- Email: [email protected]
Energy partitioning in multiply ionizing collisions of C6+ ions with Ne
378
Nuclear Instruments and Methods in Physics Research B53 (1991) 378-382 North-Holland
Energy partitioning
in multiply
R.E. Olson, C.O. Reinhold
and D.R. Schultz
Physics Department,
University of Missouri-Rolla,
ionizing collisions
of C6+ ions with Ne
Rolla, MO 65401, USA
The 10 MeV (0.83 MeV/u) C6+ + Ne collision system is studied in order to illustrate the partitioning of the energy loss of the projectile in multiply ionizing collisions. The n-body classical trajectory Monte Carlo method is employed to determine (i) stopping powers, (ii) total cross sections as a function of recoil ion charge state and (iii) differential cross sections as a function of the angle and energy of the ionized electrons for different recoil ion charge states. The ionized-electron spectra are found to be more sharply peaked near zero electron energy for low recoil ion charge states than for high. Also, ionized electrons associated with low recoil ion charge states are found to be scattered to larger angles than those associated with high charge states. The angular distributions of the recoil ions are also presented and are found to be broadly peaked about 90 O. The calculated total cross sections, the energy loss as a function of the recoil ion charge state and the stopping powers, are in reasonable agreement with available experimental data.
1. Introduction Within the last decade, the study of multiply ionizing collision processes has reached a sophisticated stage of development. Experimentalists have been able to go beyond simple measurements of the net ionization cross sections and have obtained total cross sections for ionization and electron capture as a function of the recoil ion charge state [l]. More recently, experimentalists have been able to perform measurements of the energy and angular distributions of the ionized electrons [2], as well as the transverse momentum distributions of the recoil ion [3] and projectile [4] in coincidence with recoil ion charge. Of importance to several practical problems such as cancer radiotherapy or cosmic ray damage to satellite semiconductors, is the energy deposition caused by a fast heavy ion traversing a thick target [5]. However, quantitative understanding of the partitioning of the energy loss into components due to ionized electrons, target atom recoil and excitation, and electron capture is still at a primitive stage of development. To this point, attempts to model ion induced damage have been largely qualitative. That is, experimentally it is impossible to observe collisional phenomena inside a thick target, and theoretically it is extremely difficult to model a complex n-body system with sufficient accuracy. For example, determination of the stopping power, not to mention its components, is a difficult theoretical task since it is a product of the energy loss and the cross section for this loss, which requires a comprehensive study of all inelastic collision mechanisms. Recently, the first measurements of the energy loss as a function of recoil ion charge state have been performed under single collision conditions [4] for the 0168-583X/91/$03.50
10 MeV C6++ Ne system. This type of measurement is extremely difficult since the experimental apparatus must have an energy resolution sufficient to determine energy losses with an accuracy of tens of eV out of several MeV. Consequently, special techniques had to be developed and employed since current accelerators do not even produce a beam that is stable in energy to one part in 10’. In this work it is demonstrated that the n-body classical trajectory Monte Carlo (nCTMC) method is sufficiently accurate, and versatile, to be applied to the fundamental 10 MeV C6++ Ne system. Moreover, this theoretical method is used to provide an absolute scale to the energy loss in coincidence with electron capture, determine the components of the stopping power, and make predictions as to the energy and angular dependences of the ionized electrons and recoil ion in coincidence with recoil charge state. The C6++ Ne system provides a stringent test of theory because excitation, ionization and electron capture channels are open during the collision. At present, quantum mechanical models using basis set expansions are currently intractable due to the n-body aspects of this problem.
2. Results As noted above, a difficult test of theory is the determination of the stopping power, which requires knowledge of the energy loss cross section, da/dE, for multiple ionization, electron capture and excitation. The stopping power is then obtained by integrating this cross section over E dE. Calculational methods should also describe the partitioning of the energy loss into the possible reaction channels in order to provide important
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
R. E. Olson et al. / Multiply ionizing collisions of C6 + with Ne
Table 1 10 MeV C6+ + Ne stopping power (units of 10-r’ eV/(atom/ cm*)) Component Ionization potentials Ionized electrons without charge exchange Electron removalwith charge exchange Excitation Total
Stopping power
% of total
71
28
102
41
51 21
23 8
251
information to improve the understanding of the various mechanisms of energy deposition. In table 1 are presented the results of the stopping power calculation. The total stopping power is found to be 251 x lo-i5 eV/(atom/cm2), in agreement with the value estimated from the tables of Northcliffe and Schilling [6] of 279 X lo-l5 eV/(atom/cm2). This value was determined assuming a Z2 scaling of the tabulated stopping power (191 x lOpi5 eV/(atom/cm-2)) with a thick target equilibrium charge state for carbon of 4.96. Of the calculated stopping power, we estimate that 28% of the energy loss is due to the ionization potentials required to remove the electrons from their initial bound state to the continuum. In addition, 41% of the energy lost goes to the translation energy of the ionized electrons. Another 23% is lost to the electrons (translational energy) produced in coincidence with electron capture. The relative importance of the electron capture stopping power is accentuated by the need to accelerate the captured electron from the rest frame of the target to that of the projectile. Neglecting the initial and final bound state energies, this corresponds to 453 eV for a 10 MeV carbon ion. Finally, the remaining 8% of the energy lost is found to be due to excitation. The calculated total cross sections for ionization and single electron capture as a function of the neon ion recoil charge state are presented in fig. 1. Experimental data for 12 MeV @+impact from Gray et al. [7] and Freyou et al. [8] are shown along with 10 MeV values of Schuch et al. [9,10]. SCA calculations by these latter authors [9] are also displayed. In general, there is reasonable agreement between theory and experiment. However, we note that the behavior of experimental total cross sections for pure ionization are not completely consistent with one another. That is, the relative shape of the ionization values from Schuch et al. [9] for the 1 + to 3 + neon recoil charge states are in poor agreement with the calculations and the other experiments. Moreover, the shape of the SCA calculations is not borne out by the other data. In addition, the calcu-
319
lated (nCTMC) ionization cross sections appear to be too small by about 50%. The mean energy loss of the projectile as a function of recoil ion charge state is displayed in fig. 2 for both pure ionization and single electron capture. The magnitude of energy loss is on the order of ten eV to a few keV, and it increases rapidly with increasing recoil ion charge state (i.e. decreasing impact parameter). Since the experimental values of Schuch et al. [4] and Schone et al. [12] are relative, we have normalized them to the nCTMC results for Ne+. There is reasonable overall agreement between theory and experiment except in the shape of the electron capture cross sections for low recoil ion charge states. The experimental values display a rise of only 50 eV between Net and Ne2+, whereas theory indicates an increase of 210 eV. We have found no explanation for the difference. The projectile energy loss converted to the kinetic energy of the recoil target ion is shown in fig. 3. Here we see that the recoil ions are produced translationally cold, with energies only on the order of an eV or less. No experimental measurements of this quantity exist for the present system, but good agreement was found previously between nCTMC and experiment for collisions of 1.4 MeV/u U32+ ions with Ne [13]. It is
0
0.83
&V/u
2
4
Net+ Recoil
C6+ + Ne
Charge
6
a State
Fig. 1. Total cross sections for C6+ +Ne collisions as a function of neon recoil ion charge state. Ionization (ION): this work (solid line), Schuch et al. [9] (solid circles), Freyou et al. [8] (solid triangles), Gray et al. [7] (solid squares) normalized to the net ionization values of Be et al. [ll], and SCA calculations of Schuch et al. [9] (dashed line). Single electron capture (CAP): this work (solid line), Schuch et al. [lo] (open circles), Freyou et al. [8] (open triangles), and Gray et al. [7] (open squares).
380
R.E. Olson et al. / Multiply ionizing collisions of C6 + with Ne 0.03
MeV/u
C6*
+ Ne
2500 F 2
I
1
I
I
I
012345670
Recoil
Ne’+
Charge
State
Fig. 2. Projectile mean energy loss as a function of the recoil ion charge state. Ionization (ION): this work (solid circles interpolated by solid line), Schuch et al. [4] (open circles), and Schijne et al. [12] (open triangles). Single electron capture (CAP): this work (solid squares interpolated by solid line), Schuch et al. [4] (open squares), and Schone et al. 1121 (open triangles).
0.83
MeV/u
C6+
interesting to note that the nuclear-nuclear interaction plays a minor role in the energy loss process. To date, no experimental or theoretical information has been presented as to the ionized electron spectra associated with various recoil ion charge states. These cross sections are a by-product of the present calculations and we present them here since they yield further insight into the collisions dynamics. In fig. 4 we display the ionization cross section differential in the ionized electron for the C6++ Ne collision system. The cross section, da/dE, summed over all recoil ion charge states is shown, along with those associated with the production of a low charge state recoil ion, Ne+, and a moderately high charge state ion, Ne4+. The behavior of the cross sections for different charge states may be understood in terms of the relation between electron energy and impact parameter. That is, it is generally assumed that fast electrons originate in small impact parameter collisions, whereas slow electrons mainly originate in large impact parameter collisions. Therefore, at low electron energies the cross section associated with lower charge state ion should be expected to dominate since the multiple ionization probability is relatively small. On the other hand, at high electron energies multiple ionization dominates and the cross section associated with the higher charge state is larger. The mechanisms which lead to the behavior of the angular differential cross sections as a function of recoil ion charge state are more complex. For example, in fig. 5 it is shown that the large impact parameter collisions
0.63
+ Ne
MeV/u
C6*
+ Ne
1.2 ‘o-T--!
2
0.6
c : w 0.6 : n = z c?
0.4
0.2
a o
1
I
I
I
1
2
3
4
1 6
6 Electron
Ne’+
Recoil
Charge
State
Fig. 3. Calculated mean translational energy of the neon recoil ion as a function of its charge state.
Energy
(ev]
Fig. 4. Ionized electron cross sections differential in energy associated with Ne+ and Ne4+ recoil ions along with the cross section summed over all product states (TOTAL).
381
R. E. Olson et al. / Multiply ionizing collisions of C6 + with Ne
IO
0.83
-15
MeV/u
C6* + Ne
0.83
lo-l6 IO
-16
IO
-19
MeV/u
I?
+ Ne
r--T
A ,
0
,
I
1
30
,
,
60
Angle
,
,
,
90
,
,
,
,
120
,
,
150
,
t, ,
100
(degrees)
Fig. 5. Ionized electron cross sections differential in angle.
Notation is the same as in fig. 4.
0
30
Recoil
60 Ion
90
120 150 160
Angle
(degrees)
Fig. 6. Ionization cross section differential in the angle of the Ne*+, Ne4+, and Ne6+ recoil ions. The error bars are statistical uncertainties at the one standard deviation limit.
leading to low recoil charge state production dominate at angles between 60” and 120°, while hard collisions leading to high recoil charge states contribute significantly to the small angle scattering of the total electron spectra. We note that the nCTMC results indicate that two center effects determine the soft collision spectra with the electrons preferentially localized between the two nuclear centers near the distance of closest approach. In contrast, small impact parameter collisions which lead to multiple ionization result in a relatively greater production of electrons ejected to small angles. The study of the angular scattering of the recoil ions in multiply ionizing collisions provides information as to the interplay of electronic and nuclear interactions during the collision. If one assumes a two-body model with the main interaction being between the two heavy nuclei and the electrons being spectators, the recoil ion should be found primarily near 90 o since the longitudinal components of the impulse before and after the collision cancel one another and only the transverse component remains. If one includes an inelasticity of the reaction on the order of 1 keV, one would expect the recoil ions to be sharply peaked at an angle slightly less than 90 “. In fig. 6 are displayed the recoil ion angular distributions for a Ne target initially at room temperature. The recoil angles for the low charge state ions are distributed nearly isotropically, while for a high state recoil ion such as Ne6+, the spectrum is broadly peaked about 90 O. In the latter case, there is an asymmetry to the backward direction, most likely because the incom-
ing portion of the trajectory leads to a point charge-induced dipole interaction between target and projectile, while on the outgoing portion of the trajectory there is a
0.63
0 Ne’+
30
MeV/u C6* + Ne
60
90
Aecoi 1 Angle
120 I50
180
(degrees)
Fig. 7. Doubly differential cross section as a function of angle of the Ne4+ recoil ion produced in 10 MeV C6+ +Ne collisions for different translational energies of 15 meV, 73.1 meV and 266 meV. The error bars are statistical uncertainties at the one standard deviation limit.
strong Coulomb repulsion between the resulting positive ions. Furthermore, it is found that even within a given recoiI ion charge state, the spectrum varies greatly with the translational energy of the recoil ion as may be seen in fig. 7. In this figure we show the doubly differential cross section as a function of energy and angle of the recoil ion for Ne4+. For low translational energies, the spectrum is found to be isotropic, whereas for high energies it is narrowly peaked about 90 O.
This wark was supported by the Office of Fusion Energy of the IJS Department of Energy. References [l] R.E. Olson, Electronic and Atomic Collisions,
[2] [3]
3. CooeIudIng remarks The 10 MeV C’++ Ne system has been studied to provide new information as to the energy partitioning in muhipJy ionizing collisions. Sufficient experimental data exists to validate the present model and provide a reasonable basis for new predictions. For example, we have presented new theoretical results for the stopping power and its components, and provide an absolute scale of the projectile energy loss due to ionization, charge exchange and excitation. Of particular interest is the result that the ionized electrons produced in soft collisions not only dominate the low energy components of the spectra, but also the wide angles (60 to 120” range). Conversely, the cross section for ionized eleetrons associated with high charge states of the recoil ion is larger than that associated with low charge states at high energies and small angles. The recoil ion angular distribution was found to be isotropic for low recoil charge states, but becomes peaked about 9Q” for high recoil charge states or high translational energies of the ion.
]4]
[S] [6] [7] [8] f9] IlO] [H]
[12]
[13]
eds. H.B. Gilbody, W.R. Newell, F.H. Read and A.C.H. Smith (Elsevier. Amsterdam 1988) pp. 271-85. C. Kelbch, RX, Olson, S. Schmidt and H. Schmidt%ockiug, J. Phys. B22 (1989) 2171. J. Uflrich, R.E. Oison, R. D&ner, V. Dangendorf, S. Kelbch, H. Berg and H. ~h~dt-B~~g, J. Fhys. %22 (1989) 627. R. Schuch, H. Schone, P.D. Miller, HF. Krause, P.F. Dittner, S. Datz and RE. Olson, Phys. Rev. Lett. 60 (1988) 925. G. Kraft, Nuclear Science Applications (Harwood Academic Pub., UK, 1987) vol. 3, pp. l-28, L.C. Northchffe and R.F. Schilhng, Nucl. Data Tables A7 (1970) 233. T.J. Gray, CL, Cocke and E Justiniano, Phys. Rev. A22 (1980) 849. J. Freyou, M. Breinig, CC. Gaitber III and T.A. Underwood, Pbys. Rev. A41 (1999) 1315. R. Schuch, L. Andersson, H. S&&e and S. Datz, Nucf. Instr. and Meth. %42 (1989) 566. R. Schuch, S. Data, P.F. Dinner, R Hippler, HF. Krause and PD. Miller, Nucl. Jr&r. and Meth. A262 (1987) 6. S.H. Be, T. Tonuma, H. Kumagai, H. Shibata, M. Kase, T. Kambara, 1. Kohno and H. Tawara, J. Phys. B19 (1986) 1771. H. Schone, R. Schuch, S. Datz, P.F. Dittner, J.P. Oiese, H.F. Krause, MSchulz and Q. Kessel, Nucl. Instr. and Meth, %40,/42 (1989) 141. R.E. Olson, J. Ulhich and H. Schmidt-%i5ckmg, J. Phys. B2O (1987) J.809.
Nuclear Instruments and Methods in Physics Research B53 (1991) 378-382 North-Holland
Energy partitioning
in multiply
R.E. Olson, C.O. Reinhold
and D.R. Schultz
Physics Department,
University of Missouri-Rolla,
ionizing collisions
of C6+ ions with Ne
Rolla, MO 65401, USA
The 10 MeV (0.83 MeV/u) C6+ + Ne collision system is studied in order to illustrate the partitioning of the energy loss of the projectile in multiply ionizing collisions. The n-body classical trajectory Monte Carlo method is employed to determine (i) stopping powers, (ii) total cross sections as a function of recoil ion charge state and (iii) differential cross sections as a function of the angle and energy of the ionized electrons for different recoil ion charge states. The ionized-electron spectra are found to be more sharply peaked near zero electron energy for low recoil ion charge states than for high. Also, ionized electrons associated with low recoil ion charge states are found to be scattered to larger angles than those associated with high charge states. The angular distributions of the recoil ions are also presented and are found to be broadly peaked about 90 O. The calculated total cross sections, the energy loss as a function of the recoil ion charge state and the stopping powers, are in reasonable agreement with available experimental data.
1. Introduction Within the last decade, the study of multiply ionizing collision processes has reached a sophisticated stage of development. Experimentalists have been able to go beyond simple measurements of the net ionization cross sections and have obtained total cross sections for ionization and electron capture as a function of the recoil ion charge state [l]. More recently, experimentalists have been able to perform measurements of the energy and angular distributions of the ionized electrons [2], as well as the transverse momentum distributions of the recoil ion [3] and projectile [4] in coincidence with recoil ion charge. Of importance to several practical problems such as cancer radiotherapy or cosmic ray damage to satellite semiconductors, is the energy deposition caused by a fast heavy ion traversing a thick target [5]. However, quantitative understanding of the partitioning of the energy loss into components due to ionized electrons, target atom recoil and excitation, and electron capture is still at a primitive stage of development. To this point, attempts to model ion induced damage have been largely qualitative. That is, experimentally it is impossible to observe collisional phenomena inside a thick target, and theoretically it is extremely difficult to model a complex n-body system with sufficient accuracy. For example, determination of the stopping power, not to mention its components, is a difficult theoretical task since it is a product of the energy loss and the cross section for this loss, which requires a comprehensive study of all inelastic collision mechanisms. Recently, the first measurements of the energy loss as a function of recoil ion charge state have been performed under single collision conditions [4] for the 0168-583X/91/$03.50
10 MeV C6++ Ne system. This type of measurement is extremely difficult since the experimental apparatus must have an energy resolution sufficient to determine energy losses with an accuracy of tens of eV out of several MeV. Consequently, special techniques had to be developed and employed since current accelerators do not even produce a beam that is stable in energy to one part in 10’. In this work it is demonstrated that the n-body classical trajectory Monte Carlo (nCTMC) method is sufficiently accurate, and versatile, to be applied to the fundamental 10 MeV C6++ Ne system. Moreover, this theoretical method is used to provide an absolute scale to the energy loss in coincidence with electron capture, determine the components of the stopping power, and make predictions as to the energy and angular dependences of the ionized electrons and recoil ion in coincidence with recoil charge state. The C6++ Ne system provides a stringent test of theory because excitation, ionization and electron capture channels are open during the collision. At present, quantum mechanical models using basis set expansions are currently intractable due to the n-body aspects of this problem.
2. Results As noted above, a difficult test of theory is the determination of the stopping power, which requires knowledge of the energy loss cross section, da/dE, for multiple ionization, electron capture and excitation. The stopping power is then obtained by integrating this cross section over E dE. Calculational methods should also describe the partitioning of the energy loss into the possible reaction channels in order to provide important
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
R. E. Olson et al. / Multiply ionizing collisions of C6 + with Ne
Table 1 10 MeV C6+ + Ne stopping power (units of 10-r’ eV/(atom/ cm*)) Component Ionization potentials Ionized electrons without charge exchange Electron removalwith charge exchange Excitation Total
Stopping power
% of total
71
28
102
41
51 21
23 8
251
information to improve the understanding of the various mechanisms of energy deposition. In table 1 are presented the results of the stopping power calculation. The total stopping power is found to be 251 x lo-i5 eV/(atom/cm2), in agreement with the value estimated from the tables of Northcliffe and Schilling [6] of 279 X lo-l5 eV/(atom/cm2). This value was determined assuming a Z2 scaling of the tabulated stopping power (191 x lOpi5 eV/(atom/cm-2)) with a thick target equilibrium charge state for carbon of 4.96. Of the calculated stopping power, we estimate that 28% of the energy loss is due to the ionization potentials required to remove the electrons from their initial bound state to the continuum. In addition, 41% of the energy lost goes to the translation energy of the ionized electrons. Another 23% is lost to the electrons (translational energy) produced in coincidence with electron capture. The relative importance of the electron capture stopping power is accentuated by the need to accelerate the captured electron from the rest frame of the target to that of the projectile. Neglecting the initial and final bound state energies, this corresponds to 453 eV for a 10 MeV carbon ion. Finally, the remaining 8% of the energy lost is found to be due to excitation. The calculated total cross sections for ionization and single electron capture as a function of the neon ion recoil charge state are presented in fig. 1. Experimental data for 12 MeV @+impact from Gray et al. [7] and Freyou et al. [8] are shown along with 10 MeV values of Schuch et al. [9,10]. SCA calculations by these latter authors [9] are also displayed. In general, there is reasonable agreement between theory and experiment. However, we note that the behavior of experimental total cross sections for pure ionization are not completely consistent with one another. That is, the relative shape of the ionization values from Schuch et al. [9] for the 1 + to 3 + neon recoil charge states are in poor agreement with the calculations and the other experiments. Moreover, the shape of the SCA calculations is not borne out by the other data. In addition, the calcu-
319
lated (nCTMC) ionization cross sections appear to be too small by about 50%. The mean energy loss of the projectile as a function of recoil ion charge state is displayed in fig. 2 for both pure ionization and single electron capture. The magnitude of energy loss is on the order of ten eV to a few keV, and it increases rapidly with increasing recoil ion charge state (i.e. decreasing impact parameter). Since the experimental values of Schuch et al. [4] and Schone et al. [12] are relative, we have normalized them to the nCTMC results for Ne+. There is reasonable overall agreement between theory and experiment except in the shape of the electron capture cross sections for low recoil ion charge states. The experimental values display a rise of only 50 eV between Net and Ne2+, whereas theory indicates an increase of 210 eV. We have found no explanation for the difference. The projectile energy loss converted to the kinetic energy of the recoil target ion is shown in fig. 3. Here we see that the recoil ions are produced translationally cold, with energies only on the order of an eV or less. No experimental measurements of this quantity exist for the present system, but good agreement was found previously between nCTMC and experiment for collisions of 1.4 MeV/u U32+ ions with Ne [13]. It is
0
0.83
&V/u
2
4
Net+ Recoil
C6+ + Ne
Charge
6
a State
Fig. 1. Total cross sections for C6+ +Ne collisions as a function of neon recoil ion charge state. Ionization (ION): this work (solid line), Schuch et al. [9] (solid circles), Freyou et al. [8] (solid triangles), Gray et al. [7] (solid squares) normalized to the net ionization values of Be et al. [ll], and SCA calculations of Schuch et al. [9] (dashed line). Single electron capture (CAP): this work (solid line), Schuch et al. [lo] (open circles), Freyou et al. [8] (open triangles), and Gray et al. [7] (open squares).
380
R.E. Olson et al. / Multiply ionizing collisions of C6 + with Ne 0.03
MeV/u
C6*
+ Ne
2500 F 2
I
1
I
I
I
012345670
Recoil
Ne’+
Charge
State
Fig. 2. Projectile mean energy loss as a function of the recoil ion charge state. Ionization (ION): this work (solid circles interpolated by solid line), Schuch et al. [4] (open circles), and Schijne et al. [12] (open triangles). Single electron capture (CAP): this work (solid squares interpolated by solid line), Schuch et al. [4] (open squares), and Schone et al. 1121 (open triangles).
0.83
MeV/u
C6+
interesting to note that the nuclear-nuclear interaction plays a minor role in the energy loss process. To date, no experimental or theoretical information has been presented as to the ionized electron spectra associated with various recoil ion charge states. These cross sections are a by-product of the present calculations and we present them here since they yield further insight into the collisions dynamics. In fig. 4 we display the ionization cross section differential in the ionized electron for the C6++ Ne collision system. The cross section, da/dE, summed over all recoil ion charge states is shown, along with those associated with the production of a low charge state recoil ion, Ne+, and a moderately high charge state ion, Ne4+. The behavior of the cross sections for different charge states may be understood in terms of the relation between electron energy and impact parameter. That is, it is generally assumed that fast electrons originate in small impact parameter collisions, whereas slow electrons mainly originate in large impact parameter collisions. Therefore, at low electron energies the cross section associated with lower charge state ion should be expected to dominate since the multiple ionization probability is relatively small. On the other hand, at high electron energies multiple ionization dominates and the cross section associated with the higher charge state is larger. The mechanisms which lead to the behavior of the angular differential cross sections as a function of recoil ion charge state are more complex. For example, in fig. 5 it is shown that the large impact parameter collisions
0.63
+ Ne
MeV/u
C6*
+ Ne
1.2 ‘o-T--!
2
0.6
c : w 0.6 : n = z c?
0.4
0.2
a o
1
I
I
I
1
2
3
4
1 6
6 Electron
Ne’+
Recoil
Charge
State
Fig. 3. Calculated mean translational energy of the neon recoil ion as a function of its charge state.
Energy
(ev]
Fig. 4. Ionized electron cross sections differential in energy associated with Ne+ and Ne4+ recoil ions along with the cross section summed over all product states (TOTAL).
381
R. E. Olson et al. / Multiply ionizing collisions of C6 + with Ne
IO
0.83
-15
MeV/u
C6* + Ne
0.83
lo-l6 IO
-16
IO
-19
MeV/u
I?
+ Ne
r--T
A ,
0
,
I
1
30
,
,
60
Angle
,
,
,
90
,
,
,
,
120
,
,
150
,
t, ,
100
(degrees)
Fig. 5. Ionized electron cross sections differential in angle.
Notation is the same as in fig. 4.
0
30
Recoil
60 Ion
90
120 150 160
Angle
(degrees)
Fig. 6. Ionization cross section differential in the angle of the Ne*+, Ne4+, and Ne6+ recoil ions. The error bars are statistical uncertainties at the one standard deviation limit.
leading to low recoil charge state production dominate at angles between 60” and 120°, while hard collisions leading to high recoil charge states contribute significantly to the small angle scattering of the total electron spectra. We note that the nCTMC results indicate that two center effects determine the soft collision spectra with the electrons preferentially localized between the two nuclear centers near the distance of closest approach. In contrast, small impact parameter collisions which lead to multiple ionization result in a relatively greater production of electrons ejected to small angles. The study of the angular scattering of the recoil ions in multiply ionizing collisions provides information as to the interplay of electronic and nuclear interactions during the collision. If one assumes a two-body model with the main interaction being between the two heavy nuclei and the electrons being spectators, the recoil ion should be found primarily near 90 o since the longitudinal components of the impulse before and after the collision cancel one another and only the transverse component remains. If one includes an inelasticity of the reaction on the order of 1 keV, one would expect the recoil ions to be sharply peaked at an angle slightly less than 90 “. In fig. 6 are displayed the recoil ion angular distributions for a Ne target initially at room temperature. The recoil angles for the low charge state ions are distributed nearly isotropically, while for a high state recoil ion such as Ne6+, the spectrum is broadly peaked about 90 O. In the latter case, there is an asymmetry to the backward direction, most likely because the incom-
ing portion of the trajectory leads to a point charge-induced dipole interaction between target and projectile, while on the outgoing portion of the trajectory there is a
0.63
0 Ne’+
30
MeV/u C6* + Ne
60
90
Aecoi 1 Angle
120 I50
180
(degrees)
Fig. 7. Doubly differential cross section as a function of angle of the Ne4+ recoil ion produced in 10 MeV C6+ +Ne collisions for different translational energies of 15 meV, 73.1 meV and 266 meV. The error bars are statistical uncertainties at the one standard deviation limit.
strong Coulomb repulsion between the resulting positive ions. Furthermore, it is found that even within a given recoiI ion charge state, the spectrum varies greatly with the translational energy of the recoil ion as may be seen in fig. 7. In this figure we show the doubly differential cross section as a function of energy and angle of the recoil ion for Ne4+. For low translational energies, the spectrum is found to be isotropic, whereas for high energies it is narrowly peaked about 90 O.
This wark was supported by the Office of Fusion Energy of the IJS Department of Energy. References [l] R.E. Olson, Electronic and Atomic Collisions,
[2] [3]
3. CooeIudIng remarks The 10 MeV C’++ Ne system has been studied to provide new information as to the energy partitioning in muhipJy ionizing collisions. Sufficient experimental data exists to validate the present model and provide a reasonable basis for new predictions. For example, we have presented new theoretical results for the stopping power and its components, and provide an absolute scale of the projectile energy loss due to ionization, charge exchange and excitation. Of particular interest is the result that the ionized electrons produced in soft collisions not only dominate the low energy components of the spectra, but also the wide angles (60 to 120” range). Conversely, the cross section for ionized eleetrons associated with high charge states of the recoil ion is larger than that associated with low charge states at high energies and small angles. The recoil ion angular distribution was found to be isotropic for low recoil charge states, but becomes peaked about 9Q” for high recoil charge states or high translational energies of the ion.
]4]
[S] [6] [7] [8] f9] IlO] [H]
[12]
[13]
eds. H.B. Gilbody, W.R. Newell, F.H. Read and A.C.H. Smith (Elsevier. Amsterdam 1988) pp. 271-85. C. Kelbch, RX, Olson, S. Schmidt and H. Schmidt%ockiug, J. Phys. B22 (1989) 2171. J. Uflrich, R.E. Oison, R. D&ner, V. Dangendorf, S. Kelbch, H. Berg and H. ~h~dt-B~~g, J. Fhys. %22 (1989) 627. R. Schuch, H. Schone, P.D. Miller, HF. Krause, P.F. Dittner, S. Datz and RE. Olson, Phys. Rev. Lett. 60 (1988) 925. G. Kraft, Nuclear Science Applications (Harwood Academic Pub., UK, 1987) vol. 3, pp. l-28, L.C. Northchffe and R.F. Schilhng, Nucl. Data Tables A7 (1970) 233. T.J. Gray, CL, Cocke and E Justiniano, Phys. Rev. A22 (1980) 849. J. Freyou, M. Breinig, CC. Gaitber III and T.A. Underwood, Pbys. Rev. A41 (1999) 1315. R. Schuch, L. Andersson, H. S&&e and S. Datz, Nucf. Instr. and Meth. %42 (1989) 566. R. Schuch, S. Data, P.F. Dinner, R Hippler, HF. Krause and PD. Miller, Nucl. Jr&r. and Meth. A262 (1987) 6. S.H. Be, T. Tonuma, H. Kumagai, H. Shibata, M. Kase, T. Kambara, 1. Kohno and H. Tawara, J. Phys. B19 (1986) 1771. H. Schone, R. Schuch, S. Datz, P.F. Dittner, J.P. Oiese, H.F. Krause, MSchulz and Q. Kessel, Nucl. Instr. and Meth, %40,/42 (1989) 141. R.E. Olson, J. Ulhich and H. Schmidt-%i5ckmg, J. Phys. B2O (1987) J.809.