the (~~o~,-/u~~c
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. AU rights reserved SSDI 0168-583X(95)00132-8
3.2. COLLISIONS
WITH HEAVY PARTICLES
A. Warczak et al. / Nucl. Instr. and Meth. in Phys. Rex B 98 (1995) 303-306
304
a)DREC
I
blRDEC
ple of detailed balance the cross section for REC as well as for RDEC is given by:
Odpdh4,
Fig. 1. Schematic presentation of double electron capture processes: (a) double radiative electron capture (DREC) with emission of two photons, (b) radiative double electron capture (RDEC) with emission of one photon with twice as large energy.
ratio can be obtained by assuming R(K,,/K,,) = oaoEc/aan,. In Fig. 2 the theoretical R values for innershell transitions [7] are plotted versus projectile atomic number Z, (solid line). In fact, within the RDEC process the two quasi-free continuum electrons make a jump into the projectile Kshell. Therefore, a more reliable estimate of the ratios can be provided by considering RDEC *FDEC /%EC as a time reversal of double photoionization. By the princi-
(2)
where Z, is the target atomic number, hw and ho’ the corresponding energies for single and double photoionization (energy of single or double REC photons), m the electron rest mass, c the speed of light, p the projectile velocity in units of c, y the Lorentz factor, up,, and oddp,, the corresponding cross sections for single and double photoionization. The factor A, with A 5 1, describes the phase-space fraction accessible to RDEC. It depends on the energy distribution as well as on the angular distribution of the two photoelectrons. These distributions, on the other hand, depend crucially on the total photon energy and on the projectile atomic number Z, [&lo]. The factor A becomes 1 only in the case where the two photoelectrons are emitted colinearly whereby the energy is shared equally between them. The best approach of this particular situation is provided for Z, x=-2 in the high energy limit where the photon energy considerably exceeds the threshold for doubie photoionization [&lo]. However, even in that case, the relative angular distribution of the two photoelectrons is nearly isotropic, thus, keeping A always smaler than 1. Using Eqs. (1) and (2) one obtains:
(3)
.E
lpi
i, +
t;
rjj
‘\
‘g, L\
1 lo-‘>
t,
_
_
2
,”
Within the RDEC process where ho’ = 2hw, one gets:
i
l
..k_._.
=A(Z2
-
~+,W4
1)
(4) q&W
\;....
10’ y
y.
.._.._. .\ .‘..., ‘.....
*. -.
-....... --._
106:
Y g 10-7
%DEC/%EC
~,,W)
y..
iii
0
q&W
-
8
--__
. . . . . . .._
......... -a__--__ -_
, I I I , I , I 20 LO 60 80 100 Atomic Number - Z,
Fig. 2. Calculated ratios o ar,EC /uasc obtained within models discussed in the text: solid line - K,, branching ratios R ([7]), dotted line - high energy limit for double photoionization according to Ref. [lo], dashed line - high energy limit for double photoionization according to Ref. [8], dash-dotted line - high energy approximation of TEM according to Ref. [12]. The data are plotted for Z, = 2. The photoionization curves are shown for A = 1. The upper limit estimate obtained in the RDEC experiment is plotted for Zt = 18. At Z, = 92 the experimental result for double electron capture is shown, as discussed in the text.
For a grven Z, the 5dph/up,, ratio approaches, with increasing photon energy above the threshold, almost a constant value. In this high energy limit one obtains Q,,,/u~,, = 0.0932/(Z,12 [lo]. A very similar dependence of this ratio is predicted in Ref. [8]. In Fig. 2 the estimates of ~aDEC/~aEC ratio, given by Eq. (41, are plotted in the high energy limit according to Refs. [8,10] (camp. dashed and dotted line, respectively). For these calculations the required up,(2hw)/u,,(hw) ratios were taken from tabulated cross section values [ll] for the high energy limit as well (for energies three times above the threshold). Finally, the third estimate for the (~~~c.u~c ratio is plotted in Fig. 2 (dash-dotted line) according to the twoelectron model (TEM) [12]. This model considers, in the high energy limit, the joint jump of two quasi-free target electrons within the first Born approximation. The data presented in Fig. 2 were calculated for photon energies which exceed the threshold for double photoionization by
A. Warczak et al. /Nucl. Instr. and Meth. in Phys. Res. B 98 (1995) 303-306
k-i
305
data
processing
II
80
60 11.4
FC % 0 Fig. 3. Schematic view of the experimental observation of RDEC photons.
arrangement
used for
a factor of 3. The nonrelativistic calculations, already applied in Ref. [12], were performed only for Z, I 40. As shown in Fig. 2, where all the calculated data obtained within the different approaches are presented, the applied theoretical estimations differ by a factor of about 100 and give a very crude guess for (~a,,~~ values.
3. Experiments and data discussion For the RDEC experiment, bare Ar ions at 11.4 MeV/u from the UNILAC of GSI in Darmstadt were used. The experimental arrangement is shown schematically in Fig. 3. To obtain as high as possible rates for double charge exchange in one collision, solid carbon targets were chosen. On the other hand, in order to keep all double collision processes at a low level, target thicknesses of 4-10 p,g/cm’ were used. After passing through the target, the ion beam was charge-state analysed in a dipole magnet. The projectiles which captured one or two electrons were registered in plastic scintillator detectors, separately for single and double charge-exchanged ions. The spectra of the X-ray detectors were recorded event-by-event in coincidence with the particles that captured two electrons. In order to avoid pileup effects the following arrangements were applied. First, X-ray absorbers (50 Frn, stainless steel) were inserted between target and X-ray detectors. The absorber thickness chosen guaranteed a strong suppression (by a factor of 1000) of single REC photons that could potentially produce a pileup signal in the energy region expected for RDEC. Second, a fast electronic pileup rejection was installed using standard NIM modules. In Fig. 4 a typical X-ray spectrum is shown, associated with the double charge exchange of Ar18+ ions. The X-ray spectrum was recorded by one of the Ge(i) detectors (Fig. 3) and generated by putting a window on the prompt peak of the corresponding time spectrum. The spectrum shown in Fig. 4 extends between 8 and 28 keV and includes the region around the energy for single REC photons (centroid
10
14 X-Ray
18 Energy
22
26
( keV1
Fig. 4. Typical X-ray spectrum associated with double charge exchange, obtained in the experiment with Arl*+ ions. The spectrum is not corrected for the detection efficiency. Two regions of interest (REC and RDEC) are indicated by bars. The bar width is equal to the FWHM of the corresponding process, according to the description given in the text.
energy at 10.6 keV) as well as the region around the energy for the expected RDEC photons (centroid energy at 21.2 keV). Both the regions are marked in the figure by bars with the width of the calculated FWHM of the corresponding spectral distribution. According to Ref. [12] the FWHM for RDEC spectrum is assumed to be twice as large as that for single REC. The spectrum in Fig. 4 is dominated by the single REC peak although it was strongly suppressed by the applied X-ray absorbers. This dominance is due to the still intense double collision processes in the solid target, producing single REC photons associated with double charge exchange and resulting in a modest true-to-random ratio of about 0.2 obtained in the experiment. In the RDEC region of the spectrum (Fig. 4) no line structure is observed which could be attributed to the investigated process. The smooth background in this spectrum region is most probably due to the high energy tail of single REC photons as well as due to the secondary electron bremsstrahlung (SEB). After subtracting from this spectrum the corresponding random spectrum, that exhibits the same shape as the one shown in Fig. 4, one obtains an upper limit estimate for RDEC cross section. The number of counts in the RDEC energy window, considered within the 3a statistics (a means one standard deviation), provides the upper limit of 5.2 mb (uRDEc I 5.2 mb). The corresponding upper limit for cRDEc/gREC ratio is indicated in Fig. 2. This value of 3.1 X 10d6 is by a factor of about 10 below the theoretical curves, based on the double photoionization and plotted for A = 1 in Fig. 2 (dotted and dashed line). This factor may be used to predict an upper limit for parameter A, i.e., A I 0.1. One has to mention that only a part of the collected data was used for the presented preliminary analysis of the experiment. A further analysis, in particular the use of the registered information on X-ray-X-ray coincidences, 3.2. COLLISIONS
WITH HEAVY PARTICLES
306
A. Warczak et al. /Nucl.
Instr. and Meth. in Phys. Res. B 98 (1995) 303-306
should give a new insight into the observed REC processes. Additional information on double electron capture, in a collision system where charge-exchange processes are fully determined by radiative transitions, was obtained in a complementary measurement with bare U ions at 295 MeV/u, parasitically to another experiment [13], by using the high-resolution ion-optical spectrometer of GSI in Darmstadt (FRS). From the measurement we extracted the value for the fraction F of ions which captured two electrons in the foil with respect to the ions which captured only one electron. For bare U ions traversing a 400 p,g/cm2 thick C foil one obtains F = (4.52 f 0.23) x 10m3. Here, charge exchange is dominated by single REC with the measured cross section of uanc = 685 f 40 b. For the analysis of the processes in the foil we applied the method proposed in Ref. [5] to get the contribution of the double charge-changing events associated with sequential single collisions. Assuming, however, that these sequential collisions are the only channel for double charge exchange, one obtains from model calculations [5] F = (3.5 i 0.2) X 10p3, which is considerably smaller than the directly measured value mentioned above. Accordance between the model calculations and the experiment would require the presence of a double charge-exchange process, occurring in one collision, with the cross section as large as 0.7 + 0.1 b. This process is certainly related to REC, as the nonradiative capture with the cross section of 3.8 b for single charge exchange [13] can be neglected. Among possible double charge-exchange processes just DREC and RDEC can be taken into account. However, the estimation for DREC according to Ref. [5] yields a cross section of only 5 mb. For RDEC even a smaller value is expected on the basis of Fig. 2. Thus, the proposed estimates (Fig. 2) are not able to describe this particular result. For comparison this data point is plotted in Fig. 2. A similar unexpected large value of the cross section for double charge exchange was reported for collisions of bare Xe ions with Be targets at 82 MeV/u [5] as well as for 170 MeV/u bare and He-like U ions within the electron cooler of a storage ring
h41. 4.Conclusions A comparison of calculated total cross sections for radiative double electron capture (RDEC) shows a strong
scattering of the theoretical data over almost two orders of magnitude. It clearly demonstrates that more experimental as well as theoretical efforts are required. An attempt to observe the RDEC photons in Ar”’ collisions with carbon atoms provides an upper limit estimate of 5.2 mb for the corresponding cross section. The reported strong enhancement of double charge exchange in relativistic collisions of bare ions with atoms suggests a significant role of radiative processes related to double capture and will be investigated furthermore. Experiments with bare decelerated heavy ions interacting with electron targets (e.g. electron coolers of storage rings) would be welcome, since the study of new exotic processes going beyond the independent electron model provides a way to make progress in our understanding of electron-electron correlation effects in electromagnetic fields, in particular of those processes which involve double continuum states.
Acknowledgements Three of us (A.W., M.K., Z.S.) very much appreciate the support of GSI in Darmstadt as well as good collaboration with the Atomic Physics Group at GSI.
References [l] H.W. Schnopper et al., Phys. Rev. Lett. 29 (1972) 898. [2] M. Stobbe, Ann. Phys. 7 (1930) 661. [3] A. Ichihara, T. Shirai and J. Eichler, Phys. Rev A 49 (1994) 1875. [4] Th. StGhlker et al., Z. Physik D 23 (1992) 121. [5] W.E. Meyerhof et al., Phys. Rev. A 32 (1985) 3291. [6] W. Wiilfli et al., Phys. Rev. Lett. 35 (1975) 656. [7] M. Gavrila and J.E. Hansen, Phys. L&t. A 58 (1976) 158. IS] Z. Smit, M. Kreger and D. GlaviE-Cindro, Phys. Rev. A 40 (1989) 6303. [9] A.R.P. Rau, J. Phys. B 9 (1976) L283. [lo] M.Ya. Amusia et al., J. Phys. B 8 (1975) 1248. [ll] W.J. Veigele, Atomic Data 5 (1973) 51. [12] J.E. Miraglia and MS. Gravielle, XVI ICPEAC, Brighton 1987, Book of Abstracts, p. 517. [13] Th. Stijhlker et al., preprint GSI-94-50 (1994). [14] R. Moshammer et al., GSI Scientific Report 1992, GSI Report 93-1, p. 187.
Nuclear Instruments and Methods in Physics Research B 98 (1995) 303-306
__ __
MIMI
B
Beam Interactions with Materials & Atoms
@
EISEVIER
Radiative double electron capture in heavy-ion atom collisions
’
*,
A. Warczak aY M. Kucharski a, Z. Stachura b, H. Geissel ‘, H. Irnich ‘, T. Kandler ‘, C. Kozhuharov ‘, P.H. Mokler ‘, G. Miinzenberg ‘, F. Nickel ‘, C. Scheidenberger ‘, Th. Stijhlker ‘, T. Suzuki ‘, P. Rymuza d a Uniwersytet Jagiellohki,
Instytut Fizyki, 30-059 Krakch, Poland b Instytut Fizyki Jqdrowej, 31-342 Kratiw, Poland ’ Gesellschafijiir Schwerionenforschung, 64220 Darmstadt, Germany d Instytat Problem6w Jpdrowych, 05-400 iwierk, Poland
Abstract Total cross sections for radiative double electron capture (RDEC) in collisions of fast highly charged ions with light target atoms were estimated. The applied method is based on the principle of detailed balance using the cross sections for the double photoionization process. Preliminary results of a dedicated RDEC experiment aiming at the observation of photons with twice the single REC photon energy, associated with double charge exchange, are discussed. Additionally, results of complementary measurements of double capture (without photon registration) by fully stripped U ions in collisions with C atoms at 295 MeV/u are presented. Here, a surprisingly enhanced cross section for double electron capture is found in accordance with observations reported in the literature.
1. Introduction Radiative electron capture (REC) was observed for the first time in fast heavy-ion atom collisions in the early seventies [I]. Within the impulse approximation, where the active target electron is treated as a quasi-free particle, REC can be considered as the time-reversed photoionization. It allows, by using the principle of detailed balance, to calculate REC cross sections directly from photoionization cross sections [2,3]. Among charge-exchange processes the leading role of single REC in fast collisions of fully stripped ions with light atoms is established. Moreover, theory [2,3] as well as experiments [4] clearly show that single REC into the projectile K-shell (K REC) is the dominant REC channel. Double radiative electron capture (DREC) has been addressed only theoretically [5]. Here, if the independent electron model (IEM) is assumed, the filling of both K-shell vacancies in one collision via electrons from a multi-electron target-atom can be discussed as two independent transitions followed by the emission of two single REC photons with energy ho = E, + E, (Fig. la). Going beyond the IEM, a certain fraction of the transitions of two
* This work was supported in part by the State Committee for Scientific Research (Poland) under research grant No. 201779101. * Corresponding author.
target electrons into the projectile K-shell should occur with the emission of one photon with twice the energy of single REC photons (Fig. lb). Hence, by taking into account the electron-electron interaction, an exotic double charge-exchange process can be discussed - radiative double electron capture (RDEC).
2. Cross section estimation for RDEC We estimate the ratio of the RDEC cross section (U aDEC) with respect to single REC cross section (ma& in three different ways: (1) by using the relationship of RDEC to two-electron one-photon transitions (K,, transitions [6]), (ii) by using the relationship of RDEC to the double photoionization process, (iii) by applying the twoelectron model (TEM) where the two active electrons are considered as one quasiparticle. Two-electron one-photon transitions are forbidden within the IEM in which the same central field is adopted for the initial and final states. However, they become possible if one allows for a change in the atomic field due to the change in the atomic configuration between the initial and the final state. This property of electronic transitions has been already applied in order to calculate the branching ratio R [7] between the K,, transition rates and the hypersatellite (K,,) transition rates. Similarly, it has been used in calculations of cross sections for double photoionization [8]. The first guess for the (~~o~,-/u~~c
0168-583X/95/$09.50 0 1995 Elsevier Science B.V. AU rights reserved SSDI 0168-583X(95)00132-8
3.2. COLLISIONS
WITH HEAVY PARTICLES
A. Warczak et al. / Nucl. Instr. and Meth. in Phys. Rex B 98 (1995) 303-306
304
a)DREC
I
blRDEC
ple of detailed balance the cross section for REC as well as for RDEC is given by:
Odpdh4,
Fig. 1. Schematic presentation of double electron capture processes: (a) double radiative electron capture (DREC) with emission of two photons, (b) radiative double electron capture (RDEC) with emission of one photon with twice as large energy.
ratio can be obtained by assuming R(K,,/K,,) = oaoEc/aan,. In Fig. 2 the theoretical R values for innershell transitions [7] are plotted versus projectile atomic number Z, (solid line). In fact, within the RDEC process the two quasi-free continuum electrons make a jump into the projectile Kshell. Therefore, a more reliable estimate of the ratios can be provided by considering RDEC *FDEC /%EC as a time reversal of double photoionization. By the princi-
(2)
where Z, is the target atomic number, hw and ho’ the corresponding energies for single and double photoionization (energy of single or double REC photons), m the electron rest mass, c the speed of light, p the projectile velocity in units of c, y the Lorentz factor, up,, and oddp,, the corresponding cross sections for single and double photoionization. The factor A, with A 5 1, describes the phase-space fraction accessible to RDEC. It depends on the energy distribution as well as on the angular distribution of the two photoelectrons. These distributions, on the other hand, depend crucially on the total photon energy and on the projectile atomic number Z, [&lo]. The factor A becomes 1 only in the case where the two photoelectrons are emitted colinearly whereby the energy is shared equally between them. The best approach of this particular situation is provided for Z, x=-2 in the high energy limit where the photon energy considerably exceeds the threshold for doubie photoionization [&lo]. However, even in that case, the relative angular distribution of the two photoelectrons is nearly isotropic, thus, keeping A always smaler than 1. Using Eqs. (1) and (2) one obtains:
(3)
.E
lpi
i, +
t;
rjj
‘\
‘g, L\
1 lo-‘>
t,
_
_
2
,”
Within the RDEC process where ho’ = 2hw, one gets:
i
l
..k_._.
=A(Z2
-
~+,W4
1)
(4) q&W
\;....
10’ y
y.
.._.._. .\ .‘..., ‘.....
*. -.
-....... --._
106:
Y g 10-7
%DEC/%EC
~,,W)
y..
iii
0
q&W
-
8
--__
. . . . . . .._
......... -a__--__ -_
, I I I , I , I 20 LO 60 80 100 Atomic Number - Z,
Fig. 2. Calculated ratios o ar,EC /uasc obtained within models discussed in the text: solid line - K,, branching ratios R ([7]), dotted line - high energy limit for double photoionization according to Ref. [lo], dashed line - high energy limit for double photoionization according to Ref. [8], dash-dotted line - high energy approximation of TEM according to Ref. [12]. The data are plotted for Z, = 2. The photoionization curves are shown for A = 1. The upper limit estimate obtained in the RDEC experiment is plotted for Zt = 18. At Z, = 92 the experimental result for double electron capture is shown, as discussed in the text.
For a grven Z, the 5dph/up,, ratio approaches, with increasing photon energy above the threshold, almost a constant value. In this high energy limit one obtains Q,,,/u~,, = 0.0932/(Z,12 [lo]. A very similar dependence of this ratio is predicted in Ref. [8]. In Fig. 2 the estimates of ~aDEC/~aEC ratio, given by Eq. (41, are plotted in the high energy limit according to Refs. [8,10] (camp. dashed and dotted line, respectively). For these calculations the required up,(2hw)/u,,(hw) ratios were taken from tabulated cross section values [ll] for the high energy limit as well (for energies three times above the threshold). Finally, the third estimate for the (~~~c.u~c ratio is plotted in Fig. 2 (dash-dotted line) according to the twoelectron model (TEM) [12]. This model considers, in the high energy limit, the joint jump of two quasi-free target electrons within the first Born approximation. The data presented in Fig. 2 were calculated for photon energies which exceed the threshold for double photoionization by
A. Warczak et al. /Nucl. Instr. and Meth. in Phys. Res. B 98 (1995) 303-306
k-i
305
data
processing
II
80
60 11.4
FC % 0 Fig. 3. Schematic view of the experimental observation of RDEC photons.
arrangement
used for
a factor of 3. The nonrelativistic calculations, already applied in Ref. [12], were performed only for Z, I 40. As shown in Fig. 2, where all the calculated data obtained within the different approaches are presented, the applied theoretical estimations differ by a factor of about 100 and give a very crude guess for (~a,,~~ values.
3. Experiments and data discussion For the RDEC experiment, bare Ar ions at 11.4 MeV/u from the UNILAC of GSI in Darmstadt were used. The experimental arrangement is shown schematically in Fig. 3. To obtain as high as possible rates for double charge exchange in one collision, solid carbon targets were chosen. On the other hand, in order to keep all double collision processes at a low level, target thicknesses of 4-10 p,g/cm’ were used. After passing through the target, the ion beam was charge-state analysed in a dipole magnet. The projectiles which captured one or two electrons were registered in plastic scintillator detectors, separately for single and double charge-exchanged ions. The spectra of the X-ray detectors were recorded event-by-event in coincidence with the particles that captured two electrons. In order to avoid pileup effects the following arrangements were applied. First, X-ray absorbers (50 Frn, stainless steel) were inserted between target and X-ray detectors. The absorber thickness chosen guaranteed a strong suppression (by a factor of 1000) of single REC photons that could potentially produce a pileup signal in the energy region expected for RDEC. Second, a fast electronic pileup rejection was installed using standard NIM modules. In Fig. 4 a typical X-ray spectrum is shown, associated with the double charge exchange of Ar18+ ions. The X-ray spectrum was recorded by one of the Ge(i) detectors (Fig. 3) and generated by putting a window on the prompt peak of the corresponding time spectrum. The spectrum shown in Fig. 4 extends between 8 and 28 keV and includes the region around the energy for single REC photons (centroid
10
14 X-Ray
18 Energy
22
26
( keV1
Fig. 4. Typical X-ray spectrum associated with double charge exchange, obtained in the experiment with Arl*+ ions. The spectrum is not corrected for the detection efficiency. Two regions of interest (REC and RDEC) are indicated by bars. The bar width is equal to the FWHM of the corresponding process, according to the description given in the text.
energy at 10.6 keV) as well as the region around the energy for the expected RDEC photons (centroid energy at 21.2 keV). Both the regions are marked in the figure by bars with the width of the calculated FWHM of the corresponding spectral distribution. According to Ref. [12] the FWHM for RDEC spectrum is assumed to be twice as large as that for single REC. The spectrum in Fig. 4 is dominated by the single REC peak although it was strongly suppressed by the applied X-ray absorbers. This dominance is due to the still intense double collision processes in the solid target, producing single REC photons associated with double charge exchange and resulting in a modest true-to-random ratio of about 0.2 obtained in the experiment. In the RDEC region of the spectrum (Fig. 4) no line structure is observed which could be attributed to the investigated process. The smooth background in this spectrum region is most probably due to the high energy tail of single REC photons as well as due to the secondary electron bremsstrahlung (SEB). After subtracting from this spectrum the corresponding random spectrum, that exhibits the same shape as the one shown in Fig. 4, one obtains an upper limit estimate for RDEC cross section. The number of counts in the RDEC energy window, considered within the 3a statistics (a means one standard deviation), provides the upper limit of 5.2 mb (uRDEc I 5.2 mb). The corresponding upper limit for cRDEc/gREC ratio is indicated in Fig. 2. This value of 3.1 X 10d6 is by a factor of about 10 below the theoretical curves, based on the double photoionization and plotted for A = 1 in Fig. 2 (dotted and dashed line). This factor may be used to predict an upper limit for parameter A, i.e., A I 0.1. One has to mention that only a part of the collected data was used for the presented preliminary analysis of the experiment. A further analysis, in particular the use of the registered information on X-ray-X-ray coincidences, 3.2. COLLISIONS
WITH HEAVY PARTICLES
306
A. Warczak et al. /Nucl.
Instr. and Meth. in Phys. Res. B 98 (1995) 303-306
should give a new insight into the observed REC processes. Additional information on double electron capture, in a collision system where charge-exchange processes are fully determined by radiative transitions, was obtained in a complementary measurement with bare U ions at 295 MeV/u, parasitically to another experiment [13], by using the high-resolution ion-optical spectrometer of GSI in Darmstadt (FRS). From the measurement we extracted the value for the fraction F of ions which captured two electrons in the foil with respect to the ions which captured only one electron. For bare U ions traversing a 400 p,g/cm2 thick C foil one obtains F = (4.52 f 0.23) x 10m3. Here, charge exchange is dominated by single REC with the measured cross section of uanc = 685 f 40 b. For the analysis of the processes in the foil we applied the method proposed in Ref. [5] to get the contribution of the double charge-changing events associated with sequential single collisions. Assuming, however, that these sequential collisions are the only channel for double charge exchange, one obtains from model calculations [5] F = (3.5 i 0.2) X 10p3, which is considerably smaller than the directly measured value mentioned above. Accordance between the model calculations and the experiment would require the presence of a double charge-exchange process, occurring in one collision, with the cross section as large as 0.7 + 0.1 b. This process is certainly related to REC, as the nonradiative capture with the cross section of 3.8 b for single charge exchange [13] can be neglected. Among possible double charge-exchange processes just DREC and RDEC can be taken into account. However, the estimation for DREC according to Ref. [5] yields a cross section of only 5 mb. For RDEC even a smaller value is expected on the basis of Fig. 2. Thus, the proposed estimates (Fig. 2) are not able to describe this particular result. For comparison this data point is plotted in Fig. 2. A similar unexpected large value of the cross section for double charge exchange was reported for collisions of bare Xe ions with Be targets at 82 MeV/u [5] as well as for 170 MeV/u bare and He-like U ions within the electron cooler of a storage ring
h41. 4.Conclusions A comparison of calculated total cross sections for radiative double electron capture (RDEC) shows a strong
scattering of the theoretical data over almost two orders of magnitude. It clearly demonstrates that more experimental as well as theoretical efforts are required. An attempt to observe the RDEC photons in Ar”’ collisions with carbon atoms provides an upper limit estimate of 5.2 mb for the corresponding cross section. The reported strong enhancement of double charge exchange in relativistic collisions of bare ions with atoms suggests a significant role of radiative processes related to double capture and will be investigated furthermore. Experiments with bare decelerated heavy ions interacting with electron targets (e.g. electron coolers of storage rings) would be welcome, since the study of new exotic processes going beyond the independent electron model provides a way to make progress in our understanding of electron-electron correlation effects in electromagnetic fields, in particular of those processes which involve double continuum states.
Acknowledgements Three of us (A.W., M.K., Z.S.) very much appreciate the support of GSI in Darmstadt as well as good collaboration with the Atomic Physics Group at GSI.
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