- Email: [email protected]
Multiple ionization of He, Ne, and Ar by high velocity N7+ ions
Nuclear Instruments North-Holland
and Methods
in Physics
Research
B56/57
15
(1991) 15-17
Multiple ionization of He, Ne, and Ar by high velocity N7+ ions 0. Heber I, R.L. Watson, G. Sampoll, V. Horvat 2, B. Hill and T. Lotze Cyclotron Institute and Department of Chemutly, Texas A&M Uniuerslty, College Statron, TX 77840, USA
The yields time-of-fhght by theoretical experimental
of He, Ne, and Ar recoil ions produced in collisions with lo-40 MeV/amu N’* -projectiles were measured by the technique. The ratio of the yields for double and single ionization of He and Ne were found to be higher than predicted and semiempincal calculations. The role of electron correlation in multiple ionization was assessed by comparing the data for Ne and Ar with the results of an independent electron approximation analysis.
1. Introduction Multielectron ionizing collisions in the velocity regime where electron-electron correlation plays an important role are difficult to deal with theoretically because many-body calculations are required for a complete description of the process. Nevertheless, considerable progress has been made in the treatment of double ionization over the past few years. Both quantum mechanical calculations employing the forced impulse method (FIM) [l] and classical trajectory Monte Carlo calculations [2] have been successful at reproducing the general features of the cross section ratios for double and single ionization (R) of helium by protons and antiprotons [3]. Other investigators have approached this problem by invoking a number of mechanisms (associated with the first and second order terms of the Born expansion) to describe various aspects of double ionization, namely the double collision (or TS-2) mechanism, the electron scattering (or TS-1) mechanism, and the shakeoff mechanism [3,4]. According to Andersen et al. [3], the ratio R for any projectile charge q may be expressed in the form R = R, + q2R,, - 2qRint,
(1)
where R, is the portion of the cross section ratio for protons attributed to the indirect processes (i.e. TS-1 and shakeoff), RI, is the portion of the cross section ratio for protons attributed to the direct process, and R,,, is the portion of the cross section ratio for protons attributed to interference between the direct and the indirect processes. In terms of this formulation, the
large differences in R observed for protons and antiprotons arise as a consequence of the opposite signs of the interference term for the two projectiles. At high velocities, however, the ratios R,, and R,,, are expected to become negligible and R, becomes nearly constant. Therefore, the ratio R is predicted to eventually reach the limiting value of R,, which is independent of projectile charge. This behavior has been experimentally verified for electrons, protons, antiprotons, and alpha particles [3]. Recently, the yields He2+ and He’+ produced by lo-30 MeV/amu N 7+ ions were measured [5]. The resulting R values were found to remain nearly constant over this velocity range at a value approximately 4.5 times larger than the high velocity limit established by the data for q = 1. Moreover, R values for N7+ projectiles deviated from the theoretical predictions of Reading and Ford, and the semiempirical predictions of Knudsen et al. [6] by a factor of 2 or more beyond 20 MeV/amu. The present paper reports new measurements extending the R values for N7+ projectiles up to 40 MeV/amu and presents the results of multiple ionization yield measurements for Ne and Ar over the velocity range corresponding to lo-40 MeV/amu.
2. Experimental methods Beams of nitrogen ions having charges of 3 + , 4 + , or 5 + (depending on the desired energy) were extracted from the Texas A&M K500 superconducting cyclotron and sent through several focusing and steering elements. After passing through a 200 ug/cm2 Al foil, fully stripped
’ Present address: Department of Nuclear Physics, The Weizmann Institute of Science, Rehovot
’ On leave from the Department and Mathematics, University Yugoslavia. 0168-583X/91/$03.50
76100, Israel. of Physics, Faculty of Science of Zagreb, Zagreb, Croatia,
0 1991 - Elsevier Science Publishers
ions
were
magnet
and
directed
gas
into
either
cell
selected
by
through a Si surface
means
of an
a differentially barrier
analyzing pumped
detector
or
a
microchannel plate detector. The gas cell contained the target gas (He, Ne, or Ar at a pressure of 1 mTorr) and served as the first stage of a time-of-flight (TOF) spec-
B.V. (North-Holland)
I. ATOMIC/MOLECULAR
PHYSICS
16
0. Heber et al. / Multiple lomzatlon by N’+
trometer. The ions produced in collisions with N’+ projectiles were accelerated out of the gas cell by an electric field oriented transverse to the beam into a 12 cm flight tube. Upon reaching the end of the flight tube, the ions were further accelerated into a chevron microchannel plate assembly where they generated start signals for a time-to-amplitude converter (TAC). The TAC was stopped by delayed signals from the projectile detector. Time spectra generally required accumulation times of l-5 h at an incident projectile rate of 2000/s to obtain reasonable counting statistics for He2+ and the highest charge states of the Ne and Ar recoil ions.
zom
14
2’ 0
I 10
20 PROJECTILE
3. Results and discussion The R values obtained for He are shown in fig. 1. The new data point at 40 MeV/amu resolves the question of whether the ratios are really decreasing with increasing projectile energy. It is clear that the R values for N’+ projectiles do not reach the limiting value defined by the electron and proton data in the energy range investigated so far. A linear extrapolation suggests that this may occur between 60 and 70 MeV/amu. Also shown in fig. 1 are the results of several theoretical or semiempirical analyses for N’+ projectiles. The dotted curve shows the R values predicted by the FIM calculations of Reading and Ford (multiplied by a factor of 1.35) [1,8]. The solid curve shows the R values given by the semiempirical formula of Knudsen et al. [6], which is based on a fit of eq. (1) to experimental data at considerably lower energies. The dashed curve was constructed by extrapolating the values of R,, R,,, and R,,, given by Andersen et al. [3,9] for He and using them in eq. (1). Andersen et al. obtained R, and R,, by
100
r.
1 .
NITROGEN
A PROTON \
v
\
1
’ 0
ELECTRON
I 30
20
10 PROJECTILE
ENERGY
40
50
(MeV/omu)
Fig. 1. Energy dependence of the R values for electrons, protons and N 7f ions on He. The data points for N ions below 5 MeV/amu are from refs. [6,7]. Also shown are predictions based on the work of Reading and Ford [1,8], dotted curve; Andersen et al. [3], dashed curve; and Kundsen et al. [6], solid curve.
30 ENERGY
40
50
(MeV/amu)
Fig. 2. Energy dependence of the R values for N7+ ions on Ne. The solid curve shows the predictions based on the work of Andersen et al. [3].
theoretical methods and R,,, from experimental data for protons, antiprotons, and alpha particles. Although the R values calculated from the work of Andersen et al. agree with the data much better than do those from the other two analyses, they still decrease more rapidly with increasing energy than the experimental R values. This discrepancy may be an indication that the neglect of small contributions from higher order Born terms (having higher powers of 4) in the semiempirical analysis of the low energy/low q data leads to significant errors in the extrapolation to high energy for q = 7. The R values obtained for Ne are shown in fig. 2. The solid curve was determined by extrapolating the Ne RI, R,,, and R,,, values given by Andersen et al. [3], as discussed above. While the results of this semiempirical analysis are in fair agreement with the experimental data, it is apparent that fairly large discrepancies arise in the high energy region. It should be noted, however, that in the case of Ne, an additional contribution to R from Auger decay following K-shell ionization could be present in the experimental data. While such contributions are expected to be small for Ne, this is certainly not the case for Ar, where direct L-shell ionization followed by Auger decay makes a substantial contribution to the yield of Ar2+. The energy dependences of the Ne and Ar recoil-ion charge state fractions are shown in figs. 3 and 4, respectively. In order to estimate how large a role electronelectron correlation plays in the multiple ionization process, analyses employing the independent electron approximation (IEA) were carried out for these data. Since this approximation accounts for only the direct ionization process, differences between the IEA predictions and the experimental data provide an estimate of the degree to which indirect processes are involved. In applying the IEA, the methods described in ref. [lo] were used. The impact parameter dependent single-electron ionization probability was represented by an ex-
17
0. Heber et al. / Multiple iomzation by N 7+ ions
,0-l
9 w * ;
tion. The results are shown by the various curves in figs. 3 and 4. It is evident that the IEA predictions become increasingly worse as the velocity and charge increase. The overall poor agreement between the experimental and calculated recoil-ion relative yields is in marked contrast to previous findings for collisions of 0 and F projectiles with Ne and Ar in the 1 MeV/amu energy region [lo].
_‘” :P
:“
10-Z
.’ -El
4
Y 10-3 i
\
‘I\ Acknowledgements
,o-41
I\ 0
I 10
20 PROJECTILE
30 ENERGY
50
40
60
(MeV/amu)
Fig. 3. Energy dependence of the relative yields of Ne recoil ions produced in collisions with N’+ projectiles. The data points at 1.4 MeV/amu are from refs. [6,7].
100
9
lo-
w *
10-4
”
1
I. t---__
‘0..
.-
\
0
\I
n
m
---------. . v
T
0
0
0
’
0
IEA
EXP
-
1+
v
--
2+
v
3+
0 l
--4+
- -_ - ._ 0
10
20 PROJECTILE
30 ENERGY
3
1 40
50
60
(MeV/amu)
Fig. 4. Energy dependence of the relative yields of Ar recoil ions produced in collisions with N’+ prolectiles. The data points at 1.4 MeV/amu are from refs. [6,7].
ponential function that was normalized to the well known ve2 In v single ionization cross section velocity dependence. In the case of Ar, L-shell ionization followed by Auger decay was also included in the calcula-
This work was supported by the Office of Chemical Sciences of the U.S. Department of Energy and the Robert A. Welch Foundation.
References 111 J.F. Reading and A.L. Ford, Phys. Rev. Lett. 58 (1987) 543. PI R.E. Olson, Phys. Rev. A36 (1987) 1519. t31 L.H. Andersen, P. Hvelplund, H. Knudsen, S.P. Moller, A.H. Sorensen, K. Elsener, K.-G. Rensfelt and E. Uggerhoj, Phys. Rev. A36 (1987) 3612. 141 J.H. McGuire, Phys. Rev. Lett. 49 (1982) 1153; Nucl. Instr. and Meth. A262 (1987) 48. [51 0. Heber, B.B. Bandong, G. Sampoll, and R.L. Watson, Phys. Rev. Lett. 64 (1990) 851. WI H. Knudsen, L.H. Andersen, P. Hvelplund, C. Astner, H. Cederquist, H. Danared, L. Liljeby and K.-G. Rensfelt, J. Phys. B17 (1984) 3545. t71 A. Muller, B. Schuch, W. Groh and E. Salzbom, Z. Phys. D7 (1987) 251. PI J.F. Reading and A.L. Ford, private communication. 191 L.H. Andersen, F. Hvelplund, H. Knudsen, S.P. Moller, J.O.P. Pedersen, A.H. Sorensen, E. Uggerhoj, K. Elsener and E. Morenzoni, comment in Phys. Rev. Lett. 65 (1990) 1687. WI 0. Heber, G. Sampoll, B.B. Bandong, R.J. Maurer, E. Moler, R. L. Watson, I. Ben-Itzhak, J.L. Shinpaugh, J.M. Sanders, L. Hefner and P. Richard, Phys. Rev. A39 (1989) 4898.
I. ATOMIC/MOLECULAR
PHYSICS
and Methods
in Physics
Research
B56/57
15
(1991) 15-17
Multiple ionization of He, Ne, and Ar by high velocity N7+ ions 0. Heber I, R.L. Watson, G. Sampoll, V. Horvat 2, B. Hill and T. Lotze Cyclotron Institute and Department of Chemutly, Texas A&M Uniuerslty, College Statron, TX 77840, USA
The yields time-of-fhght by theoretical experimental
of He, Ne, and Ar recoil ions produced in collisions with lo-40 MeV/amu N’* -projectiles were measured by the technique. The ratio of the yields for double and single ionization of He and Ne were found to be higher than predicted and semiempincal calculations. The role of electron correlation in multiple ionization was assessed by comparing the data for Ne and Ar with the results of an independent electron approximation analysis.
1. Introduction Multielectron ionizing collisions in the velocity regime where electron-electron correlation plays an important role are difficult to deal with theoretically because many-body calculations are required for a complete description of the process. Nevertheless, considerable progress has been made in the treatment of double ionization over the past few years. Both quantum mechanical calculations employing the forced impulse method (FIM) [l] and classical trajectory Monte Carlo calculations [2] have been successful at reproducing the general features of the cross section ratios for double and single ionization (R) of helium by protons and antiprotons [3]. Other investigators have approached this problem by invoking a number of mechanisms (associated with the first and second order terms of the Born expansion) to describe various aspects of double ionization, namely the double collision (or TS-2) mechanism, the electron scattering (or TS-1) mechanism, and the shakeoff mechanism [3,4]. According to Andersen et al. [3], the ratio R for any projectile charge q may be expressed in the form R = R, + q2R,, - 2qRint,
(1)
where R, is the portion of the cross section ratio for protons attributed to the indirect processes (i.e. TS-1 and shakeoff), RI, is the portion of the cross section ratio for protons attributed to the direct process, and R,,, is the portion of the cross section ratio for protons attributed to interference between the direct and the indirect processes. In terms of this formulation, the
large differences in R observed for protons and antiprotons arise as a consequence of the opposite signs of the interference term for the two projectiles. At high velocities, however, the ratios R,, and R,,, are expected to become negligible and R, becomes nearly constant. Therefore, the ratio R is predicted to eventually reach the limiting value of R,, which is independent of projectile charge. This behavior has been experimentally verified for electrons, protons, antiprotons, and alpha particles [3]. Recently, the yields He2+ and He’+ produced by lo-30 MeV/amu N 7+ ions were measured [5]. The resulting R values were found to remain nearly constant over this velocity range at a value approximately 4.5 times larger than the high velocity limit established by the data for q = 1. Moreover, R values for N7+ projectiles deviated from the theoretical predictions of Reading and Ford, and the semiempirical predictions of Knudsen et al. [6] by a factor of 2 or more beyond 20 MeV/amu. The present paper reports new measurements extending the R values for N7+ projectiles up to 40 MeV/amu and presents the results of multiple ionization yield measurements for Ne and Ar over the velocity range corresponding to lo-40 MeV/amu.
2. Experimental methods Beams of nitrogen ions having charges of 3 + , 4 + , or 5 + (depending on the desired energy) were extracted from the Texas A&M K500 superconducting cyclotron and sent through several focusing and steering elements. After passing through a 200 ug/cm2 Al foil, fully stripped
’ Present address: Department of Nuclear Physics, The Weizmann Institute of Science, Rehovot
’ On leave from the Department and Mathematics, University Yugoslavia. 0168-583X/91/$03.50
76100, Israel. of Physics, Faculty of Science of Zagreb, Zagreb, Croatia,
0 1991 - Elsevier Science Publishers
ions
were
magnet
and
directed
gas
into
either
cell
selected
by
through a Si surface
means
of an
a differentially barrier
analyzing pumped
detector
or
a
microchannel plate detector. The gas cell contained the target gas (He, Ne, or Ar at a pressure of 1 mTorr) and served as the first stage of a time-of-flight (TOF) spec-
B.V. (North-Holland)
I. ATOMIC/MOLECULAR
PHYSICS
16
0. Heber et al. / Multiple lomzatlon by N’+
trometer. The ions produced in collisions with N’+ projectiles were accelerated out of the gas cell by an electric field oriented transverse to the beam into a 12 cm flight tube. Upon reaching the end of the flight tube, the ions were further accelerated into a chevron microchannel plate assembly where they generated start signals for a time-to-amplitude converter (TAC). The TAC was stopped by delayed signals from the projectile detector. Time spectra generally required accumulation times of l-5 h at an incident projectile rate of 2000/s to obtain reasonable counting statistics for He2+ and the highest charge states of the Ne and Ar recoil ions.
zom
14
2’ 0
I 10
20 PROJECTILE
3. Results and discussion The R values obtained for He are shown in fig. 1. The new data point at 40 MeV/amu resolves the question of whether the ratios are really decreasing with increasing projectile energy. It is clear that the R values for N’+ projectiles do not reach the limiting value defined by the electron and proton data in the energy range investigated so far. A linear extrapolation suggests that this may occur between 60 and 70 MeV/amu. Also shown in fig. 1 are the results of several theoretical or semiempirical analyses for N’+ projectiles. The dotted curve shows the R values predicted by the FIM calculations of Reading and Ford (multiplied by a factor of 1.35) [1,8]. The solid curve shows the R values given by the semiempirical formula of Knudsen et al. [6], which is based on a fit of eq. (1) to experimental data at considerably lower energies. The dashed curve was constructed by extrapolating the values of R,, R,,, and R,,, given by Andersen et al. [3,9] for He and using them in eq. (1). Andersen et al. obtained R, and R,, by
100
r.
1 .
NITROGEN
A PROTON \
v
\
1
’ 0
ELECTRON
I 30
20
10 PROJECTILE
ENERGY
40
50
(MeV/omu)
Fig. 1. Energy dependence of the R values for electrons, protons and N 7f ions on He. The data points for N ions below 5 MeV/amu are from refs. [6,7]. Also shown are predictions based on the work of Reading and Ford [1,8], dotted curve; Andersen et al. [3], dashed curve; and Kundsen et al. [6], solid curve.
30 ENERGY
40
50
(MeV/amu)
Fig. 2. Energy dependence of the R values for N7+ ions on Ne. The solid curve shows the predictions based on the work of Andersen et al. [3].
theoretical methods and R,,, from experimental data for protons, antiprotons, and alpha particles. Although the R values calculated from the work of Andersen et al. agree with the data much better than do those from the other two analyses, they still decrease more rapidly with increasing energy than the experimental R values. This discrepancy may be an indication that the neglect of small contributions from higher order Born terms (having higher powers of 4) in the semiempirical analysis of the low energy/low q data leads to significant errors in the extrapolation to high energy for q = 7. The R values obtained for Ne are shown in fig. 2. The solid curve was determined by extrapolating the Ne RI, R,,, and R,,, values given by Andersen et al. [3], as discussed above. While the results of this semiempirical analysis are in fair agreement with the experimental data, it is apparent that fairly large discrepancies arise in the high energy region. It should be noted, however, that in the case of Ne, an additional contribution to R from Auger decay following K-shell ionization could be present in the experimental data. While such contributions are expected to be small for Ne, this is certainly not the case for Ar, where direct L-shell ionization followed by Auger decay makes a substantial contribution to the yield of Ar2+. The energy dependences of the Ne and Ar recoil-ion charge state fractions are shown in figs. 3 and 4, respectively. In order to estimate how large a role electronelectron correlation plays in the multiple ionization process, analyses employing the independent electron approximation (IEA) were carried out for these data. Since this approximation accounts for only the direct ionization process, differences between the IEA predictions and the experimental data provide an estimate of the degree to which indirect processes are involved. In applying the IEA, the methods described in ref. [lo] were used. The impact parameter dependent single-electron ionization probability was represented by an ex-
17
0. Heber et al. / Multiple iomzation by N 7+ ions
,0-l
9 w * ;
tion. The results are shown by the various curves in figs. 3 and 4. It is evident that the IEA predictions become increasingly worse as the velocity and charge increase. The overall poor agreement between the experimental and calculated recoil-ion relative yields is in marked contrast to previous findings for collisions of 0 and F projectiles with Ne and Ar in the 1 MeV/amu energy region [lo].
_‘” :P
:“
10-Z
.’ -El
4
Y 10-3 i
\
‘I\ Acknowledgements
,o-41
I\ 0
I 10
20 PROJECTILE
30 ENERGY
50
40
60
(MeV/amu)
Fig. 3. Energy dependence of the relative yields of Ne recoil ions produced in collisions with N’+ projectiles. The data points at 1.4 MeV/amu are from refs. [6,7].
100
9
lo-
w *
10-4
”
1
I. t---__
‘0..
.-
\
0
\I
n
m
---------. . v
T
0
0
0
’
0
IEA
EXP
-
1+
v
--
2+
v
3+
0 l
--4+
- -_ - ._ 0
10
20 PROJECTILE
30 ENERGY
3
1 40
50
60
(MeV/amu)
Fig. 4. Energy dependence of the relative yields of Ar recoil ions produced in collisions with N’+ prolectiles. The data points at 1.4 MeV/amu are from refs. [6,7].
ponential function that was normalized to the well known ve2 In v single ionization cross section velocity dependence. In the case of Ar, L-shell ionization followed by Auger decay was also included in the calcula-
This work was supported by the Office of Chemical Sciences of the U.S. Department of Energy and the Robert A. Welch Foundation.
References 111 J.F. Reading and A.L. Ford, Phys. Rev. Lett. 58 (1987) 543. PI R.E. Olson, Phys. Rev. A36 (1987) 1519. t31 L.H. Andersen, P. Hvelplund, H. Knudsen, S.P. Moller, A.H. Sorensen, K. Elsener, K.-G. Rensfelt and E. Uggerhoj, Phys. Rev. A36 (1987) 3612. 141 J.H. McGuire, Phys. Rev. Lett. 49 (1982) 1153; Nucl. Instr. and Meth. A262 (1987) 48. [51 0. Heber, B.B. Bandong, G. Sampoll, and R.L. Watson, Phys. Rev. Lett. 64 (1990) 851. WI H. Knudsen, L.H. Andersen, P. Hvelplund, C. Astner, H. Cederquist, H. Danared, L. Liljeby and K.-G. Rensfelt, J. Phys. B17 (1984) 3545. t71 A. Muller, B. Schuch, W. Groh and E. Salzbom, Z. Phys. D7 (1987) 251. PI J.F. Reading and A.L. Ford, private communication. 191 L.H. Andersen, F. Hvelplund, H. Knudsen, S.P. Moller, J.O.P. Pedersen, A.H. Sorensen, E. Uggerhoj, K. Elsener and E. Morenzoni, comment in Phys. Rev. Lett. 65 (1990) 1687. WI 0. Heber, G. Sampoll, B.B. Bandong, R.J. Maurer, E. Moler, R. L. Watson, I. Ben-Itzhak, J.L. Shinpaugh, J.M. Sanders, L. Hefner and P. Richard, Phys. Rev. A39 (1989) 4898.
I. ATOMIC/MOLECULAR
PHYSICS