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A comment on the equivalence of the innershell ionization by proton and electron impact at sufficiently high velocities
Volume 5 9A, number 3
PHYSICS LETFERS
29 November 1976
A COMMENT ON THE EQUIVALENCE OF THE INNERSHELL IONIZATION BY PROTON AND ELECTRON IMPACT AT SUFFICIENTLY HIGH VELOCITIES H. TAWARA Nuclear Engineering Department, Kyushu University, Fukuoka, 812 Japan Received 25 February 1976 The equivalence is discussed of the innersheli ionization by proton and electron impact at high velocities.
It is predicted in the Bethe-Bom approximation [1] that, m the limit of sufficiently high velocity, the total ionization cross section in proton impact is equal to that m electron impact at the equal velocity. This fact has been pointed out by a number of theoretical papers [2, 3]. Therefore, a comparison of the measured cross sections in proton and electron impact at sufficiently high energies is very important and interesting for testing the theories. Some comparisons for the ionization of some gases have been done by Hooper et al. [4] and by de Heer et al. [5] Their results indicate that the prediction by the Born approximation is correct at least for these outershell ionizations. Up to now, however, no comparisons have been made yet for the innershell ionization. One of the reasons is due to the fact that no data for the innershell ionization are available at sufficiently high proton velocities. Very recently Burch [6] has reported the K-shell ionization cross sections for carbon for 1—18 MeV proton impact. On the other hand, similar data to be compared for electron impact at relatively high energies have already been measured by Tawara et al. [7] and Hink and Paschke [8]. In this letter we report a comparison of the K-shell ionization cross sections of carbon by proton and electron impact at the same velocities to test the prediction of the Born approximation. In fig. 1 are shown the outershell ionization cross sections of helium by proton and electron impact at the same velocity scale, together with the prediction of the Born approximation calculated by Peach [9] for comparison. It is clear that, at lower energies, the ionization by protons is more efficient than that by electrons. This is due to the fact that the available .
-
kinetic energy, which becomes important at lower im-
I
-16
-
.
-
deHeer Gilbody
proton
~
..
•
Pivovar Peach —
.-----~.
I Fedorenko Hooper
+ -
Solovev
.
‘N-.
,<•‘
He-is
~
electron Rapp
2
+
Peach -18
19
-
E~(MeV) 01
.i
I
i
10 Ee(kev) Fig. 1. Ionization cross section for helium by electron and proton impact
pact energies, is larger in proton impact than in electron impact. The calculation by Peach shows that the ionization cross sections for helium in electron and proton impact coincide at an electron energy of 300 eV which corresponds to 550 keV of proton. Though it is rather difficult to determine the accurate velocity where the ionization cross sections in proton and electron impact coincide each other because these experimental data have typical uncertainties of about 10—15%, it may be concluded that the agreement between the experiments and the prediction of the Born approximation is reasonably good for the outershell ionization. In fig. 2 is shown such a comparison for carbon Kshell ionization. Experimental data for electrons are taken from Tawara et al. [7] who measured X-rays using CH4 gas target and from Hink and Paschke [8] who also measured X-rays from very thin carbon foils. 199
Volume 59A, number 3
-18
-
PHYSICS LETTERS
proton
~•:~* ~
a
-
2
.•
energy range investigated, though the relative energy dependence at energies higher than 3 keV seems to be identical with the data. For comparison, the semiempirical prediction by Lotz with the relativistic correction discussed by Pessa and Newell [15] is also
electron iawara ~
10
-2C
100 I
Ep(MeV) I .1
for impact by the Davidovic and Moiseiwitsch not electron in agreement with experimental data for all are the
I rBurch-Toburen I Stolterfoht L Khandelwal - --
IHink Davidovic LLotz-Pessa
i,,. I
1
10
I 100
Ee(keV) Fig. 2. Ionization cross section for carbon K-shell by electron and proton impact,
The K-shell ionization cross sections are obtained using the fluorescence yield of 0.00269 [7] which was determined from Auger data of Glupe and Mehlhorn [10] and X-ray data [7]. On the other hand, those for proton impact at relatively low energies are from Stolterfoht et al. [11] and Toburen [12] who both measured the Auger electrons and those at high energies are from Burch [6] who measured relative X-ray intensity and normalized to the Auger electron data of Toburen at 1 MeV impact energy. The theoretical curve for proton impact is obtained from the table of Khandelwal et al. [13] (non-relativistic) and that for electron impact is from the prediction of the Born approximation (fully-relativistic) by Davidovic and Moiseiwitsch [14]. The procedures in both calculations based on the Born approximation are not the complete same, but the calculated cross sections for K-shell ionization of carbon in proton and electrom impact coincide at energies higher than 2.5—3 keV of electrons which correspond to 4—5.5 MeV of protons. On the other hand, however, the experimental data for carbon K-shell ionization do not coincide yet up to 10 keV electron and 18 MeV proton impact. At the highest energy, the measured ionization cross section in proton impact is still larger by about 30% than that in electron impact. Also the absolute values of data for proton impact at high energies are systematically larger than the predicted values by 15—20% which is well beyond the experimental uncertainty limit, but their relative energy dependence is almost the same at energies higher than 3—4 MeV. The calculated values 200
29 November 1976
shown fig. 2. At relatively high predictions ofinsemi-empirical formula byenergies, Lotz andthe PessaNewell are smaller by about 40% than those of the Born approximation and the experimental data are in between these two predictions. When a comparison is made between Khandelwal calculation for proton impact and Lotz and Pessa-Newell calculation for electron impact, the theoretical K-shell ionization cross sections in proton and electron impact do not coincide yet at the highest proton energy of 18 MeV corresponding to 10 keV for electrons, as observed in the experimental data. Though a part of the discrepancy between these calculations and experimental data in both proton and electron impact might be due to the fluorescence yield used in converting the X-ray cross section to the ionization cross section, it is difficult to say from these comparisons whether theoretical predictions are incorrect or the experimental data are correct. It is, however, clear from the present discussion that, to test the validity of the Born approximation for the innershell ionization, the cross sections for the innershell ionization by proton impact should be measured accurately at higher energies, for example, up to 50—100 MeV for carbon K-shell and those by electron impact up to 100 keV and, at the same time, the consistent calculations of the ionization cross sections for both proton and electron impact should be made.
References [1] H.A. Bethe, Ann. Phys. 5
(1930) 325; M. Inokuti, Rev, mod. Phys. 43 (1971) 297.
[2] D.R. 961. Bates and G. Griffing, Proc. Phys. Soc. A 66 (1953) [3] R.A. Mapleton, Phys. Rev. 109 (1958) 1166. [4]J.W. looper, D.S. Harmer, D.W. Martin and E.W. McDaniel, Phys. Rev. 125 (1962) 2000. [5] FJ. de Heer, J. Schutten and H. Moustafa, Physica 32 (1966) 1766. [6] D.F. Burch, Phys. Rev. A 12(1975) 2225. [7] H. Tawara, K.G. Harrison and FJ. de Heer, Physica 63 (1973) 351.
Volume 59A, number 3 [8] [9] [10] [11]
PHYSICS LETTERS
W. link and H. Paschke, Z. Phys. 244 (1971) 140. G. Peach, Proc. Phys. Soc. 85 (1965) 709. G. Glupe and W. Mehlhorn, Phys. Lett. 25 A (1967) 274. N. Stolterfoht. D. Schneider and K.G. Harrison, Phys. Rev. A 8 (1973) 2363. [12] L.H. Toburen, Phys. Rev. A 9(1974) 2505.
29 November 1976
[13] G.S. Khandelwal, B.H. Choi and E. Merzbacher, At. Data 1(1969)103. [14] D.M. Davidovic and B.L. Moiseiwitsch, J. Phys. B 8 (1975) 447. [15] V.M. Pessa and W.R. Newell, Physica Scripta 3 (1971) 165.
201
PHYSICS LETFERS
29 November 1976
A COMMENT ON THE EQUIVALENCE OF THE INNERSHELL IONIZATION BY PROTON AND ELECTRON IMPACT AT SUFFICIENTLY HIGH VELOCITIES H. TAWARA Nuclear Engineering Department, Kyushu University, Fukuoka, 812 Japan Received 25 February 1976 The equivalence is discussed of the innersheli ionization by proton and electron impact at high velocities.
It is predicted in the Bethe-Bom approximation [1] that, m the limit of sufficiently high velocity, the total ionization cross section in proton impact is equal to that m electron impact at the equal velocity. This fact has been pointed out by a number of theoretical papers [2, 3]. Therefore, a comparison of the measured cross sections in proton and electron impact at sufficiently high energies is very important and interesting for testing the theories. Some comparisons for the ionization of some gases have been done by Hooper et al. [4] and by de Heer et al. [5] Their results indicate that the prediction by the Born approximation is correct at least for these outershell ionizations. Up to now, however, no comparisons have been made yet for the innershell ionization. One of the reasons is due to the fact that no data for the innershell ionization are available at sufficiently high proton velocities. Very recently Burch [6] has reported the K-shell ionization cross sections for carbon for 1—18 MeV proton impact. On the other hand, similar data to be compared for electron impact at relatively high energies have already been measured by Tawara et al. [7] and Hink and Paschke [8]. In this letter we report a comparison of the K-shell ionization cross sections of carbon by proton and electron impact at the same velocities to test the prediction of the Born approximation. In fig. 1 are shown the outershell ionization cross sections of helium by proton and electron impact at the same velocity scale, together with the prediction of the Born approximation calculated by Peach [9] for comparison. It is clear that, at lower energies, the ionization by protons is more efficient than that by electrons. This is due to the fact that the available .
-
kinetic energy, which becomes important at lower im-
I
-16
-
.
-
deHeer Gilbody
proton
~
..
•
Pivovar Peach —
.-----~.
I Fedorenko Hooper
+ -
Solovev
.
‘N-.
,<•‘
He-is
~
electron Rapp
2
+
Peach -18
19
-
E~(MeV) 01
.i
I
i
10 Ee(kev) Fig. 1. Ionization cross section for helium by electron and proton impact
pact energies, is larger in proton impact than in electron impact. The calculation by Peach shows that the ionization cross sections for helium in electron and proton impact coincide at an electron energy of 300 eV which corresponds to 550 keV of proton. Though it is rather difficult to determine the accurate velocity where the ionization cross sections in proton and electron impact coincide each other because these experimental data have typical uncertainties of about 10—15%, it may be concluded that the agreement between the experiments and the prediction of the Born approximation is reasonably good for the outershell ionization. In fig. 2 is shown such a comparison for carbon Kshell ionization. Experimental data for electrons are taken from Tawara et al. [7] who measured X-rays using CH4 gas target and from Hink and Paschke [8] who also measured X-rays from very thin carbon foils. 199
Volume 59A, number 3
-18
-
PHYSICS LETTERS
proton
~•:~* ~
a
-
2
.•
energy range investigated, though the relative energy dependence at energies higher than 3 keV seems to be identical with the data. For comparison, the semiempirical prediction by Lotz with the relativistic correction discussed by Pessa and Newell [15] is also
electron iawara ~
10
-2C
100 I
Ep(MeV) I .1
for impact by the Davidovic and Moiseiwitsch not electron in agreement with experimental data for all are the
I rBurch-Toburen I Stolterfoht L Khandelwal - --
IHink Davidovic LLotz-Pessa
i,,. I
1
10
I 100
Ee(keV) Fig. 2. Ionization cross section for carbon K-shell by electron and proton impact,
The K-shell ionization cross sections are obtained using the fluorescence yield of 0.00269 [7] which was determined from Auger data of Glupe and Mehlhorn [10] and X-ray data [7]. On the other hand, those for proton impact at relatively low energies are from Stolterfoht et al. [11] and Toburen [12] who both measured the Auger electrons and those at high energies are from Burch [6] who measured relative X-ray intensity and normalized to the Auger electron data of Toburen at 1 MeV impact energy. The theoretical curve for proton impact is obtained from the table of Khandelwal et al. [13] (non-relativistic) and that for electron impact is from the prediction of the Born approximation (fully-relativistic) by Davidovic and Moiseiwitsch [14]. The procedures in both calculations based on the Born approximation are not the complete same, but the calculated cross sections for K-shell ionization of carbon in proton and electrom impact coincide at energies higher than 2.5—3 keV of electrons which correspond to 4—5.5 MeV of protons. On the other hand, however, the experimental data for carbon K-shell ionization do not coincide yet up to 10 keV electron and 18 MeV proton impact. At the highest energy, the measured ionization cross section in proton impact is still larger by about 30% than that in electron impact. Also the absolute values of data for proton impact at high energies are systematically larger than the predicted values by 15—20% which is well beyond the experimental uncertainty limit, but their relative energy dependence is almost the same at energies higher than 3—4 MeV. The calculated values 200
29 November 1976
shown fig. 2. At relatively high predictions ofinsemi-empirical formula byenergies, Lotz andthe PessaNewell are smaller by about 40% than those of the Born approximation and the experimental data are in between these two predictions. When a comparison is made between Khandelwal calculation for proton impact and Lotz and Pessa-Newell calculation for electron impact, the theoretical K-shell ionization cross sections in proton and electron impact do not coincide yet at the highest proton energy of 18 MeV corresponding to 10 keV for electrons, as observed in the experimental data. Though a part of the discrepancy between these calculations and experimental data in both proton and electron impact might be due to the fluorescence yield used in converting the X-ray cross section to the ionization cross section, it is difficult to say from these comparisons whether theoretical predictions are incorrect or the experimental data are correct. It is, however, clear from the present discussion that, to test the validity of the Born approximation for the innershell ionization, the cross sections for the innershell ionization by proton impact should be measured accurately at higher energies, for example, up to 50—100 MeV for carbon K-shell and those by electron impact up to 100 keV and, at the same time, the consistent calculations of the ionization cross sections for both proton and electron impact should be made.
References [1] H.A. Bethe, Ann. Phys. 5
(1930) 325; M. Inokuti, Rev, mod. Phys. 43 (1971) 297.
[2] D.R. 961. Bates and G. Griffing, Proc. Phys. Soc. A 66 (1953) [3] R.A. Mapleton, Phys. Rev. 109 (1958) 1166. [4]J.W. looper, D.S. Harmer, D.W. Martin and E.W. McDaniel, Phys. Rev. 125 (1962) 2000. [5] FJ. de Heer, J. Schutten and H. Moustafa, Physica 32 (1966) 1766. [6] D.F. Burch, Phys. Rev. A 12(1975) 2225. [7] H. Tawara, K.G. Harrison and FJ. de Heer, Physica 63 (1973) 351.
Volume 59A, number 3 [8] [9] [10] [11]
PHYSICS LETTERS
W. link and H. Paschke, Z. Phys. 244 (1971) 140. G. Peach, Proc. Phys. Soc. 85 (1965) 709. G. Glupe and W. Mehlhorn, Phys. Lett. 25 A (1967) 274. N. Stolterfoht. D. Schneider and K.G. Harrison, Phys. Rev. A 8 (1973) 2363. [12] L.H. Toburen, Phys. Rev. A 9(1974) 2505.
29 November 1976
[13] G.S. Khandelwal, B.H. Choi and E. Merzbacher, At. Data 1(1969)103. [14] D.M. Davidovic and B.L. Moiseiwitsch, J. Phys. B 8 (1975) 447. [15] V.M. Pessa and W.R. Newell, Physica Scripta 3 (1971) 165.
201