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Binding energy enhancement in the isocharge sequence of ions in collisions with Ne
Nuclear Instruments and Methods in Physics Research B 225 (2004) 185–190 www.elsevier.com/locate/nimb
Binding energy enhancement in the isocharge sequence of ions in collisions with Ne Xiaohong Cai a
a,* ,
Deyang Yu a, Rongchun Lu a, Zhurong Cao a, Wei Yang a, Caojie Shao a, Ximeng Chen b, Xinwen Ma a
Atomic Physics, Institute of Modern Physics, Chinese Academy of Sciences, P.O. Box 31, Lanzhou 730000, China b Department of Modern Physics, Lanzhou University, Lanzhou 730000, China Received 22 August 2003; received in revised form 21 April 2004
Abstract The dependence of the ratio R1 for transfer ionization to single capture for Cqþ , Nqþ , Oqþ , Neqþ ions on Ne target upon the electronic structure of the projectile is studied by using position sensitive and time-of-flight techniques. It is found that for Aqþ –Ne collisions the ratio R1 decreases as the atomic number of the projectile increases for q ¼ 4; 5; 6; 7 sequences which differs markedly from the results we obtained for Aqþ –Ar collisions. The difference is explained by using a statistical model and the orbital penetration picture. Comparison of the R1 ratios of A4þ –Ne and A4þ –Ar collisions provides strong evidence for the increase of the binding energy of the target valence electron after single electron capture. The increase in binding energy depends both upon the atomic number of the projectile Z1 and the target atom Z2 . The larger Z1 , the larger the increase in binding energy, while the larger Z2 , the smaller the increase in binding energy. 2004 Published by Elsevier B.V. PACS: 34.50.Fa; 34.70.+e Keywords: Ion-atom collision; Charge exchange
1. Introduction Multi-electron process in the collisions of highly charged ions with multi-electron atoms has been a very active area of atomic physics research [1,2]. The simultaneous electron emission and electron transfer are the most interesting multi-electron processes in the study of ion–atom collisions at low energies where the electron correlation effect plays *
Corresponding author. Tel./fax: +86-931-4969500. E-mail address: [email protected] (X. Cai).
0168-583X/$ - see front matter 2004 Published by Elsevier B.V. doi:10.1016/j.nimb.2004.04.173
an important role [3–5]. Knowledge of the cross section for electron transfer is not only useful in the evaluation of the impurity content and temperature of confined plasmas, but also important for the study of astrophysics [6]. The method based on the process of charge-exchange between a neutral hydrogen beam and the plasma has been widely used as a conventional diagnostic technique. Single and multiple electron capture and transfer ionization are the main electron transfer processes. To date, the major processes in low energy ion–atom collisions have been understood. The single capture
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process can be well described by the classical overbarrier model [7,8] and coupled channel treatment [9]. For processes with more than two active electrons and for higher projectile charges, the availability of theoretical calculations is limited. A full quantum mechanical treatment of the charge transfer process becomes difficult due to the large number of reaction channels involved. Compared to the single electron process, the experimental data for multi-electron processes are still limited. Early work on the study of charge transfer and ionization includes the study on low energy Arqþ –Ne collisions by Justiniano et al. [10] and collisions of lithium by 15–200 keV protons and helium ions by DuBois [11] where they found that transfer ionization is an important channel for large q and the most natural form of transfer ionization to occur in the low energy Arqþ –Ne collisions is through the population of doubly or multiply excited states on the final Ar ion. Montenegro et al. [12] measured the ratios of the cross sections for the processes of transfer ionization and single capture for 2 MeV/u Clqþ and Tiqþ projectiles on He target. The measured ratio shows a strong dependence with the projectile and the charge state. Different authors have investigated the transfer ionization process by measuring the angular distribution of the emitted electrons [3,13–17]. It is found that the second electron of the transfer ionization process recoils with the speed of the projectile ion vp , resulting in a pronounced peak at about 90 in the angular distribution of the electron emitted with matching velocity ve ¼ vp . The peak was first observed in 1 MeV proton on He collisions by P alink as et al. [13]. Mergel et al. [14] found further evidence of the correlated motion of the emitted and captured electrons for the same collision systems. Sarkadi et al. [3] observed the electron cusp in 100–300 keV He2þ –He collisions, and identified the processes of electron capture to the continuum (ECC), and ECC accompanied by bound-state capture (transfer ionization or TI) by detecting the electrons in coincidence with the charge-state-analyzed outgoing He2þ and Heþ ions. The above experiments were all performed at intermediate (several hundred keV) and high (MeV) collision energies. These studies provide strong evidence for electron correlation in transfer ionization. Mancev [15] calcu-
lated the total cross section for single capture and transfer ionization in Li3þ –He collisions using a four-body distorted-wave formalism. Comparison between the calculations and the experimental data measured at 50–5000 keV/amu yields satisfactory agreement [5]. Up to now, systematic studies of TI and its dependence upon the collision parameters for low energy ion–atom collisions are scarce [12–14]. We have recently reported on the study of TI in the isonuclear sequence of Arqþ ions in collisions with helium, neon and argon atoms [18] and TI in the isocharge sequence of ions (q ¼ 4; 5; 6; 7) in collisions with argon atoms [19]. We have found that the process of TI depends obviously upon the projectile charge state for an isonuclear sequence of ions in collisions with atoms, and also depends upon the electronic structure of the projectile for an isocharge sequence of ions and atom collisions. To further understand the TI process for different collision systems, we have measured the TI to single capture ratios R1 for isocharge Cqþ , Nqþ , Oqþ , Neqþ ions on Ne atoms by using position sensitive and time-of-flight techniques. For an isocharge ion sequence the velocity of the ion is selected to be the same in order to clarify the projectile electronic structure dependence on R1 . It is found that for Aqþ –Ne collisions the ratio R1 decreases as the atomic number Z1 of the projectile increases for q ¼ 4; 5; 6; 7 sequences and differs markedly from the results we obtained for Aqþ –Ar collisions [19]. The difference is explained using a statistical model and the orbital penetration picture. Comparison of the R1 ratios of A4þ –Ne and A4þ –Ar collisions provides the strongest evidence for the enhancement of the binding energy of the target valence electron after single electron capture. The enhancement of the binding energy depends both upon Z1 and Z2 (where Z2 is the atomic number of the target atom). The larger Z1 , the larger the increase in binding energy, while the larger Z2 , the smaller the increase in binding energy.
2. Experimental technique The experiments were performed at the 14.5GHz ECR platform of the Institute of Modern
X. Cai et al. / Nucl. Instr. and Meth. in Phys. Res. B 225 (2004) 185–190
10
Present experiment statistical model
4+
A -Ne
R1
1
0.1
0.01 6
7
8
9
10
Z1 Fig. 1. Ratio R1 of transfer ionization to single capture for C4þ , N4þ , O4þ and Ne4þ on Ne. All ions have the same velocity equal to 0.21 a.u. Z1 is the atomic number of the projectile A4þ .
0.4 5+
A -Ne R1
Physics, Chinese Academy of Sciences. Highly charged ions produced in the ion source were extracted and m=q-selected (where m is the ion mass and q is the ion charge) by the analyzing magnet. The maximum extraction voltage of the ECR source is 25 kV and the voltage can be changed between 10 and 25 kV. The ion beam was collimated by two two-dimensional collimators to a size less than 0.3 · 0.3 mm2 . The ion beams were charge state-selected again before entering into the target chamber by a 64 coaxial static analyzer to ensure the purity of the charge state of the projectile. The ion beam interacted with a gas jet at the center of the target chamber. The recoil ions were extracted from the interaction zone by a static electric field and detected by a channel electron multiplier after passing through a fieldfree tube. The scattered ions were charged stateanalyzed by a parallel plate field and then detected by a position sensitive channel plate detector. The charge state of the recoil ion was determined by measuring the differences of the time-of-flight between the scattered ions and the recoil ions. A multi-parameter acquisition system was used to measure the time-of-flight spectrum of the scattered and recoil ions [2]. Isocharge ion sequences Cqþ , Nqþ , Oqþ , Neqþ were used. The energies of the ion sequence were selected to be 4, 5, 6 and 7 keV/u for projectile charge states 4, 5, 6 and 7 which correspond to the ion velocities of 0.21, 0.24, 0.26 and 0.28 a.u., respectively.
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7
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3. Results and discussion
Fig. 2. Same as for Fig. 1 but for C5þ , N5þ and O5þ on Ne. All ions have the same velocity equal to 0.24 a.u.
The ratios R1 for Aqþ ions on Ne atoms are shown in Figs. 1–4. The charge states are selected to be q ¼ 4; 5 for carbon, q ¼ 4–6 for nitrogen, q ¼ 4–7 for oxygen, and q ¼ 4; 6–9 for neon projectiles, respectively. The fully stripped ions of C6þ , N7þ , O8þ and Ne10þ were not used because these ions have a charge to mass ratio of 1/2 and cannot be separated from other contaminants with the same charge to mass ratio. From Figs. 1 to 4 it can be seen that the ratio R1 decreases as the atomic number Z1 increases for q ¼ 4; 5; 6; 7 sequences which differs markedly
from the results obtained for Aqþ –Ar collisions [19]. In the study of Aqþ –Ar collisions, we found that the ratio R1 increases as the atomic number Z1 increases for q ¼ 4 sequence, it goes through a minimum for Z1 ¼ 7 and Z1 ¼ 8 for q ¼ 5 and q ¼ 6 sequences, respectively, and R1 decreases as Z1 increases for q ¼ 7 sequence. For comparison in Fig. 5 we show the results of the q ¼ 4 sequence for A4þ –Ar collisions together with that of the q ¼ 4 sequence for A4þ –Ne collisions. To explain these results we may use the concepts of the statistical energy deposition model
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0.8 6+
4+
A -Ne 4+ A -Ar
1
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R1
A -Ne
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6
7
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Z1
6
7
8
9
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z1
Fig. 3. Same as for Fig. 1 but for N6þ , O6þ and Ne6þ on Ne. All ions have the same velocity equal to 0.26 a.u.
Fig. 5. Comparison of the ratio R1 for A4þ –Ne and A4þ –Ar collisions. All ions have the same velocity equal to 0.21 a.u. Z1 is the atomic number of the projectile A4þ .
0.60
7+
A -Ne
R1
0.55
0.50
0.45 7
8
9
10
11
Z1 Fig. 4. Same as for Fig. 1 but for O7þ and Ne7þ on Ne. All ions have the same velocity equal to 0.28 a.u.
[20–22]. The electron capture process is an exoergic reaction, and the target electron will gain an energy DE during single capture [20]. In the statistical model the energy deposited in the target atom is considered to be distributed statistically among the remaining target electrons. One or more target electrons may then be evaporated. The probability that the electrons may gain enough energy to overcome their binding energy and escape from the target atom is proportional to the energy gain DE. If we consider the transfer ioni-
zation in a two-step framework, the transfer ionization is a successive process of single electron capture followed by the ionization of a second or more target electrons. To first order the probability of transfer ionization may then be considered to be given by the product of the probabilities for single capture and the ionization of the second electron. So the R1 ratio may be considered to be approximately proportional to the ionization cross section of the second electron. As mentioned above the second electron may be ionized or ‘‘evaporated’’ if it gets enough energy. The maximum energy deposited Em is the difference between ðqÞ the qth ionization energy of the projectile IA and ð1Þ the first ionization energy IT of the target atom, ðqÞ ð1Þ i.e. DEm ¼ IA INe for a neon target. 4þ For 4 keV/u C on Ne collisions the distance of closest approach rmin is rmin 0:06 a.u. After the C4þ ion captures one electron from the Ne atom at the capture distance of 6.3 a.u., the ion needs about 7.3 · 1016 s to arrive to rmin . Considering that the typical lifetime of the autoionization state of the target atom is of the order of 1015 s, autoionization should mostly occur in the vicinity of rmin . Since the radius of the valence state (2s) of the Ne atom is about 0.4 a.u., and the projectile C4þ ion has a valence state (1s) radius of 0.17 a.u. it is much smaller than that of the Ne valence state.
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Thus, we may assume that the C4þ ion penetrates the 2s electron orbit of the Ne atom, and the valence target electrons then move in the combined Coulomb field of the C4þ and Ne nuclei, as shown in the picture of Fig. 6. The effective charge seen by the target valence electrons will be Z1eff þ Z2eff , where Z1eff ¼ Z1 2 and Z2eff ¼ Z2 2 for C4þ on Ne collisions and Z1 and Z2 are the atomic numbers of the projectile and target atom. According to this picture the binding energy of the target valence electrons will then be proportional to 2 2 ðZ1eff þ Z2eff Þ instead of ðZ2eff Þ . In the case of C4þ –Ne collisions, the binding energy of the neon valence electrons will increase to be about 2.2 times the original binding energy according to the estimation based upon the hydrogen-like atom. This will result in the decrease of the ionization probability of the target valence electrons, and the transfer ionization probability will therefore also be considerably decreased. For Ne4þ –Ne collisions the target binding energy will increase to be about four times the original one. As the atomic number of the projectile Z1 increases the binding energy of the target valence electron will increase markedly while the transfer ionization probability will therefore decrease with increasing Z1 as shown in Fig. 1.
Fig. 6. Sketch map of the orbital penetration model. The 1s orbital of C4þ is seen to be considerably smaller that the 2s orbital of neon, but larger than the distance of closest approach rmin .
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For A4þ –Ar collisions the effect of the enhancement of the binding energy [19] due to the orbital penetration is small. The factors of the binding 2 2 energy enhancement, ðZ1eff þ Z2eff Þ =ðZ2eff Þ , are 4þ 4þ about 2.2 and 1.5 for C –Ne and C –Ar collisions, respectively. For the collision of ion sequence q ¼ 4 (C4þ , N4þ , O4þ and Ne4þ ) with argon, the fourth ionization energies are 64.49, 77.47, 77.41 and 97.12 eV [23], corresponding to DEm values of 48.73, 61.17, 61.65 and 81.36 eV, respectively. We note that for carbon, nitrogen and neon projectiles the fourth ionization energy increases with the projectile atomic number Z1 , which therefore also increases the maximum energy deposited DEm . The second ionization energy of argon is 27.63 eV, and it will increase to be 43.17, 47.59, 52.24 and 62.17 eV for the collision with ion sequence q ¼ 4 (C4þ , N4þ , O4þ and Ne4þ ) due to the binding energy enhancement effect discussed above. Since DEm for carbon, nitrogen and neon ions is larger than the enhanced ionization energy of the second electron of argon, the second electron may be ionized. According to the above discussion then, the ionization probability of the second target electron will increase as the projectile atomic number Z1 increases for A4þ –Ar collisions. Fig. 1 also shows the calculated ratio using the statistical energy deposition model. Fig. 1 shows an overestimation of the calculated R1 ratios and the calculated and the measured data have a different Z1 dependence. In the calculation the enhancement of the binding energy was not included and this is the main reason for the disagreement between the calculated results and the present data. Neglecting the effect of the binding energy enhancement may result in the overestimation of R1 and the flat Z1 dependence observed in the calculation. Furthermore, in our calculations the maximum energy deposited DEm is calculated assuming that the electrons will always be captured into the lowest unoccupied energy levels. In fact the electrons are mostly captured into the higher excited energy levels, and the principal quantum number of the captured electrons increases with the charge state of the projectile [7]. This assumption will lead to the overestimation of DEm , and therefore to the overestimation of the transfer ionization probability. Thus, the
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calculated R1 ratios will be larger than the measured data. The results shown in Figs. 2–4 can also be qualitatively explained using the pictures. The experimental uncertainty shown in Figs. 1– 5 is within 10% which comes mainly from the statistical error.
4. Summary The dependence of the transfer ionization to single capture ratio R1 for Cqþ , Nqþ , Oqþ , Neqþ ions on Ne target upon the electronic structure of the projectile is studied using position sensitive and time-of-flight techniques. For an isocharge ion sequence the velocity of the ion is selected to be the same in order to clarify the projectile electronic structure dependences of the ratios mentioned above. It is found that for Aqþ –Ne collisions the ratio R1 decreases as the projectile atomic number Z1 increases for q ¼ 4–7 sequences which differs remarkably from the results we obtained for Aqþ – Ar collisions. The difference may be explained using a statistical model and the orbital penetration model. Comparison of the R1 ratios of A4þ – Ne and A4þ –Ar collisions provides the strongest evidence for the enhancement of the binding energy of the target valence electron after single electron capture. The enhancement of the binding energy depends both upon the atomic number of the projectile and the target atom. The larger Z1 , the larger the increase in binding energy, while the larger the atomic number of the target atom Z2 , the smaller the increase in binding energy.
Acknowledgements We are grateful for the help offered by the staff of the ECR laboratory at the Institute of Modern Physics, Chinese Academy of Sciences during the experiment. This work is supported by the National Natural Science Foundation of China under contract numbers 10134010, 10375080 and 10134019. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
[10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
S. Bliman et al., Phys. Rev. A 66 (2002) 052707. X. Cai et al., Eur. Phys. J. D 6 (1999) 23. L. Sarkadi et al., J. Phys. B 34 (2001) 4901. M. Zamkov et al., Phys. Rev. A 66 (2002) 042714. H. Merabet et al., Phys. Rev. A 59 (1999) R3158. J.D. Gillaspy, J. Phys. B 34 (2001) R93. A. Niehaus, J. Phys. B 19 (1986) 2925. F. Sattin, J. Phys. B 33 (2000) 861. B.H. Bransden, M.R.C. McDowell, Charge Exchange and the Theory of Ion–Atom Collisions, Clarendon Press, Oxford, 1992. E. Justiniano et al., Phys. Rev. A 24 (1981) 2953. R.D. DuBois, Phys. Rev. A 32 (1985) 3319. E.C. Montenegro et al., Phys. Rev. A 55 (1997) 2009. J. Palinkas et al., Phys. Rev. Lett. 63 (1989) 2464. V. Mergel et al., Phys. Rev. Lett. 86 (2001) 2257. I. Mancev, Phys. Rev. A 64 (2001) 012708. N. Selberg, C. Biedermann, H. Cerderquist, Phys. Rev. A 56 (1997) 4623. G. Lubinski et al., Phys. Rev. Lett. 86 (2001) 616. X. Cai et al., Phys. Scripta. 68 (2003) 227. X. Cai et al., Chin. Phys., in press. A. M€ uller, W. Groh, E. Salzborn, Phys. Rev. Lett. 51 (1983) 107. A. Russek, Phys. Rev. 132 (1963) 246. A. Russek, J. Meli, Physica 46 (1970) 222. D.R. Lide, Handbook of Chemistry and Physics, 80th ed., CRC Press, Boca Raton, 1999–2000, p. 10.
Binding energy enhancement in the isocharge sequence of ions in collisions with Ne Xiaohong Cai a
a,* ,
Deyang Yu a, Rongchun Lu a, Zhurong Cao a, Wei Yang a, Caojie Shao a, Ximeng Chen b, Xinwen Ma a
Atomic Physics, Institute of Modern Physics, Chinese Academy of Sciences, P.O. Box 31, Lanzhou 730000, China b Department of Modern Physics, Lanzhou University, Lanzhou 730000, China Received 22 August 2003; received in revised form 21 April 2004
Abstract The dependence of the ratio R1 for transfer ionization to single capture for Cqþ , Nqþ , Oqþ , Neqþ ions on Ne target upon the electronic structure of the projectile is studied by using position sensitive and time-of-flight techniques. It is found that for Aqþ –Ne collisions the ratio R1 decreases as the atomic number of the projectile increases for q ¼ 4; 5; 6; 7 sequences which differs markedly from the results we obtained for Aqþ –Ar collisions. The difference is explained by using a statistical model and the orbital penetration picture. Comparison of the R1 ratios of A4þ –Ne and A4þ –Ar collisions provides strong evidence for the increase of the binding energy of the target valence electron after single electron capture. The increase in binding energy depends both upon the atomic number of the projectile Z1 and the target atom Z2 . The larger Z1 , the larger the increase in binding energy, while the larger Z2 , the smaller the increase in binding energy. 2004 Published by Elsevier B.V. PACS: 34.50.Fa; 34.70.+e Keywords: Ion-atom collision; Charge exchange
1. Introduction Multi-electron process in the collisions of highly charged ions with multi-electron atoms has been a very active area of atomic physics research [1,2]. The simultaneous electron emission and electron transfer are the most interesting multi-electron processes in the study of ion–atom collisions at low energies where the electron correlation effect plays *
Corresponding author. Tel./fax: +86-931-4969500. E-mail address: [email protected] (X. Cai).
0168-583X/$ - see front matter 2004 Published by Elsevier B.V. doi:10.1016/j.nimb.2004.04.173
an important role [3–5]. Knowledge of the cross section for electron transfer is not only useful in the evaluation of the impurity content and temperature of confined plasmas, but also important for the study of astrophysics [6]. The method based on the process of charge-exchange between a neutral hydrogen beam and the plasma has been widely used as a conventional diagnostic technique. Single and multiple electron capture and transfer ionization are the main electron transfer processes. To date, the major processes in low energy ion–atom collisions have been understood. The single capture
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process can be well described by the classical overbarrier model [7,8] and coupled channel treatment [9]. For processes with more than two active electrons and for higher projectile charges, the availability of theoretical calculations is limited. A full quantum mechanical treatment of the charge transfer process becomes difficult due to the large number of reaction channels involved. Compared to the single electron process, the experimental data for multi-electron processes are still limited. Early work on the study of charge transfer and ionization includes the study on low energy Arqþ –Ne collisions by Justiniano et al. [10] and collisions of lithium by 15–200 keV protons and helium ions by DuBois [11] where they found that transfer ionization is an important channel for large q and the most natural form of transfer ionization to occur in the low energy Arqþ –Ne collisions is through the population of doubly or multiply excited states on the final Ar ion. Montenegro et al. [12] measured the ratios of the cross sections for the processes of transfer ionization and single capture for 2 MeV/u Clqþ and Tiqþ projectiles on He target. The measured ratio shows a strong dependence with the projectile and the charge state. Different authors have investigated the transfer ionization process by measuring the angular distribution of the emitted electrons [3,13–17]. It is found that the second electron of the transfer ionization process recoils with the speed of the projectile ion vp , resulting in a pronounced peak at about 90 in the angular distribution of the electron emitted with matching velocity ve ¼ vp . The peak was first observed in 1 MeV proton on He collisions by P alink as et al. [13]. Mergel et al. [14] found further evidence of the correlated motion of the emitted and captured electrons for the same collision systems. Sarkadi et al. [3] observed the electron cusp in 100–300 keV He2þ –He collisions, and identified the processes of electron capture to the continuum (ECC), and ECC accompanied by bound-state capture (transfer ionization or TI) by detecting the electrons in coincidence with the charge-state-analyzed outgoing He2þ and Heþ ions. The above experiments were all performed at intermediate (several hundred keV) and high (MeV) collision energies. These studies provide strong evidence for electron correlation in transfer ionization. Mancev [15] calcu-
lated the total cross section for single capture and transfer ionization in Li3þ –He collisions using a four-body distorted-wave formalism. Comparison between the calculations and the experimental data measured at 50–5000 keV/amu yields satisfactory agreement [5]. Up to now, systematic studies of TI and its dependence upon the collision parameters for low energy ion–atom collisions are scarce [12–14]. We have recently reported on the study of TI in the isonuclear sequence of Arqþ ions in collisions with helium, neon and argon atoms [18] and TI in the isocharge sequence of ions (q ¼ 4; 5; 6; 7) in collisions with argon atoms [19]. We have found that the process of TI depends obviously upon the projectile charge state for an isonuclear sequence of ions in collisions with atoms, and also depends upon the electronic structure of the projectile for an isocharge sequence of ions and atom collisions. To further understand the TI process for different collision systems, we have measured the TI to single capture ratios R1 for isocharge Cqþ , Nqþ , Oqþ , Neqþ ions on Ne atoms by using position sensitive and time-of-flight techniques. For an isocharge ion sequence the velocity of the ion is selected to be the same in order to clarify the projectile electronic structure dependence on R1 . It is found that for Aqþ –Ne collisions the ratio R1 decreases as the atomic number Z1 of the projectile increases for q ¼ 4; 5; 6; 7 sequences and differs markedly from the results we obtained for Aqþ –Ar collisions [19]. The difference is explained using a statistical model and the orbital penetration picture. Comparison of the R1 ratios of A4þ –Ne and A4þ –Ar collisions provides the strongest evidence for the enhancement of the binding energy of the target valence electron after single electron capture. The enhancement of the binding energy depends both upon Z1 and Z2 (where Z2 is the atomic number of the target atom). The larger Z1 , the larger the increase in binding energy, while the larger Z2 , the smaller the increase in binding energy.
2. Experimental technique The experiments were performed at the 14.5GHz ECR platform of the Institute of Modern
X. Cai et al. / Nucl. Instr. and Meth. in Phys. Res. B 225 (2004) 185–190
10
Present experiment statistical model
4+
A -Ne
R1
1
0.1
0.01 6
7
8
9
10
Z1 Fig. 1. Ratio R1 of transfer ionization to single capture for C4þ , N4þ , O4þ and Ne4þ on Ne. All ions have the same velocity equal to 0.21 a.u. Z1 is the atomic number of the projectile A4þ .
0.4 5+
A -Ne R1
Physics, Chinese Academy of Sciences. Highly charged ions produced in the ion source were extracted and m=q-selected (where m is the ion mass and q is the ion charge) by the analyzing magnet. The maximum extraction voltage of the ECR source is 25 kV and the voltage can be changed between 10 and 25 kV. The ion beam was collimated by two two-dimensional collimators to a size less than 0.3 · 0.3 mm2 . The ion beams were charge state-selected again before entering into the target chamber by a 64 coaxial static analyzer to ensure the purity of the charge state of the projectile. The ion beam interacted with a gas jet at the center of the target chamber. The recoil ions were extracted from the interaction zone by a static electric field and detected by a channel electron multiplier after passing through a fieldfree tube. The scattered ions were charged stateanalyzed by a parallel plate field and then detected by a position sensitive channel plate detector. The charge state of the recoil ion was determined by measuring the differences of the time-of-flight between the scattered ions and the recoil ions. A multi-parameter acquisition system was used to measure the time-of-flight spectrum of the scattered and recoil ions [2]. Isocharge ion sequences Cqþ , Nqþ , Oqþ , Neqþ were used. The energies of the ion sequence were selected to be 4, 5, 6 and 7 keV/u for projectile charge states 4, 5, 6 and 7 which correspond to the ion velocities of 0.21, 0.24, 0.26 and 0.28 a.u., respectively.
187
0.2
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6
7
8
Z1
3. Results and discussion
Fig. 2. Same as for Fig. 1 but for C5þ , N5þ and O5þ on Ne. All ions have the same velocity equal to 0.24 a.u.
The ratios R1 for Aqþ ions on Ne atoms are shown in Figs. 1–4. The charge states are selected to be q ¼ 4; 5 for carbon, q ¼ 4–6 for nitrogen, q ¼ 4–7 for oxygen, and q ¼ 4; 6–9 for neon projectiles, respectively. The fully stripped ions of C6þ , N7þ , O8þ and Ne10þ were not used because these ions have a charge to mass ratio of 1/2 and cannot be separated from other contaminants with the same charge to mass ratio. From Figs. 1 to 4 it can be seen that the ratio R1 decreases as the atomic number Z1 increases for q ¼ 4; 5; 6; 7 sequences which differs markedly
from the results obtained for Aqþ –Ar collisions [19]. In the study of Aqþ –Ar collisions, we found that the ratio R1 increases as the atomic number Z1 increases for q ¼ 4 sequence, it goes through a minimum for Z1 ¼ 7 and Z1 ¼ 8 for q ¼ 5 and q ¼ 6 sequences, respectively, and R1 decreases as Z1 increases for q ¼ 7 sequence. For comparison in Fig. 5 we show the results of the q ¼ 4 sequence for A4þ –Ar collisions together with that of the q ¼ 4 sequence for A4þ –Ne collisions. To explain these results we may use the concepts of the statistical energy deposition model
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0.8 6+
4+
A -Ne 4+ A -Ar
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R1
A -Ne
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7
8
9
10
11
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6
7
8
9
10
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Fig. 3. Same as for Fig. 1 but for N6þ , O6þ and Ne6þ on Ne. All ions have the same velocity equal to 0.26 a.u.
Fig. 5. Comparison of the ratio R1 for A4þ –Ne and A4þ –Ar collisions. All ions have the same velocity equal to 0.21 a.u. Z1 is the atomic number of the projectile A4þ .
0.60
7+
A -Ne
R1
0.55
0.50
0.45 7
8
9
10
11
Z1 Fig. 4. Same as for Fig. 1 but for O7þ and Ne7þ on Ne. All ions have the same velocity equal to 0.28 a.u.
[20–22]. The electron capture process is an exoergic reaction, and the target electron will gain an energy DE during single capture [20]. In the statistical model the energy deposited in the target atom is considered to be distributed statistically among the remaining target electrons. One or more target electrons may then be evaporated. The probability that the electrons may gain enough energy to overcome their binding energy and escape from the target atom is proportional to the energy gain DE. If we consider the transfer ioni-
zation in a two-step framework, the transfer ionization is a successive process of single electron capture followed by the ionization of a second or more target electrons. To first order the probability of transfer ionization may then be considered to be given by the product of the probabilities for single capture and the ionization of the second electron. So the R1 ratio may be considered to be approximately proportional to the ionization cross section of the second electron. As mentioned above the second electron may be ionized or ‘‘evaporated’’ if it gets enough energy. The maximum energy deposited Em is the difference between ðqÞ the qth ionization energy of the projectile IA and ð1Þ the first ionization energy IT of the target atom, ðqÞ ð1Þ i.e. DEm ¼ IA INe for a neon target. 4þ For 4 keV/u C on Ne collisions the distance of closest approach rmin is rmin 0:06 a.u. After the C4þ ion captures one electron from the Ne atom at the capture distance of 6.3 a.u., the ion needs about 7.3 · 1016 s to arrive to rmin . Considering that the typical lifetime of the autoionization state of the target atom is of the order of 1015 s, autoionization should mostly occur in the vicinity of rmin . Since the radius of the valence state (2s) of the Ne atom is about 0.4 a.u., and the projectile C4þ ion has a valence state (1s) radius of 0.17 a.u. it is much smaller than that of the Ne valence state.
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Thus, we may assume that the C4þ ion penetrates the 2s electron orbit of the Ne atom, and the valence target electrons then move in the combined Coulomb field of the C4þ and Ne nuclei, as shown in the picture of Fig. 6. The effective charge seen by the target valence electrons will be Z1eff þ Z2eff , where Z1eff ¼ Z1 2 and Z2eff ¼ Z2 2 for C4þ on Ne collisions and Z1 and Z2 are the atomic numbers of the projectile and target atom. According to this picture the binding energy of the target valence electrons will then be proportional to 2 2 ðZ1eff þ Z2eff Þ instead of ðZ2eff Þ . In the case of C4þ –Ne collisions, the binding energy of the neon valence electrons will increase to be about 2.2 times the original binding energy according to the estimation based upon the hydrogen-like atom. This will result in the decrease of the ionization probability of the target valence electrons, and the transfer ionization probability will therefore also be considerably decreased. For Ne4þ –Ne collisions the target binding energy will increase to be about four times the original one. As the atomic number of the projectile Z1 increases the binding energy of the target valence electron will increase markedly while the transfer ionization probability will therefore decrease with increasing Z1 as shown in Fig. 1.
Fig. 6. Sketch map of the orbital penetration model. The 1s orbital of C4þ is seen to be considerably smaller that the 2s orbital of neon, but larger than the distance of closest approach rmin .
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For A4þ –Ar collisions the effect of the enhancement of the binding energy [19] due to the orbital penetration is small. The factors of the binding 2 2 energy enhancement, ðZ1eff þ Z2eff Þ =ðZ2eff Þ , are 4þ 4þ about 2.2 and 1.5 for C –Ne and C –Ar collisions, respectively. For the collision of ion sequence q ¼ 4 (C4þ , N4þ , O4þ and Ne4þ ) with argon, the fourth ionization energies are 64.49, 77.47, 77.41 and 97.12 eV [23], corresponding to DEm values of 48.73, 61.17, 61.65 and 81.36 eV, respectively. We note that for carbon, nitrogen and neon projectiles the fourth ionization energy increases with the projectile atomic number Z1 , which therefore also increases the maximum energy deposited DEm . The second ionization energy of argon is 27.63 eV, and it will increase to be 43.17, 47.59, 52.24 and 62.17 eV for the collision with ion sequence q ¼ 4 (C4þ , N4þ , O4þ and Ne4þ ) due to the binding energy enhancement effect discussed above. Since DEm for carbon, nitrogen and neon ions is larger than the enhanced ionization energy of the second electron of argon, the second electron may be ionized. According to the above discussion then, the ionization probability of the second target electron will increase as the projectile atomic number Z1 increases for A4þ –Ar collisions. Fig. 1 also shows the calculated ratio using the statistical energy deposition model. Fig. 1 shows an overestimation of the calculated R1 ratios and the calculated and the measured data have a different Z1 dependence. In the calculation the enhancement of the binding energy was not included and this is the main reason for the disagreement between the calculated results and the present data. Neglecting the effect of the binding energy enhancement may result in the overestimation of R1 and the flat Z1 dependence observed in the calculation. Furthermore, in our calculations the maximum energy deposited DEm is calculated assuming that the electrons will always be captured into the lowest unoccupied energy levels. In fact the electrons are mostly captured into the higher excited energy levels, and the principal quantum number of the captured electrons increases with the charge state of the projectile [7]. This assumption will lead to the overestimation of DEm , and therefore to the overestimation of the transfer ionization probability. Thus, the
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calculated R1 ratios will be larger than the measured data. The results shown in Figs. 2–4 can also be qualitatively explained using the pictures. The experimental uncertainty shown in Figs. 1– 5 is within 10% which comes mainly from the statistical error.
4. Summary The dependence of the transfer ionization to single capture ratio R1 for Cqþ , Nqþ , Oqþ , Neqþ ions on Ne target upon the electronic structure of the projectile is studied using position sensitive and time-of-flight techniques. For an isocharge ion sequence the velocity of the ion is selected to be the same in order to clarify the projectile electronic structure dependences of the ratios mentioned above. It is found that for Aqþ –Ne collisions the ratio R1 decreases as the projectile atomic number Z1 increases for q ¼ 4–7 sequences which differs remarkably from the results we obtained for Aqþ – Ar collisions. The difference may be explained using a statistical model and the orbital penetration model. Comparison of the R1 ratios of A4þ – Ne and A4þ –Ar collisions provides the strongest evidence for the enhancement of the binding energy of the target valence electron after single electron capture. The enhancement of the binding energy depends both upon the atomic number of the projectile and the target atom. The larger Z1 , the larger the increase in binding energy, while the larger the atomic number of the target atom Z2 , the smaller the increase in binding energy.
Acknowledgements We are grateful for the help offered by the staff of the ECR laboratory at the Institute of Modern Physics, Chinese Academy of Sciences during the experiment. This work is supported by the National Natural Science Foundation of China under contract numbers 10134010, 10375080 and 10134019. References [1] [2] [3] [4] [5] [6] [7] [8] [9]
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