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Measurement of Auger electrons emitted through Coster–Kronig transitions under irradiation of fast C2+ ions
Nuclear Inst. and Methods in Physics Research B xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Measurement of Auger electrons emitted through Coster–Kronig transitions under irradiation of fast C+2 ions Y. Shiinaa, R. Kinoshitaa, S. Funadaa, M. Matsudab, M. Imaic, K. Kawatsurad, M. Satakae, K. Sasae, ⁎ S. Tomitaa, a
Institute of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan c Department of Nuclear Engineering, Kyoto University, Nishikyo, Kyoto 615-8540, Japan d Theoretical Radiation Research Laboratory, Sakyo, Kyoto 606-0966, Japan e Tandem Accelerator Complex, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan b
ARTICLE INFO
ABSTRACT
Keywords: Cluster effect Secondary electron Coster–Kronig transition
We measured the yield of Auger electrons emitted through Coster–Kronig transitions from Rydberg states 1s 2p ( 3P) nl (n = 7, 8 ) and 1s 22p ( 2P) nl (n = 5, 6, 7 ) of emergent atomic ions Cq + under irradiation of 3.5-MeV/ atom C+ and C+2 ions on thin C foil targets. The Auger electron yields are suppressed for C+2 irradiation compared with C+ irradiation and the relative yield becomes larger as n increases. Thus, amount of scattered electrons having lower relative energy in the projectile rest frame becomes larger. The results obtained in this study support the influence of projectile velocity on the cluster effect of secondary electron yields.
1. Introduction When fast molecular ions penetrate a material, all constituent atoms impinge within a small area, (e.g., the interatomic distance of several angstrom), within a few femtoseconds. This simultaneous irradiation of multiple atoms compared to atomic ion irradiation causes differences in many physical quantities, such as electronic stopping power [1–4], sputtering yield [5,6], and secondary electron yield [7,8], resulting in an effect known as the cluster effect. For fast molecules, the cluster effect is less understood than for low-energy molecules, in which cluster effects have been applied for industrial production. For velocities exceeding the Bohr velocity, the process of energy loss is dominated by electronic stopping, where the electronic excitation of target atoms governs the collision process. Therefore, the yield of secondary electrons by atomic ion irradiation is proportional to the electronic stopping power according to the equation below.
Ye =
dE dx
e
(1)
The above equation’s proportionality holds for a wide range of incident energies and particles, the parameter representing material parameter [9]. In 0.5 MeV/atom C+n cluster ion bombardments, the energy loss of incident ions is weakly suppressed by about 1% compared with that of atomic ion bombardments [4], whereas the secondary electron ⁎
yield is suppressed by 20–50% [8]. Thus, the proportionality in Eq. (1) does not hold for cluster ion bombardments. The cluster effect in electronic stopping power is understood owing to the interference of wake-fields caused by individual atomic ions [10,11], which disappears when interatomic distance exceeds v/ p [1], where p is plasmon frequency of the target material and v is the velocity of the projectile ion. The corresponding foil thickness is less than 10 µ g/cm2. However, it is reported that the cluster effect on secondary electron yield remains for thick targets, while the effect diminishes for electronic stopping [12,13]. This discrepancy indicates that the mechanism of secondary electron suppression cannot be explained by electronic stopping. Normally, the production of secondary electrons is considered in three steps. Scattered electrons are first generated by collisions between incident ions and target atoms. A fraction of the scattered electrons is then transported to the material surface and transmitted through the material surface over the barrier of the work function. The breakdown of the proportionality in Eq. (1) implies that the suppression mechanism of secondary electrons results from either the transport process of scattered electrons inside the material or the transmission process through the surface barrier. Therefore, understanding the energy distribution of scattered electrons in the target material becomes important for further study of the cluster effect on secondary electron yields. In the present work, we measured the yield of Auger electrons emitted through Coster–Kronig transitions from Rydberg states,
Corresponding author. E-mail address: [email protected] (S. Tomita).
https://doi.org/10.1016/j.nimb.2018.10.041 Received 27 August 2018; Received in revised form 23 October 2018; Accepted 30 October 2018 0168-583X/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Shiina, Y., Nuclear Inst. and Methods in Physics Research B, https://doi.org/10.1016/j.nimb.2018.10.041
Nuclear Inst. and Methods in Physics Research B xxx (xxxx) xxx–xxx
Y. Shiina et al.
1s 2p ( 3P) nl and 1s 22p ( 2P) nl , of emergent atomic ions Cq +. These high Rydberg states are formed at emergence from the target surface by capturing the scattered electron moving together with projectile ions. Hence, the yields of Auger electrons from high Rydberg states offer information about the velocity distribution of scattered electrons.
where and are the electron energy in the laboratory rest frame and projectile rest frame, respectively [18]. The relationship between the energies is
=
The experiments were conducted at the 20-MV tandem accelerator in the Nuclear Science Research Institute of Japan Atomic Energy Agency (JAEA). The carbon cluster ions, C+n were generated from benzene gas with an electron cyclotron resonance ion source located on the high-voltage terminal of the accelerator [14]. The extracted cluster ions were mass selected by a 180-degree magnet, which is also located on the high-voltage terminal, and accelerated by the accelerator in a manner similar to a single Van de Graaff accelerator, so that the molecular ions can be accelerated without fragmentation due to transmission through charge exchange foils. The C+n ions (n = 1, 2 ) were accelerated to an energy of 3.5 MeV/atom and transported to the experimental chamber. A schematic diagram of the experimental setup is shown in Fig. 1. Once inside the chamber, the accelerated ions impinged on the amorphous carbon foil, purchased from ACF-Metals, The Arizona Carbon Foil Co., Inc. The thicknesses of the foils used in the present experiments were 10.5 and 29.7 µ g/cm2 in nominal value. The energies of electrons emitted in the beam direction were analyzed by a tandem-type 45° parallel-plate electrostatic spectrometer [15]. The first spectrometer in the setup was used as a deflector to separate the electrons from the transmitted ions and suppress background stray electrons coming from edge scattering of entrance slits. The second spectrometer was used to determine the energy of the electrons with high resolution. To improve electron energy resolution, the deflected electrons were decelerated to 50 eV by a retarding electric field located in the region between the two spectrometers. The relative energy resolution of the spectrometer setup is 3.2%, which corresponds to 1.6 eV in absolute energy. The acceptance angle of the spectrometer from the target foil is ± 0.5°. The beam current was monitored by a Faraday cup placed just beyond the spectrometer to normalize electron energy spectra. The average equilibrium charge for 3.5-MeV C on a carbon target is about 3.7 according to [16]. At emergence from the foil, the equilibrium charge state of a molecular ion differs from that of an atomic ion by about 10% for the C+3 ions with an energy of 2.0 MeV/ atom [17]. Thus, the normalization error of the present experiments was estimated to be about 10%.
dd
=
.
d d
2
1s22pnl
12
Yield per atom (arb. unit)
10
Forward
n=4
8
Backward 6
4 0
Faraday cup
e-
Series limit
Series limit
(2)
Foil
1s22s + l' n=8 n=7 n=6 n=5
n=7 Beam
(4)
are shown together, where n is the principal quantum number, Q is the charge number of the atomic core seen by the Rydberg electron, µl is the quantum defect calculated by Theodosiou et al. [20] and R is the Rydberg energy (13.606 eV). The energy difference ( E ) between the 2s and 2p states were taken from National Institute of Standards and Technology (NIST) database [21]. The peaks that correspond to the 1s 22p ( 2P) nl 1s 22s ( 2S 1 ) + l and Coster–Kronig transitions
The obtained electron energy spectra were transformed into the projectile rest frame using the relationship between the double differ2 2 ential cross section d in the laboratory rest frame and that d in the dd d d projectile rest frame,
d2
Q 2R (n µl )2
Enl = E
3. Results and discussion
1/2
(3)
0,
where 0 is the kinetic energy of an electron with the same velocity as a projectile ion. In the present experiment, electrons emitted to 0° and 180° to the beam direction are observed, so that the peak broadening effect owing to the finite acceptance angle cancels in the first order, that enables us high resolution spectroscopy of Auger electrons from fast projectiles [19]. The obtained electron energy spectra under C+ bombardments are shown in Fig. 2 in the projectile rest frame. The positions of the peaks in both the forward and backward direction agree very well. In the figure, the electron energies calculated by quantum defect theory [20]
2. Experiments
d2
+
n=10 n=9 n=8 1s2pnl 2
4
1s2s + l' 6
8
10
Electron energy (eV)
Spectrometer
Fig. 2. Electron energy spectra for 3.5-MeV C+ on 10.5-µ g/cm2 carbon foils in the projectile rest frame. The intensities are obtained from forward emission and backward emission. The electron energies calculated using Eq. (4) corre1s 22s ( 2S 1 ) + l and sponding to the Coster–Kronig transitions of 1s 22p ( 2P) nl
Channeltron
2
1s 2p ( 3P) nl 1s 2s ( 3S1) + l are shown together. The calculated values are shown in Table 1.
Fig. 1. A schematic diagram of the experimental setup. 2
Nuclear Inst. and Methods in Physics Research B xxx (xxxx) xxx–xxx
Y. Shiina et al.
1.2
Table 1 Auger electron energies calculated by quantum defect theory [20]. Auger electron energies from the Coster–Kronig transitions 1s 22p ( 2P3 ) nl 1s 22s ( 2S 1 ) + l and 1s 2p ( 3P0) nl 1s 2s ( 3S1) + l are shown.
1.0
n
1s22pns (eV)
1s22pnp (eV)
1s22pnd (eV)
4 5 6 7 8
2.3565 4.1787 5.2432 5.9185
2.7632 4.4078 5.3847 6.0119
0.2841 3.0739 4.5859 5.4961 6.0862
1s2pns
1s2pnp
1s2pnd
n
(eV)
(eV)
(eV)
7 8 9 10
0.7842 1.8974 2.6545 3.1926
0.9409 2.0017 2.7274 3.2456
0.9982 2.0401 2.7543 3.2652
Y(C2+)/2Y(C+)
2
2
0.8 0.6 0.4 0.2
Yield per atom (arb. unit)
1.5
1s22pnl n=4
0.0
1s22s + l' n=6 n=7 n=8 n=9
n=5
1.0
n=6
n=7
Principal quantum number n
n≥8
Fig. 4. Ratio of the yields of electrons, Y (C+2 )/2Y (C+) , attributed to electron 1s 22s + l , plotted as a emission, via the Coster–Kronig transitions 1s 22pnl function of the principal quantum number, n. Target foil thicknesses are 10.5 (circles) and 29.7 µ g/cm2 (crosses), respectively.
0.5
Fig. 4 as a function of the quantum principal number, n, for the target thicknesses of 10.5 and 29.7 µ g/cm2. The suppression effect was weaker for larger values for the quantum number, n, of initial states. This trend is consistent with the cluster effect on convoy electron yields [13], which corresponds to the case of n , where the electron yield is considerably enhanced. The ratio was generally independent of target thickness and the suppression effect remained consistent even for the target thickness of 29.7 µ g/cm2. The high Rydberg states are formed at the emergence from the target material capturing scattered electrons whose wave functions have enough overlap with the high n states of the emergent atom. The higher n states are formed by capturing lower relative energy electrons. Thus, it seems that the observed suppression effect on the Rydberg states results from the difference between the energy distribution of scattered electrons under C+2 bombardments and that under C+ bombardments. For cluster injection cases, the amount of low energy electrons is enhanced, as observed in convoy electron yields [13], while the amount of electrons which form lower n states is reduced as observed in the present study. During the penetration of projectile ions, the scattered low relative energy electrons move together with projectile ions, repeating electron capture and loss process from high Rydberg states [22]. Considering the orbital radii of the high Rydberg states, the low energy electrons attracted by multiple ions for cluster injections. Thus, the relative velocity to the projectile ion is important parameter for the electron transport in the target material. Furthermore, the strongest cluster effect is expected for electrons with the same velocity of the projectile ions. Since a typical energy distribution of secondary electrons has its maximum around 5 eV [23], we expect that the cluster effect on secondary electron yields would be strongest when the projectile velocity is close to the velocity corresponding to 5 eV in electron energy. It is pointed out by Kudo et al. [8] that the secondary electron yields, Yn , of fast cluster ion A+n are well reproduced by a simple empirical formula
0.0
-0.5
n=5
Series limit
n=7
0
n=8 n=9 n=10
2
1s2pnl Series limit
4
6
1s2s + l'
8
10
Electron energy (eV) Fig. 3. Electron energy spectra for 3.5-MeV/atom C+ (solid line) and C+2 (dashed line) in the projectile rest frame. The target thickness is 10.5-µ g/cm2. Underlying backgrounds of continuum components, resulting from secondary electrons, convoy electrons and field ionization in the first spectrometer, have been subtracted.
1s 2p ( 3P) nl 1s2s ( 3S1) + l are clearly observed. The calculated values for Auger electron energies are shown in Table 1. The comparison of the electron energy spectra from C+ and C+2 bombardments are shown in Fig. 3. Electron yields are normalized to electron yields per constituent atom of projectiles. Underlying backgrounds of continuum components, resulting from secondary electrons, convoy electrons and field ionization in the first spectrometer, have been subtracted. Auger electron peaks attributed to transitions of high Rydberg states of carbon atoms are observed also in the case of C+2 bombardments. The interatomic distances after penetration through 10.5- and 29.7-µ g/cm2 C-foil are estimated to be 4 Å and 12 Å, respectively, based on the Coulomb explosion of charged particles with an equilibrium charge of 3.7 [16]. On the other hand, the orbital radii of the Rydberg states 1s 2 2p5l are calculated to be 6.61 Å and 4.85 Å for l = 0 and 4, respectively. Likewise, those of 1s 2 2p6l are 9.52 Å and 6.88 Å for l = 0 and 5, and those of 1s 2 2p7l are 13.0 Å and 9.26 Å for l = 0 and 6, respectively. It is important to note that the interatomic distances are comparable to the orbital radii of the Rydberg states. Therefore, the electrons captured in high Rydberg states are affected by both ions at the target surface. At the time the autoionization takes place, the interatomic distance is long enough so that Rydberg states are regarded as that of a single atomic ion. It is also clearly seen in Fig. 3 that, in transitions 1s 22p ( 2P) nl 1s 22s ( 2S 1 ) + l (n = 5, 6, 7 ), Auger
Yn/ Y1 = 1 +
(n
1),
(5)
with a suppression coefficient, . In Fig. 5, the suppression coefficient [24] of secondary electron yields for the fast cluster irradiation of Au+n [25], H+n [26], Al+n and C+n [8] are plotted as a function of the velocity of projectile molecules. Surprisingly, the coefficients fall into a universal curve, which has a minimum around 10 keV/u. This velocity corresponds to 5 eV for an electron, which is close to the velocity where a typical energy distribution of secondary electrons reaches its maximum [23].
2
electron yields for C+2 ion bombardments were suppressed compared with that for C+ ion bombardments, and the suppression effect seems to weaken as n of the initial state increases. The ratios of the area, Y (C+2 )/2Y (C+) , of Auger electron peaks at1s 22s ( 2S 1 ) + l are shown in tributed to the transition 1s 22p ( 2P) nl 2
3
Nuclear Inst. and Methods in Physics Research B xxx (xxxx) xxx–xxx
Y. Shiina et al.
1.0
0
10
E me / mp (eV)
20
30
Acknowledgements
40
50
60
The authors would like to thank Prof. Kudo, Prof. Kaneko, and Dr. Narumi for usefull discussions. The authors also thank the staff of 20 MV tandem accelerator in JAEA for the technical supports. The work was financially supported by Cooperative Research Program of JAEA and University of Tokyo.
0.8
References
α
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0.4 0.2 0.0
0
20
40
60
80
100
E / u (keV/u) Fig. 5. The suppression coefficient of secondary electron yield in Eq. (5) for fast cluster irradiation of Au+n (triangles) [25], H+n (diamonds) [26], Al+n (crosses), and C+n (squares) [8]. The values are taken from [24].
The cluster effects on Auger electron yields from high Rydberg states, yields of convoy electrons, and low-energy secondary electrons suggest that the cluster effects of electron emission strongly depend on relative velocities of electrons to projectile ions. It seems that the cluster effects on electron emission take place during the transport of scattered electrons in the material, affecting the electron energy distribution of bounded and scattered electrons, particularly low-energy electrons relative to projectile ions. 4. Conclusion The n dependence of the Auger electron yield emitted through the Coster–Kronig transition from Rydberg states 1s 22p ( 2P) nl and 1s 2p ( 3P) nl indicates that the energy distribution of scattered electrons in the material is different with C+2 bombardments. The excited states are formed at the emergence from the target material by capturing scattered electrons whose wave functions have enough overlap with the high n states of the emergent atom. The cluster effect on the energy distribution of the scattered electrons implies that projectile velocity is important in the cluster effect on secondary electron yields. In fact, the suppression factor displays the same trend as a function of projectile velocity, meaning the minimum velocity corresponds to the electron energy of 5 eV, which is also typically the maximum of the energy distribution for secondary electrons.
4
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Measurement of Auger electrons emitted through Coster–Kronig transitions under irradiation of fast C+2 ions Y. Shiinaa, R. Kinoshitaa, S. Funadaa, M. Matsudab, M. Imaic, K. Kawatsurad, M. Satakae, K. Sasae, ⁎ S. Tomitaa, a
Institute of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki 319-1195, Japan c Department of Nuclear Engineering, Kyoto University, Nishikyo, Kyoto 615-8540, Japan d Theoretical Radiation Research Laboratory, Sakyo, Kyoto 606-0966, Japan e Tandem Accelerator Complex, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan b
ARTICLE INFO
ABSTRACT
Keywords: Cluster effect Secondary electron Coster–Kronig transition
We measured the yield of Auger electrons emitted through Coster–Kronig transitions from Rydberg states 1s 2p ( 3P) nl (n = 7, 8 ) and 1s 22p ( 2P) nl (n = 5, 6, 7 ) of emergent atomic ions Cq + under irradiation of 3.5-MeV/ atom C+ and C+2 ions on thin C foil targets. The Auger electron yields are suppressed for C+2 irradiation compared with C+ irradiation and the relative yield becomes larger as n increases. Thus, amount of scattered electrons having lower relative energy in the projectile rest frame becomes larger. The results obtained in this study support the influence of projectile velocity on the cluster effect of secondary electron yields.
1. Introduction When fast molecular ions penetrate a material, all constituent atoms impinge within a small area, (e.g., the interatomic distance of several angstrom), within a few femtoseconds. This simultaneous irradiation of multiple atoms compared to atomic ion irradiation causes differences in many physical quantities, such as electronic stopping power [1–4], sputtering yield [5,6], and secondary electron yield [7,8], resulting in an effect known as the cluster effect. For fast molecules, the cluster effect is less understood than for low-energy molecules, in which cluster effects have been applied for industrial production. For velocities exceeding the Bohr velocity, the process of energy loss is dominated by electronic stopping, where the electronic excitation of target atoms governs the collision process. Therefore, the yield of secondary electrons by atomic ion irradiation is proportional to the electronic stopping power according to the equation below.
Ye =
dE dx
e
(1)
The above equation’s proportionality holds for a wide range of incident energies and particles, the parameter representing material parameter [9]. In 0.5 MeV/atom C+n cluster ion bombardments, the energy loss of incident ions is weakly suppressed by about 1% compared with that of atomic ion bombardments [4], whereas the secondary electron ⁎
yield is suppressed by 20–50% [8]. Thus, the proportionality in Eq. (1) does not hold for cluster ion bombardments. The cluster effect in electronic stopping power is understood owing to the interference of wake-fields caused by individual atomic ions [10,11], which disappears when interatomic distance exceeds v/ p [1], where p is plasmon frequency of the target material and v is the velocity of the projectile ion. The corresponding foil thickness is less than 10 µ g/cm2. However, it is reported that the cluster effect on secondary electron yield remains for thick targets, while the effect diminishes for electronic stopping [12,13]. This discrepancy indicates that the mechanism of secondary electron suppression cannot be explained by electronic stopping. Normally, the production of secondary electrons is considered in three steps. Scattered electrons are first generated by collisions between incident ions and target atoms. A fraction of the scattered electrons is then transported to the material surface and transmitted through the material surface over the barrier of the work function. The breakdown of the proportionality in Eq. (1) implies that the suppression mechanism of secondary electrons results from either the transport process of scattered electrons inside the material or the transmission process through the surface barrier. Therefore, understanding the energy distribution of scattered electrons in the target material becomes important for further study of the cluster effect on secondary electron yields. In the present work, we measured the yield of Auger electrons emitted through Coster–Kronig transitions from Rydberg states,
Corresponding author. E-mail address: [email protected] (S. Tomita).
https://doi.org/10.1016/j.nimb.2018.10.041 Received 27 August 2018; Received in revised form 23 October 2018; Accepted 30 October 2018 0168-583X/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Shiina, Y., Nuclear Inst. and Methods in Physics Research B, https://doi.org/10.1016/j.nimb.2018.10.041
Nuclear Inst. and Methods in Physics Research B xxx (xxxx) xxx–xxx
Y. Shiina et al.
1s 2p ( 3P) nl and 1s 22p ( 2P) nl , of emergent atomic ions Cq +. These high Rydberg states are formed at emergence from the target surface by capturing the scattered electron moving together with projectile ions. Hence, the yields of Auger electrons from high Rydberg states offer information about the velocity distribution of scattered electrons.
where and are the electron energy in the laboratory rest frame and projectile rest frame, respectively [18]. The relationship between the energies is
=
The experiments were conducted at the 20-MV tandem accelerator in the Nuclear Science Research Institute of Japan Atomic Energy Agency (JAEA). The carbon cluster ions, C+n were generated from benzene gas with an electron cyclotron resonance ion source located on the high-voltage terminal of the accelerator [14]. The extracted cluster ions were mass selected by a 180-degree magnet, which is also located on the high-voltage terminal, and accelerated by the accelerator in a manner similar to a single Van de Graaff accelerator, so that the molecular ions can be accelerated without fragmentation due to transmission through charge exchange foils. The C+n ions (n = 1, 2 ) were accelerated to an energy of 3.5 MeV/atom and transported to the experimental chamber. A schematic diagram of the experimental setup is shown in Fig. 1. Once inside the chamber, the accelerated ions impinged on the amorphous carbon foil, purchased from ACF-Metals, The Arizona Carbon Foil Co., Inc. The thicknesses of the foils used in the present experiments were 10.5 and 29.7 µ g/cm2 in nominal value. The energies of electrons emitted in the beam direction were analyzed by a tandem-type 45° parallel-plate electrostatic spectrometer [15]. The first spectrometer in the setup was used as a deflector to separate the electrons from the transmitted ions and suppress background stray electrons coming from edge scattering of entrance slits. The second spectrometer was used to determine the energy of the electrons with high resolution. To improve electron energy resolution, the deflected electrons were decelerated to 50 eV by a retarding electric field located in the region between the two spectrometers. The relative energy resolution of the spectrometer setup is 3.2%, which corresponds to 1.6 eV in absolute energy. The acceptance angle of the spectrometer from the target foil is ± 0.5°. The beam current was monitored by a Faraday cup placed just beyond the spectrometer to normalize electron energy spectra. The average equilibrium charge for 3.5-MeV C on a carbon target is about 3.7 according to [16]. At emergence from the foil, the equilibrium charge state of a molecular ion differs from that of an atomic ion by about 10% for the C+3 ions with an energy of 2.0 MeV/ atom [17]. Thus, the normalization error of the present experiments was estimated to be about 10%.
dd
=
.
d d
2
1s22pnl
12
Yield per atom (arb. unit)
10
Forward
n=4
8
Backward 6
4 0
Faraday cup
e-
Series limit
Series limit
(2)
Foil
1s22s + l' n=8 n=7 n=6 n=5
n=7 Beam
(4)
are shown together, where n is the principal quantum number, Q is the charge number of the atomic core seen by the Rydberg electron, µl is the quantum defect calculated by Theodosiou et al. [20] and R is the Rydberg energy (13.606 eV). The energy difference ( E ) between the 2s and 2p states were taken from National Institute of Standards and Technology (NIST) database [21]. The peaks that correspond to the 1s 22p ( 2P) nl 1s 22s ( 2S 1 ) + l and Coster–Kronig transitions
The obtained electron energy spectra were transformed into the projectile rest frame using the relationship between the double differ2 2 ential cross section d in the laboratory rest frame and that d in the dd d d projectile rest frame,
d2
Q 2R (n µl )2
Enl = E
3. Results and discussion
1/2
(3)
0,
where 0 is the kinetic energy of an electron with the same velocity as a projectile ion. In the present experiment, electrons emitted to 0° and 180° to the beam direction are observed, so that the peak broadening effect owing to the finite acceptance angle cancels in the first order, that enables us high resolution spectroscopy of Auger electrons from fast projectiles [19]. The obtained electron energy spectra under C+ bombardments are shown in Fig. 2 in the projectile rest frame. The positions of the peaks in both the forward and backward direction agree very well. In the figure, the electron energies calculated by quantum defect theory [20]
2. Experiments
d2
+
n=10 n=9 n=8 1s2pnl 2
4
1s2s + l' 6
8
10
Electron energy (eV)
Spectrometer
Fig. 2. Electron energy spectra for 3.5-MeV C+ on 10.5-µ g/cm2 carbon foils in the projectile rest frame. The intensities are obtained from forward emission and backward emission. The electron energies calculated using Eq. (4) corre1s 22s ( 2S 1 ) + l and sponding to the Coster–Kronig transitions of 1s 22p ( 2P) nl
Channeltron
2
1s 2p ( 3P) nl 1s 2s ( 3S1) + l are shown together. The calculated values are shown in Table 1.
Fig. 1. A schematic diagram of the experimental setup. 2
Nuclear Inst. and Methods in Physics Research B xxx (xxxx) xxx–xxx
Y. Shiina et al.
1.2
Table 1 Auger electron energies calculated by quantum defect theory [20]. Auger electron energies from the Coster–Kronig transitions 1s 22p ( 2P3 ) nl 1s 22s ( 2S 1 ) + l and 1s 2p ( 3P0) nl 1s 2s ( 3S1) + l are shown.
1.0
n
1s22pns (eV)
1s22pnp (eV)
1s22pnd (eV)
4 5 6 7 8
2.3565 4.1787 5.2432 5.9185
2.7632 4.4078 5.3847 6.0119
0.2841 3.0739 4.5859 5.4961 6.0862
1s2pns
1s2pnp
1s2pnd
n
(eV)
(eV)
(eV)
7 8 9 10
0.7842 1.8974 2.6545 3.1926
0.9409 2.0017 2.7274 3.2456
0.9982 2.0401 2.7543 3.2652
Y(C2+)/2Y(C+)
2
2
0.8 0.6 0.4 0.2
Yield per atom (arb. unit)
1.5
1s22pnl n=4
0.0
1s22s + l' n=6 n=7 n=8 n=9
n=5
1.0
n=6
n=7
Principal quantum number n
n≥8
Fig. 4. Ratio of the yields of electrons, Y (C+2 )/2Y (C+) , attributed to electron 1s 22s + l , plotted as a emission, via the Coster–Kronig transitions 1s 22pnl function of the principal quantum number, n. Target foil thicknesses are 10.5 (circles) and 29.7 µ g/cm2 (crosses), respectively.
0.5
Fig. 4 as a function of the quantum principal number, n, for the target thicknesses of 10.5 and 29.7 µ g/cm2. The suppression effect was weaker for larger values for the quantum number, n, of initial states. This trend is consistent with the cluster effect on convoy electron yields [13], which corresponds to the case of n , where the electron yield is considerably enhanced. The ratio was generally independent of target thickness and the suppression effect remained consistent even for the target thickness of 29.7 µ g/cm2. The high Rydberg states are formed at the emergence from the target material capturing scattered electrons whose wave functions have enough overlap with the high n states of the emergent atom. The higher n states are formed by capturing lower relative energy electrons. Thus, it seems that the observed suppression effect on the Rydberg states results from the difference between the energy distribution of scattered electrons under C+2 bombardments and that under C+ bombardments. For cluster injection cases, the amount of low energy electrons is enhanced, as observed in convoy electron yields [13], while the amount of electrons which form lower n states is reduced as observed in the present study. During the penetration of projectile ions, the scattered low relative energy electrons move together with projectile ions, repeating electron capture and loss process from high Rydberg states [22]. Considering the orbital radii of the high Rydberg states, the low energy electrons attracted by multiple ions for cluster injections. Thus, the relative velocity to the projectile ion is important parameter for the electron transport in the target material. Furthermore, the strongest cluster effect is expected for electrons with the same velocity of the projectile ions. Since a typical energy distribution of secondary electrons has its maximum around 5 eV [23], we expect that the cluster effect on secondary electron yields would be strongest when the projectile velocity is close to the velocity corresponding to 5 eV in electron energy. It is pointed out by Kudo et al. [8] that the secondary electron yields, Yn , of fast cluster ion A+n are well reproduced by a simple empirical formula
0.0
-0.5
n=5
Series limit
n=7
0
n=8 n=9 n=10
2
1s2pnl Series limit
4
6
1s2s + l'
8
10
Electron energy (eV) Fig. 3. Electron energy spectra for 3.5-MeV/atom C+ (solid line) and C+2 (dashed line) in the projectile rest frame. The target thickness is 10.5-µ g/cm2. Underlying backgrounds of continuum components, resulting from secondary electrons, convoy electrons and field ionization in the first spectrometer, have been subtracted.
1s 2p ( 3P) nl 1s2s ( 3S1) + l are clearly observed. The calculated values for Auger electron energies are shown in Table 1. The comparison of the electron energy spectra from C+ and C+2 bombardments are shown in Fig. 3. Electron yields are normalized to electron yields per constituent atom of projectiles. Underlying backgrounds of continuum components, resulting from secondary electrons, convoy electrons and field ionization in the first spectrometer, have been subtracted. Auger electron peaks attributed to transitions of high Rydberg states of carbon atoms are observed also in the case of C+2 bombardments. The interatomic distances after penetration through 10.5- and 29.7-µ g/cm2 C-foil are estimated to be 4 Å and 12 Å, respectively, based on the Coulomb explosion of charged particles with an equilibrium charge of 3.7 [16]. On the other hand, the orbital radii of the Rydberg states 1s 2 2p5l are calculated to be 6.61 Å and 4.85 Å for l = 0 and 4, respectively. Likewise, those of 1s 2 2p6l are 9.52 Å and 6.88 Å for l = 0 and 5, and those of 1s 2 2p7l are 13.0 Å and 9.26 Å for l = 0 and 6, respectively. It is important to note that the interatomic distances are comparable to the orbital radii of the Rydberg states. Therefore, the electrons captured in high Rydberg states are affected by both ions at the target surface. At the time the autoionization takes place, the interatomic distance is long enough so that Rydberg states are regarded as that of a single atomic ion. It is also clearly seen in Fig. 3 that, in transitions 1s 22p ( 2P) nl 1s 22s ( 2S 1 ) + l (n = 5, 6, 7 ), Auger
Yn/ Y1 = 1 +
(n
1),
(5)
with a suppression coefficient, . In Fig. 5, the suppression coefficient [24] of secondary electron yields for the fast cluster irradiation of Au+n [25], H+n [26], Al+n and C+n [8] are plotted as a function of the velocity of projectile molecules. Surprisingly, the coefficients fall into a universal curve, which has a minimum around 10 keV/u. This velocity corresponds to 5 eV for an electron, which is close to the velocity where a typical energy distribution of secondary electrons reaches its maximum [23].
2
electron yields for C+2 ion bombardments were suppressed compared with that for C+ ion bombardments, and the suppression effect seems to weaken as n of the initial state increases. The ratios of the area, Y (C+2 )/2Y (C+) , of Auger electron peaks at1s 22s ( 2S 1 ) + l are shown in tributed to the transition 1s 22p ( 2P) nl 2
3
Nuclear Inst. and Methods in Physics Research B xxx (xxxx) xxx–xxx
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1.0
0
10
E me / mp (eV)
20
30
Acknowledgements
40
50
60
The authors would like to thank Prof. Kudo, Prof. Kaneko, and Dr. Narumi for usefull discussions. The authors also thank the staff of 20 MV tandem accelerator in JAEA for the technical supports. The work was financially supported by Cooperative Research Program of JAEA and University of Tokyo.
0.8
References
α
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0.4 0.2 0.0
0
20
40
60
80
100
E / u (keV/u) Fig. 5. The suppression coefficient of secondary electron yield in Eq. (5) for fast cluster irradiation of Au+n (triangles) [25], H+n (diamonds) [26], Al+n (crosses), and C+n (squares) [8]. The values are taken from [24].
The cluster effects on Auger electron yields from high Rydberg states, yields of convoy electrons, and low-energy secondary electrons suggest that the cluster effects of electron emission strongly depend on relative velocities of electrons to projectile ions. It seems that the cluster effects on electron emission take place during the transport of scattered electrons in the material, affecting the electron energy distribution of bounded and scattered electrons, particularly low-energy electrons relative to projectile ions. 4. Conclusion The n dependence of the Auger electron yield emitted through the Coster–Kronig transition from Rydberg states 1s 22p ( 2P) nl and 1s 2p ( 3P) nl indicates that the energy distribution of scattered electrons in the material is different with C+2 bombardments. The excited states are formed at the emergence from the target material by capturing scattered electrons whose wave functions have enough overlap with the high n states of the emergent atom. The cluster effect on the energy distribution of the scattered electrons implies that projectile velocity is important in the cluster effect on secondary electron yields. In fact, the suppression factor displays the same trend as a function of projectile velocity, meaning the minimum velocity corresponds to the electron energy of 5 eV, which is also typically the maximum of the energy distribution for secondary electrons.
4