- Email: [email protected]
Electron-impact single and multiple ionization of praseodymium ions
Nuclear Instruments and Methods in Physics Research B 205 (2003) 437–443 www.elsevier.com/locate/nimb
Electron-impact single and multiple ionization of praseodymium ions K. Aichele, W. Arnold, H. Br€ auning, D. Hathiramani, F. Scheuermann, R. Trassl, E. Salzborn * Institut f€ur Kernphysik, Leihgesterner Weg 217, Universit€at Giessen, 35392 Giessen, Germany
Abstract Using the dynamic crossed-beams method, the following absolute cross sections rq;qþn for single ðn ¼ 1Þ, double ðn ¼ 2Þ and triple ðn ¼ 3Þ ionization by electron impact have been measured for the reaction e þ Prqþ ! PrðqþnÞþ þðn þ 1Þe n¼1: n¼2: n¼3:
r1;3 r1;4
r2;3 r2;4 r2;5
r3;4 r3;5 r3;6
r4;5 r4;6
r6;7
r7;8
r8;9
r11;12
The measurements have been performed in an energy range from the respective threshold up to 1 keV. For the single-ionization cross sections, contributions from excitation–autoionization processes increase with increasing charge state of the parent ion. As no theoretical calculations on praseodymium ions exist, these cross sections are compared to the semi-empirical Lotz formula [Zeitschrift f€ ur Physik 232 (1970) 101]. Where contributions of indirect inner-shell processes to the cross section are expected, we conducted energy-scan measurements with high energy resolution. For multiple ionization, no theoretical calculations on praseodymium ions exist. Therefore, the measured cross sections were compared to the semi-empirical formulae by Belenger et al. [J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 2667] and Fisher et al. [J. Phys. B: At. Mol. Opt. Phys. 28 (1995) 3027]. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 34.80.Dp; 34.80.Kw Keywords: Praseodymium; Electron-impact; Ionization; Ions
1. Introduction
*
Corresponding author. E-mail address: [email protected] (E. Salzborn).
Electron-impact ionization of ions is one of the most fundamental processes in every kind of plasma. Especially in high-temperature plasmas – whether in laboratory (nuclear fusion) or in astrophysics (atmosphere of stars) – atoms become
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(03)00565-2
438
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
ionized into multiply charged ions by electron impact. The main purpose of this investigation is to unravel the contributions from different ionization mechanisms – like direct ionization (onestep process), excitation–autoionization (two-step process) and inner-shell Auger processes – to the cross sections of single ionization of highly charged Prqþ ions.
2. Experimental technique The experimental set-up used for the present work has been described in detail earlier [4,5]. The Prqþ ions were produced by evaporating praseodymium powder from an oven into the plasma of a 10 GHz ECR ion source [6]. Using an acceleration voltage of 10 kV, ion currents of up to 10 nA could be extracted. The ion beam was collimated to 2 2 mm2 after mass and energy analysis and crossed with an intense electron beam [7] providing currents up to 450 mA. The energy of the electrons can be varied between 10 and 1000 eV. After the electron–ion interaction, the product ions were separated from the incident ion beam by a 90°magnet and detected by a single-particle detector. The current of the parent ion beam was measured simultaneously in a Faraday cup. Employing the dynamic crossed-beams technique introduced by M€ uller et al. [8], where the electron beam is moved through the ion beam with simultaneous registration of the primary and the product ion intensities, absolute cross sections were obtained. The total experimental uncertainties at 95% confidence level are typically 10% at the maximum of the cross sections including systematic errors of about 8.9%. Measurement times for each absolute cross section value ranged from 50 to 2000 s. The cross sections for single ionization of Prþ and Pr9þ ions showed a dependence on the pressure in the interaction region and could therefore not be measured. As the mass-to-charge ratio for Pr5þ and Pr10þ ions equals 28.2 and 14.1, respectively, these ions could not be þ separated from Nþ 2 and N . In order to examine in detail the contributions from indirect inner-shell processes to the cross sections, energy-scan measurements with high resolution [9] have been performed in the relevant energy ranges.
3. Results 3.1. Single ionization of Pr2þ In Fig. 1 the absolute cross section for the single ionization of Pr2þ is shown. In the upper part only absolute cross section values are given while the lower part shows the results of the high-resolution energy-scan measurement. There is only a small deviation between the observed ionization threshold and the spectroscopically found ionization potential [10]. The steep rise above the onset of the cross section strongly suggests contributions of excitation–autoionization (EA) processes. The shown energy ranges for EA processes were calculated using the GRASP-code [11]. The underestimation of the measured cross section by the semi-empirical Lotz formula [1] is an additional indication of strong EA contributions, since only direct ionization processes are taken into account by this formula. The lower part of Fig. 1 shows a high-resolution energy-scan measurement in the interesting energy range from 25 to 170 eV. 5p-EA processes are responsible for the steep increase at electron energies from 25 to 35 eV. Two small peaks at 30 and 36 eV are due to resonant 5s- or 4d-excitation processes. The step at 100 eV results from 4d-EA processes. 3.2. Single ionization of Pr3þ The absolute cross section for the single ionization of Pr3þ is presented in Fig. 2. The upper part shows the absolute cross section values only, while in the lower part the result of an energy-scan measurement in the energy range from 70 to 150 eV is shown. Again the underestimation by the Lotz formula is in agreement with the strong contributions by indirect processes from the threshold on. The non-zero cross section values below the ground state ionization threshold at 37.4 eV results from metastable ions in the [Kr]4d10 5s2 5p5 4f3 configuration. The steep rise of the cross section at the threshold strongly suggests that the fraction of metastable ions in the ion beam is small. As for the Pr2þ ions, 5p-EA processes contribute to the cross section from the threshold on. The gradient decreases above the 5p-ionization
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
439
Fig. 1. Upper part: absolute cross section for the electron-impact single ionization of Pr2þ . Error bars: total experimental uncertainties. Bars: energy regions of inner-shell excitations. Arrows: ionization thresholds. Solid line: Lotz formula [1]. Lower part: high-resolution energy-scan measurement (only statistical errors are shown). All energies and thresholds corresponding to the [Xe]4f3 ground state configuration were calculated using the GRASP-code [11].
energy at 49.57 eV. The two steps at 90 and 100 eV seem to be due to 4d ! nl-EA processes and were investigated in detail (lower part of Fig. 2). The first step cannot be explained by excitations from the ground state configuration. However, a 4d ! 5p excitation from the metastable
[Kr]4d10 5s2 5p5 4f3 configuration could be found in this energy range. The contribution has to be extremely strong due to the small fraction of metastable ions in the primary ion beam. The second step at 100 eV is due to 4d ! nl excitations of the ground state configuration.
440
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
Fig. 2. Upper part: absolute cross section for the electron-impact single ionization of Pr3þ . Error bars: total experimental uncertainties. Bars: energy regions of inner-shell excitations. Arrows: ionization thresholds. Solid line: Lotz formula [1]. Cross section values below threshold are due to 4d ! 5p excitation–autoionization of the metastable [Kr]4d10 5s2 5p5 4f3 configuration. Lower part: high-resolution energy-scan measurement. Only statistical errors are shown. Bars and arrows as in upper part. All energies and thresholds corresponding to the [Xe]4f3 ground state configuration were calculated using the GRASP-code [11]. Dotted bar: energy ranges for excitations of the metastable 5p5 4f3 configuration.
3.3. Single ionization of Prqþ All measured absolute cross sections for the electron-impact single ionization of Prqþ (q ¼ 2–4, 6–8, 11) are displayed in Fig. 3 using a double
logarithmic scale. Above q P 4 all charge states show contributions of metastable ions in the ion beam, which are produced in the plasma of the ECR ion source. At higher charge states, contributions of EA processes increase compared to the
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
441
-17
2
Cross section (10 cm )
10
1
2+
Pr 4+ Pr 7+ Pr 11+ Pr
0.1
100
3+
Pr 6+ Pr 8+ Pr 1000
Electron energy (eV)
Fig. 3. Absolute cross sections for the electron-impact single ionization of Prqþ (q ¼ 2–4, 6–8, 11) on a double logarithmic scale.
direct ionization. From the structure and the shape of the cross sections it seems that a dominant contribution results from 4d-EA processes. The higher the charge state, the more the cross sections are underestimated by the Lotz formula. This formula neglects all contributions from indirect processes. Thus underestimations of the measured cross sections by a factor of up to 4 were found. It is remarkable that the cross sections for Pr6þ and Pr7þ ions are nearly identical above 500 eV. Even Pr8þ is only slightly lower. This can be explained by strong EA contributions, which increase with increasing the charge state. 3.4. Double Ionization of Prqþ The absolute cross section for the electron-impact double ionization of singly charged praseodymium ions is shown in Fig. 4. No significant contributions of 5s-excitation-double-autoionization (EDA) processes can be seen. Comparing the measured cross section to the semi-empirical formula of Belenger et al. [2] a reasonable agreement within the error margin of a factor of two, which is given for the formula, can be found. The underestimation of the formula by Fisher et al. [3] takes full use of its error range of a factor of two. Obviously at about 105 eV a two-step structure appears in the cross section. In order to investigate the step-like structure more closely, we employed
Fig. 4. Upper part: absolute cross section for the electron-impact double ionization of Pr1þ . Error bars: total experimental uncertainties. Bars: energy regions of inner-shell excitations. Arrows: ionization thresholds. Solid line: Belenger et al. [2]. Dashed line: Fisher et al. [3]. Lower part: high-resolution energy scan measurement (only statistical errors are shown). Dots: absolute cross section values (total experimental uncertainties). All calculations for the [Xe]4f3 6s ground state configuration were calculated using the GRASP-code [11].
the high-resolution energy-scan method in the energy range from 60 to 215 eV. The results are shown in the lower part of Fig. 4 and show only one step in the cross section which is due to 4dEDA processes. Fig. 5 shows all measured absolute cross sections for the processes e þ Prqþ ! Prðqþ2Þþ þ3e ðq ¼ 1; . . . ; 4Þ, on a double logarithmic scale. For q ¼ 4 contributions of metastable ions could be found. All cross sections show contributions from 4d-EDA processes. For Pr4þ , these processes contribute from the threshold on.
442
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
1
-17
2
Cross section (10 cm )
10
0.1
+
Pr 2+ Pr 3+ Pr 4+ Pr
0.01
100
1000
Electron energy (eV)
Fig. 5. Absolute cross sections for the electron-impact double ionization of Prqþ ðq ¼ 1; . . . ; 4Þ on a double logarithmic scale. Excitation–double-autoionization contributions at energies above 120 eV can be seen in most cross sections.
-18
2
Cross section (10 cm )
10
1
+
Pr 2+ Pr 3+ Pr
0.1
100
1000
Electron energy (eV)
Fig. 7. Absolute cross section for the electron-impact triple ionization of Pr2þ . Error bars: total experimental uncertainties. Bars: energy regions of inner-shell excitations. Arrows: ionization thresholds. Solid line: Belenger et al. [2]. Dashed line: Fisher et al. [3] scaled by a factor of 0.5.
Pr2þ ions (4p-ETA), respectively. For the Pr3þ ions these indirect inner-shell processes show no obvious contributions. Fig. 7 shows the cross section for the electron-impact triple ionization of Pr2þ ions compared to the semi-empirical formulae of Belenger and Fisher, respectively. The formula of Belenger et al. [2] reproduces the cross section within its error margin, but underestimates the cross section from the onset of 4p-ETA contributions. The position of the maximum is at a slightly higher energy than the measured cross section maximum. The formula of Fisher et al. [3] has its maximum at a higher energy and overestimates the cross section over the whole energy range by more than a factor of 2.
Fig. 6. Absolute cross sections for the electron-impact triple ionization of Prqþ ðq ¼ 1; . . . ; 3Þ on a double logarithmic scale.
3.5. Triple Ionization of Prqþ The results for the triple ionization of Prqþ ions in charge states q ¼ 1, 2, 3 are shown in Fig. 6. No significant contributions of metastable states could be found. The fraction of metastable ions in the ion beam should be the same as for the single- and double-ionization cross sections measurements. For Pr2þ and Pr3þ , this fraction was found to be small. Excitation–triple-autoionization (ETA) processes contribute to the cross section for the Prþ -primary ions (significant 4d-ETA and 4p-ETA) and the
References [1] W. Lotz, Zeitschrift f€ ur Physik 232 (1970) 101. [2] C. Belenger, P. Defrance, E. Salzborn, V.P. Shevelko, H. Tawara, D.B. Uskov, J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 2667. [3] V. Fisher, Y. Ralchenko, A. Goldgirsh, D. Fisher, Y. Maron, J. Phys. B: At. Mol. Opt. Phys. 28 (1995) 3027. [4] K. Tinschert, A. M€ uller, G. Hofmann, K. Huber, R. Becker, D.C. Gregory, E. Salzborn, J. Phys. B: At. Mol. Opt. 22 (1989) 531. [5] G. Hofmann, K. Tinschert, A. M€ uller, E. Salzborn, Z. Phys. D 16 (1990) 113. [6] M. Liehr, M. Schlapp, R. Trassl, G. Hofmann, M. Stenke, R. V€ olpel, E. Salzborn, Nucl. Instr. and Meth. B 79 (1993) 697.
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443 [7] R. Becker, A. M€ uller, C. Achenbach, K. Tinschert, E. Salzborn, Nucl. Instr. and Meth. B 9 (1985) 385. [8] A. M€ uller, K. Tinschert, C. Achenbach, E. Salzborn, Nucl. Instr. and Meth. B 10/11 (1985) 204. [9] A. M€ uller, G. Hofmann, K. Tinschert, E. Salzborn, G.H. Dunn, Phys. Rev. Lett. 61 (1988) 70.
443
[10] W.C. Martin, R. Zalubas, L. Hagan, Atomic Energy Levels – The Rare-Earth Elements, Institute for Basic Standards, National Bureau of Standards, Washington, D.C., 1978, p. 20234. [11] K.D. Dyall, I.P. Grant, C.D. Johnson, F.A. Parpia, E.P. Plummer, Comp. Phys. Commun. 55 (1989) 425.
Electron-impact single and multiple ionization of praseodymium ions K. Aichele, W. Arnold, H. Br€ auning, D. Hathiramani, F. Scheuermann, R. Trassl, E. Salzborn * Institut f€ur Kernphysik, Leihgesterner Weg 217, Universit€at Giessen, 35392 Giessen, Germany
Abstract Using the dynamic crossed-beams method, the following absolute cross sections rq;qþn for single ðn ¼ 1Þ, double ðn ¼ 2Þ and triple ðn ¼ 3Þ ionization by electron impact have been measured for the reaction e þ Prqþ ! PrðqþnÞþ þðn þ 1Þe n¼1: n¼2: n¼3:
r1;3 r1;4
r2;3 r2;4 r2;5
r3;4 r3;5 r3;6
r4;5 r4;6
r6;7
r7;8
r8;9
r11;12
The measurements have been performed in an energy range from the respective threshold up to 1 keV. For the single-ionization cross sections, contributions from excitation–autoionization processes increase with increasing charge state of the parent ion. As no theoretical calculations on praseodymium ions exist, these cross sections are compared to the semi-empirical Lotz formula [Zeitschrift f€ ur Physik 232 (1970) 101]. Where contributions of indirect inner-shell processes to the cross section are expected, we conducted energy-scan measurements with high energy resolution. For multiple ionization, no theoretical calculations on praseodymium ions exist. Therefore, the measured cross sections were compared to the semi-empirical formulae by Belenger et al. [J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 2667] and Fisher et al. [J. Phys. B: At. Mol. Opt. Phys. 28 (1995) 3027]. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 34.80.Dp; 34.80.Kw Keywords: Praseodymium; Electron-impact; Ionization; Ions
1. Introduction
*
Corresponding author. E-mail address: [email protected] (E. Salzborn).
Electron-impact ionization of ions is one of the most fundamental processes in every kind of plasma. Especially in high-temperature plasmas – whether in laboratory (nuclear fusion) or in astrophysics (atmosphere of stars) – atoms become
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(03)00565-2
438
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
ionized into multiply charged ions by electron impact. The main purpose of this investigation is to unravel the contributions from different ionization mechanisms – like direct ionization (onestep process), excitation–autoionization (two-step process) and inner-shell Auger processes – to the cross sections of single ionization of highly charged Prqþ ions.
2. Experimental technique The experimental set-up used for the present work has been described in detail earlier [4,5]. The Prqþ ions were produced by evaporating praseodymium powder from an oven into the plasma of a 10 GHz ECR ion source [6]. Using an acceleration voltage of 10 kV, ion currents of up to 10 nA could be extracted. The ion beam was collimated to 2 2 mm2 after mass and energy analysis and crossed with an intense electron beam [7] providing currents up to 450 mA. The energy of the electrons can be varied between 10 and 1000 eV. After the electron–ion interaction, the product ions were separated from the incident ion beam by a 90°magnet and detected by a single-particle detector. The current of the parent ion beam was measured simultaneously in a Faraday cup. Employing the dynamic crossed-beams technique introduced by M€ uller et al. [8], where the electron beam is moved through the ion beam with simultaneous registration of the primary and the product ion intensities, absolute cross sections were obtained. The total experimental uncertainties at 95% confidence level are typically 10% at the maximum of the cross sections including systematic errors of about 8.9%. Measurement times for each absolute cross section value ranged from 50 to 2000 s. The cross sections for single ionization of Prþ and Pr9þ ions showed a dependence on the pressure in the interaction region and could therefore not be measured. As the mass-to-charge ratio for Pr5þ and Pr10þ ions equals 28.2 and 14.1, respectively, these ions could not be þ separated from Nþ 2 and N . In order to examine in detail the contributions from indirect inner-shell processes to the cross sections, energy-scan measurements with high resolution [9] have been performed in the relevant energy ranges.
3. Results 3.1. Single ionization of Pr2þ In Fig. 1 the absolute cross section for the single ionization of Pr2þ is shown. In the upper part only absolute cross section values are given while the lower part shows the results of the high-resolution energy-scan measurement. There is only a small deviation between the observed ionization threshold and the spectroscopically found ionization potential [10]. The steep rise above the onset of the cross section strongly suggests contributions of excitation–autoionization (EA) processes. The shown energy ranges for EA processes were calculated using the GRASP-code [11]. The underestimation of the measured cross section by the semi-empirical Lotz formula [1] is an additional indication of strong EA contributions, since only direct ionization processes are taken into account by this formula. The lower part of Fig. 1 shows a high-resolution energy-scan measurement in the interesting energy range from 25 to 170 eV. 5p-EA processes are responsible for the steep increase at electron energies from 25 to 35 eV. Two small peaks at 30 and 36 eV are due to resonant 5s- or 4d-excitation processes. The step at 100 eV results from 4d-EA processes. 3.2. Single ionization of Pr3þ The absolute cross section for the single ionization of Pr3þ is presented in Fig. 2. The upper part shows the absolute cross section values only, while in the lower part the result of an energy-scan measurement in the energy range from 70 to 150 eV is shown. Again the underestimation by the Lotz formula is in agreement with the strong contributions by indirect processes from the threshold on. The non-zero cross section values below the ground state ionization threshold at 37.4 eV results from metastable ions in the [Kr]4d10 5s2 5p5 4f3 configuration. The steep rise of the cross section at the threshold strongly suggests that the fraction of metastable ions in the ion beam is small. As for the Pr2þ ions, 5p-EA processes contribute to the cross section from the threshold on. The gradient decreases above the 5p-ionization
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
439
Fig. 1. Upper part: absolute cross section for the electron-impact single ionization of Pr2þ . Error bars: total experimental uncertainties. Bars: energy regions of inner-shell excitations. Arrows: ionization thresholds. Solid line: Lotz formula [1]. Lower part: high-resolution energy-scan measurement (only statistical errors are shown). All energies and thresholds corresponding to the [Xe]4f3 ground state configuration were calculated using the GRASP-code [11].
energy at 49.57 eV. The two steps at 90 and 100 eV seem to be due to 4d ! nl-EA processes and were investigated in detail (lower part of Fig. 2). The first step cannot be explained by excitations from the ground state configuration. However, a 4d ! 5p excitation from the metastable
[Kr]4d10 5s2 5p5 4f3 configuration could be found in this energy range. The contribution has to be extremely strong due to the small fraction of metastable ions in the primary ion beam. The second step at 100 eV is due to 4d ! nl excitations of the ground state configuration.
440
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
Fig. 2. Upper part: absolute cross section for the electron-impact single ionization of Pr3þ . Error bars: total experimental uncertainties. Bars: energy regions of inner-shell excitations. Arrows: ionization thresholds. Solid line: Lotz formula [1]. Cross section values below threshold are due to 4d ! 5p excitation–autoionization of the metastable [Kr]4d10 5s2 5p5 4f3 configuration. Lower part: high-resolution energy-scan measurement. Only statistical errors are shown. Bars and arrows as in upper part. All energies and thresholds corresponding to the [Xe]4f3 ground state configuration were calculated using the GRASP-code [11]. Dotted bar: energy ranges for excitations of the metastable 5p5 4f3 configuration.
3.3. Single ionization of Prqþ All measured absolute cross sections for the electron-impact single ionization of Prqþ (q ¼ 2–4, 6–8, 11) are displayed in Fig. 3 using a double
logarithmic scale. Above q P 4 all charge states show contributions of metastable ions in the ion beam, which are produced in the plasma of the ECR ion source. At higher charge states, contributions of EA processes increase compared to the
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
441
-17
2
Cross section (10 cm )
10
1
2+
Pr 4+ Pr 7+ Pr 11+ Pr
0.1
100
3+
Pr 6+ Pr 8+ Pr 1000
Electron energy (eV)
Fig. 3. Absolute cross sections for the electron-impact single ionization of Prqþ (q ¼ 2–4, 6–8, 11) on a double logarithmic scale.
direct ionization. From the structure and the shape of the cross sections it seems that a dominant contribution results from 4d-EA processes. The higher the charge state, the more the cross sections are underestimated by the Lotz formula. This formula neglects all contributions from indirect processes. Thus underestimations of the measured cross sections by a factor of up to 4 were found. It is remarkable that the cross sections for Pr6þ and Pr7þ ions are nearly identical above 500 eV. Even Pr8þ is only slightly lower. This can be explained by strong EA contributions, which increase with increasing the charge state. 3.4. Double Ionization of Prqþ The absolute cross section for the electron-impact double ionization of singly charged praseodymium ions is shown in Fig. 4. No significant contributions of 5s-excitation-double-autoionization (EDA) processes can be seen. Comparing the measured cross section to the semi-empirical formula of Belenger et al. [2] a reasonable agreement within the error margin of a factor of two, which is given for the formula, can be found. The underestimation of the formula by Fisher et al. [3] takes full use of its error range of a factor of two. Obviously at about 105 eV a two-step structure appears in the cross section. In order to investigate the step-like structure more closely, we employed
Fig. 4. Upper part: absolute cross section for the electron-impact double ionization of Pr1þ . Error bars: total experimental uncertainties. Bars: energy regions of inner-shell excitations. Arrows: ionization thresholds. Solid line: Belenger et al. [2]. Dashed line: Fisher et al. [3]. Lower part: high-resolution energy scan measurement (only statistical errors are shown). Dots: absolute cross section values (total experimental uncertainties). All calculations for the [Xe]4f3 6s ground state configuration were calculated using the GRASP-code [11].
the high-resolution energy-scan method in the energy range from 60 to 215 eV. The results are shown in the lower part of Fig. 4 and show only one step in the cross section which is due to 4dEDA processes. Fig. 5 shows all measured absolute cross sections for the processes e þ Prqþ ! Prðqþ2Þþ þ3e ðq ¼ 1; . . . ; 4Þ, on a double logarithmic scale. For q ¼ 4 contributions of metastable ions could be found. All cross sections show contributions from 4d-EDA processes. For Pr4þ , these processes contribute from the threshold on.
442
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443
1
-17
2
Cross section (10 cm )
10
0.1
+
Pr 2+ Pr 3+ Pr 4+ Pr
0.01
100
1000
Electron energy (eV)
Fig. 5. Absolute cross sections for the electron-impact double ionization of Prqþ ðq ¼ 1; . . . ; 4Þ on a double logarithmic scale. Excitation–double-autoionization contributions at energies above 120 eV can be seen in most cross sections.
-18
2
Cross section (10 cm )
10
1
+
Pr 2+ Pr 3+ Pr
0.1
100
1000
Electron energy (eV)
Fig. 7. Absolute cross section for the electron-impact triple ionization of Pr2þ . Error bars: total experimental uncertainties. Bars: energy regions of inner-shell excitations. Arrows: ionization thresholds. Solid line: Belenger et al. [2]. Dashed line: Fisher et al. [3] scaled by a factor of 0.5.
Pr2þ ions (4p-ETA), respectively. For the Pr3þ ions these indirect inner-shell processes show no obvious contributions. Fig. 7 shows the cross section for the electron-impact triple ionization of Pr2þ ions compared to the semi-empirical formulae of Belenger and Fisher, respectively. The formula of Belenger et al. [2] reproduces the cross section within its error margin, but underestimates the cross section from the onset of 4p-ETA contributions. The position of the maximum is at a slightly higher energy than the measured cross section maximum. The formula of Fisher et al. [3] has its maximum at a higher energy and overestimates the cross section over the whole energy range by more than a factor of 2.
Fig. 6. Absolute cross sections for the electron-impact triple ionization of Prqþ ðq ¼ 1; . . . ; 3Þ on a double logarithmic scale.
3.5. Triple Ionization of Prqþ The results for the triple ionization of Prqþ ions in charge states q ¼ 1, 2, 3 are shown in Fig. 6. No significant contributions of metastable states could be found. The fraction of metastable ions in the ion beam should be the same as for the single- and double-ionization cross sections measurements. For Pr2þ and Pr3þ , this fraction was found to be small. Excitation–triple-autoionization (ETA) processes contribute to the cross section for the Prþ -primary ions (significant 4d-ETA and 4p-ETA) and the
References [1] W. Lotz, Zeitschrift f€ ur Physik 232 (1970) 101. [2] C. Belenger, P. Defrance, E. Salzborn, V.P. Shevelko, H. Tawara, D.B. Uskov, J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 2667. [3] V. Fisher, Y. Ralchenko, A. Goldgirsh, D. Fisher, Y. Maron, J. Phys. B: At. Mol. Opt. Phys. 28 (1995) 3027. [4] K. Tinschert, A. M€ uller, G. Hofmann, K. Huber, R. Becker, D.C. Gregory, E. Salzborn, J. Phys. B: At. Mol. Opt. 22 (1989) 531. [5] G. Hofmann, K. Tinschert, A. M€ uller, E. Salzborn, Z. Phys. D 16 (1990) 113. [6] M. Liehr, M. Schlapp, R. Trassl, G. Hofmann, M. Stenke, R. V€ olpel, E. Salzborn, Nucl. Instr. and Meth. B 79 (1993) 697.
K. Aichele et al. / Nucl. Instr. and Meth. in Phys. Res. B 205 (2003) 437–443 [7] R. Becker, A. M€ uller, C. Achenbach, K. Tinschert, E. Salzborn, Nucl. Instr. and Meth. B 9 (1985) 385. [8] A. M€ uller, K. Tinschert, C. Achenbach, E. Salzborn, Nucl. Instr. and Meth. B 10/11 (1985) 204. [9] A. M€ uller, G. Hofmann, K. Tinschert, E. Salzborn, G.H. Dunn, Phys. Rev. Lett. 61 (1988) 70.
443
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