- Email: [email protected]
Absolute cross sections for multi-electron processes in low energy Arq+−Ar collisions: Comparison with theory
Nuclear Instruments and Methods North-Holland, Amsterdam
in Physics
Research
397
B9 (1985) 397-399
ABSOLUTE CROSS SECTIONS FOR MULTI-ELECTRON COLLISIONS: COMPARISON WITH THEORY
PROCESSES
A. BAtiNY
‘), G. ASTNER”, H. CEDERQUIST *), H. DANARED P. HVELPLUND 4), A. JOHNSON ‘), H. KNUDSEN 4), L. LILJEBY
IN LOW ENERGY A1.4+-Ar
*), S. HULDT ‘), *) and K.-G. RENSFELT
*)
Ii Institute oj Theoretical Physics, Unioersity of Uppsala, S-752 38 Uppsala, Sweden ‘I Research Institute of Physics, S 104 05 Stockholm, Sweden ‘) Department of Physics, University of Lund, S-223 62 Lund, Sweden 4J Institute of Physics, University oj Aarhw, DK - 8000 Aarhus, Denmark
Absolute cross sections have been measured for a variety of multi-electron processes in low-energy collisions of multiply charged argon recoil ions with neutral argon. The cross sections are compared with theoretical estimates based on an extension of the classical barrier model. Comparison is also made with the statistical theory of Miiller et al.
1. Introduction Multiply charged ions having low kinetic energy may be produced in laboratory and astrophysical plasmas by, e.g., electron impact ionization of photoionization. Their presence constitutes an important factor influencing the non-equilibrium thermodynamic properties of the plasma [l]. For modelling and diagnostic purposes it is of some importance to know absolute cross sections of the various multi-electron processes that result when multiply charged ions collide with many-electron atoms. These collisions are characterised by the large amount of potential energy which resides in the multiply charged ion. During the collision this energy may be released and used to eject electrons or emit photons. In order to keep track of the multi-electron processes that occur, coincidence registration of the final charge states of both projectile and target is essential [2]. We have measured absolute cross sections for a large number of reactions Ar4++
X -+ Ar’q-k’++
Xtk+“)++
ne-
where X = Ne, Ar, Kr. The ions were produced in a recoil ion source at the Research Institute of Physics [3], using a beam of 110 MeV C4+ as hammer, and had charge states q ranging from 1 to 10. Projectile recoil ions were accelerated to 1.8q keV and made to collide a gas target. Charge state analysis and coincidence registration of projectiles and target ions were performed by time-of-flight techniques [4]. In this contribution we will compare our experimental results for Arq+-Ar (q = 4-8) with two theoretical models. Complete results together with full details of the experimental technique and data treatment will be given elsewhere. While single-electron processes have received much 0168-583X/85/$03.30 Q Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
attention during the last decade and several useful models have been proposed (besides more or less sophisticated close-coupling calculations), the situation is different for multi-electron processes [5]. Here there is an acute need even for a model that gives only rough quantitative results. We here use an extension of the classical barrier model (for single-electron capture [6,7]) to multi-electron processes along the lines proposed in [5]. This extension gives absolute cross sections for production of target ions of given charge state. The model does not differentiate between direct electron capture and transfer ionization when more than one electron leaves the target. This is done in the statistical theories of Miiller et al. [8] and Aberg et al. [9], but these predict only the fractions of target ions in a given charge state. To produce absolute values the theories have to be normalised to absolute cross sections for capture of a given number of electrons. We will here make a comparison with the normalised fractions of ref. [8] only, but a more detailed comparison with statistical theories will be given together with the publication of the complete results.
2. Theory We first consider the classical barrier model as applied to an electron being transferred from a core of charge z = 1 to an ion of charge q having a quasicontinuum of unoccupied energy levels. As explained, e.g. in ref. [lo], the transfer is supposed to take place when the potential barrier between the ionic attractive wells is so low that the first-order Stark-shifted binding energy of the electron equals the top of the barrier, i.e. when I. COLLISION
PROCESSES
A. Rrirrjny et al./Absolute crosssectionsfor multi-electronprocesses
398
(atomic
units are used)
f+q/R=(q’/2+1)2/R.
This condition
(1)
gives a characteristic
capture
k=l
radius
R = (2q 1’2 f 1)/z,
(2)
and a cross section e = ~11’.
(3)
In a refined version (taking the discrete energy levels of the ion into account) this model has been used with great success, in particular to single-electron capture from hydrogen to fully stripped ions. Janev and Presnyakov [5] have pointed out that for multi-electron targets the cross section (3) should be looked upon as comprising also the sum of the cross sections of all multi-electron processes that occur at smaller distances. They also proposed to estimate the influence of two-electron processes by considering the first and second electron as having capture radii (Zi is the i th ionization potential of the target) R=R,=[2(q-i+1)“‘+1]/1,,
defining the cross capture as e1 =r(Rf-R$),
i=l,2,
sections
for one-
14)
and two-electron
a,=nRi.
(5)
The original procedure neglects transfer ionization, but recently McDowell and Janev [ll] have introduced an autoionization probability w to take this process into account. The scheme used in ref. [5] can immediately be generalised to three- and more-electron processes, but the expressions (4) used for the capture radii of higher order then turn out to be too small. The reason for this is easily diagnosed by noting that the capture radius in the one-electron classical barrier model for an electron initially bound with binding energy Z in an ion of core charge z is R=
[2(qz)1’2+z],‘I.
A natural generalisation thentodefine(m=1,2,...,N) R=R,=
(6)
for multi-electron
[2(q-m+1)“2m’~2+m]/Z~,
processes
is
(7)
and ui = V( R; - R;), 02 =
r( R;
cross sections (8) should be looked upon as m o;n= c crtpk, m=1,2 ,...) N-l,
- R:),
o,=nRZ,.
If we denote by c$,~_?: the cross section for capture of k electrons while the target loses k + n electrons, the
UN =
c k+nzN
,$I k+n 44-k.
(9)
Put into words, this means that ui is the cross section for direct single-electron capture while o, is the sum of direct double capture and single capture with transfer ionization, etc. Since transfer ionization may be an important part of single capture, care must be taken in comparing ui with experimental cross sections for single capture not differentiating transfer ionization and such cross sections should rather be compared with nRf. In order to separate off the transfer ionization part of a2 from the direct double capture one can write ui (TI) = wuz , where the probability probability [ 111.
(10) factor
w is an autoionisation
3. Results Table 1 shows a comparison between our experimental absolute cross sections for Arq+-Ar with q = 4-8 and the extended classical barrier model described above and defined by eqs. (7) and (8). Within the context of such a simple theory the agreement is rather good. That the experimental values scatter around the theoretical ones could possibly be explained by our neglect of the level structure of the projectile ion. That this can be important is shown, e.g., by the energy-gain spectroscopy measurements of the same collision systems performed at Aarhus [12]. Small experimental cross section values, particularly evident when many electrons are involved, could be explained by experimental difficulties in measuring all the small cross sections that make up the sums of ey. (9). In order to test also the production of target ions of different charge states for a given projectile charge change, table 2 compares our absolute experimental cross sections with theoretical values derived from the statistical model of Mtiller et al. [S] through normalisation to uq q_lr. As discussed in ref. [8], the statistical theory should not work for the single-electron capture distribution when transfer ionization is an important process. This behaviour can indeed be seen in table 2, where the theoretical values are rather good for Q = 4 and 5 while being totally off for q = 7 and 8. For k >=2 the model values agree quite well with the experimental ones. 4. Conclusion We have shown that a simple extension of the dassical barrier model for single-electron capture to multi-
A. Blrirny
er al. /Aholure
~‘rms
se~~wns
/or mulir
electron
prwesre;r
399
1 of target ions of charge state M in collisions Absolute crash sections em (in units of 10 lo cm’) for production 1.~ keV. E: Experiments (to be published). 7’: extended classical barrier model described in text and defined
Table
Q
4 5 6 7 8
#t=l E 32 26 39 57 53
m=2
of Arq’ with Ar at by eqs. (7) and (8).
m=S
m=3
nt = 4
‘I’
E
T
7 7 7 8
4 13
6 6
I
E
I-
E
T
E
25 29 32 36 40
15 17 22 28 26
16 18 20 23 25
4 13 14 13 21
13 15 17 19 21
1 7 12 11
Table 2 Absolute cross sections e$,^‘/’ (in units of 10 ” cm ’ ) for capture of k electrons and ionizatmn of n electrons in collisions of ArY’ with Ar a~ 1.8q kcV. E: Experiments (10 be published). T: statistical model of Muller et al. ]R]. normalized for each y and k to the total capturecross section nqyy_k. The value 0 is given to cross sections smaller than 0.5 and a dash signifies an endothermic reaction. 4
A
?I=0
n-1
E
T
E
n=2 T
n=3
E
‘I‘
4 4
1 2
32 13
34 I5
2 2
1 0
5 5 5
1 2 3
26 9 5
29 12 5
8 8 1
6 6 0
6 6 6
1 2 3
39 5 4
46 9 6
17 10 6
11 7 4
1 1
0 0 0
7 7 7 7
1 2 3 4
57 4 2 1
27 2 1 1
24 10 8 3
51 11 9 3
1 2 1
4 3
8 x 8 8
1 2 3 4
53 3 2 1
11 1 0 0
23 I6 5 4
53 16 7 3
3 5 5
16 9 5 2
electron processes is possible and leads to fair predictions for the absolute cross sections in low energy collisions of ArVf-Ar with q = 4-8. The model treats the transfer of m electrons from the target to the projectile while not distinguishing as to the further fate of these electrons (autoionization or radiative stabilization). We have also compared our results with a statistical model which gives very specific predictions as to the fate of all electrons. For the capture of two or more electrons this model. properly normalised. also gives good results. References
[l] H.W. Drawin, Phys. Scripta 4 (1981) 622. [2] C.L. Cocke. R. Dubois. T.J. Gray. E. Justiniano and C. Can, Phys. Rev. Lett. 46 (1981) 1671. [3] G. Astner, A. Bar&y. H. Cederquist, H. Danared. P. Hyelplund. A. Johnson. H. Knudsen, L. Liljeby and L. Lundin. Phys. Scripta T3 (1983) 163.
E
T
._
2 0
2
0 0
[4] L. Liljeby. H. Cederyuist, H. Danared. G. Astner. A. Bhrhny and A. Johnson, in : Proc. 13th Conf. on the Physics of Electronic and Atomic Collisions, Berlin (1983). eds.. J. Eichler et al., Abstracts, p. 711. [5] R.K. Janev and L.P. Presnyakov. Phys. Reports 70 (1981) 1. [6] H. Ryufuku. K. Sasaki and T. Watanabe. Phys. Rev. A21 (1980) 745. [7] R. Mann, F. Folkmann and H.F. Bcyer. J. Phys. B 14 (1981) 1161. (81 A. Miiller, W. Groh and E. Salzborn. Phys. Rev. Lett. 51 (1983) 107. [9] T. Aberg. A. Blomberg, J. Tulkki and 0. Goscinski. Phys. Rev. Lett. 52 (1984) 1207. [IO] F. Folkmann. R. Mann and H.F. Beyer, Phys. Scripta T3 (1983) 88. [ll] M.R.C. McDowell and R.K. Janev. J. Phys. B 17 (1984) 2295. 1121 E.H. Nielsen, L.H. Andersen, A. B&any, H. Cederquist. P. Hvelplund, H. Knudsen, K.B. MacAdam and J. Sorensen, J. Phys. B 17 (1984) L 139.
in Physics
Research
397
B9 (1985) 397-399
ABSOLUTE CROSS SECTIONS FOR MULTI-ELECTRON COLLISIONS: COMPARISON WITH THEORY
PROCESSES
A. BAtiNY
‘), G. ASTNER”, H. CEDERQUIST *), H. DANARED P. HVELPLUND 4), A. JOHNSON ‘), H. KNUDSEN 4), L. LILJEBY
IN LOW ENERGY A1.4+-Ar
*), S. HULDT ‘), *) and K.-G. RENSFELT
*)
Ii Institute oj Theoretical Physics, Unioersity of Uppsala, S-752 38 Uppsala, Sweden ‘I Research Institute of Physics, S 104 05 Stockholm, Sweden ‘) Department of Physics, University of Lund, S-223 62 Lund, Sweden 4J Institute of Physics, University oj Aarhw, DK - 8000 Aarhus, Denmark
Absolute cross sections have been measured for a variety of multi-electron processes in low-energy collisions of multiply charged argon recoil ions with neutral argon. The cross sections are compared with theoretical estimates based on an extension of the classical barrier model. Comparison is also made with the statistical theory of Miiller et al.
1. Introduction Multiply charged ions having low kinetic energy may be produced in laboratory and astrophysical plasmas by, e.g., electron impact ionization of photoionization. Their presence constitutes an important factor influencing the non-equilibrium thermodynamic properties of the plasma [l]. For modelling and diagnostic purposes it is of some importance to know absolute cross sections of the various multi-electron processes that result when multiply charged ions collide with many-electron atoms. These collisions are characterised by the large amount of potential energy which resides in the multiply charged ion. During the collision this energy may be released and used to eject electrons or emit photons. In order to keep track of the multi-electron processes that occur, coincidence registration of the final charge states of both projectile and target is essential [2]. We have measured absolute cross sections for a large number of reactions Ar4++
X -+ Ar’q-k’++
Xtk+“)++
ne-
where X = Ne, Ar, Kr. The ions were produced in a recoil ion source at the Research Institute of Physics [3], using a beam of 110 MeV C4+ as hammer, and had charge states q ranging from 1 to 10. Projectile recoil ions were accelerated to 1.8q keV and made to collide a gas target. Charge state analysis and coincidence registration of projectiles and target ions were performed by time-of-flight techniques [4]. In this contribution we will compare our experimental results for Arq+-Ar (q = 4-8) with two theoretical models. Complete results together with full details of the experimental technique and data treatment will be given elsewhere. While single-electron processes have received much 0168-583X/85/$03.30 Q Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
attention during the last decade and several useful models have been proposed (besides more or less sophisticated close-coupling calculations), the situation is different for multi-electron processes [5]. Here there is an acute need even for a model that gives only rough quantitative results. We here use an extension of the classical barrier model (for single-electron capture [6,7]) to multi-electron processes along the lines proposed in [5]. This extension gives absolute cross sections for production of target ions of given charge state. The model does not differentiate between direct electron capture and transfer ionization when more than one electron leaves the target. This is done in the statistical theories of Miiller et al. [8] and Aberg et al. [9], but these predict only the fractions of target ions in a given charge state. To produce absolute values the theories have to be normalised to absolute cross sections for capture of a given number of electrons. We will here make a comparison with the normalised fractions of ref. [8] only, but a more detailed comparison with statistical theories will be given together with the publication of the complete results.
2. Theory We first consider the classical barrier model as applied to an electron being transferred from a core of charge z = 1 to an ion of charge q having a quasicontinuum of unoccupied energy levels. As explained, e.g. in ref. [lo], the transfer is supposed to take place when the potential barrier between the ionic attractive wells is so low that the first-order Stark-shifted binding energy of the electron equals the top of the barrier, i.e. when I. COLLISION
PROCESSES
A. Rrirrjny et al./Absolute crosssectionsfor multi-electronprocesses
398
(atomic
units are used)
f+q/R=(q’/2+1)2/R.
This condition
(1)
gives a characteristic
capture
k=l
radius
R = (2q 1’2 f 1)/z,
(2)
and a cross section e = ~11’.
(3)
In a refined version (taking the discrete energy levels of the ion into account) this model has been used with great success, in particular to single-electron capture from hydrogen to fully stripped ions. Janev and Presnyakov [5] have pointed out that for multi-electron targets the cross section (3) should be looked upon as comprising also the sum of the cross sections of all multi-electron processes that occur at smaller distances. They also proposed to estimate the influence of two-electron processes by considering the first and second electron as having capture radii (Zi is the i th ionization potential of the target) R=R,=[2(q-i+1)“‘+1]/1,,
defining the cross capture as e1 =r(Rf-R$),
i=l,2,
sections
for one-
14)
and two-electron
a,=nRi.
(5)
The original procedure neglects transfer ionization, but recently McDowell and Janev [ll] have introduced an autoionization probability w to take this process into account. The scheme used in ref. [5] can immediately be generalised to three- and more-electron processes, but the expressions (4) used for the capture radii of higher order then turn out to be too small. The reason for this is easily diagnosed by noting that the capture radius in the one-electron classical barrier model for an electron initially bound with binding energy Z in an ion of core charge z is R=
[2(qz)1’2+z],‘I.
A natural generalisation thentodefine(m=1,2,...,N) R=R,=
(6)
for multi-electron
[2(q-m+1)“2m’~2+m]/Z~,
processes
is
(7)
and ui = V( R; - R;), 02 =
r( R;
cross sections (8) should be looked upon as m o;n= c crtpk, m=1,2 ,...) N-l,
- R:),
o,=nRZ,.
If we denote by c$,~_?: the cross section for capture of k electrons while the target loses k + n electrons, the
UN =
c k+nzN
,$I k+n 44-k.
(9)
Put into words, this means that ui is the cross section for direct single-electron capture while o, is the sum of direct double capture and single capture with transfer ionization, etc. Since transfer ionization may be an important part of single capture, care must be taken in comparing ui with experimental cross sections for single capture not differentiating transfer ionization and such cross sections should rather be compared with nRf. In order to separate off the transfer ionization part of a2 from the direct double capture one can write ui (TI) = wuz , where the probability probability [ 111.
(10) factor
w is an autoionisation
3. Results Table 1 shows a comparison between our experimental absolute cross sections for Arq+-Ar with q = 4-8 and the extended classical barrier model described above and defined by eqs. (7) and (8). Within the context of such a simple theory the agreement is rather good. That the experimental values scatter around the theoretical ones could possibly be explained by our neglect of the level structure of the projectile ion. That this can be important is shown, e.g., by the energy-gain spectroscopy measurements of the same collision systems performed at Aarhus [12]. Small experimental cross section values, particularly evident when many electrons are involved, could be explained by experimental difficulties in measuring all the small cross sections that make up the sums of ey. (9). In order to test also the production of target ions of different charge states for a given projectile charge change, table 2 compares our absolute experimental cross sections with theoretical values derived from the statistical model of Mtiller et al. [S] through normalisation to uq q_lr. As discussed in ref. [8], the statistical theory should not work for the single-electron capture distribution when transfer ionization is an important process. This behaviour can indeed be seen in table 2, where the theoretical values are rather good for Q = 4 and 5 while being totally off for q = 7 and 8. For k >=2 the model values agree quite well with the experimental ones. 4. Conclusion We have shown that a simple extension of the dassical barrier model for single-electron capture to multi-
A. Blrirny
er al. /Aholure
~‘rms
se~~wns
/or mulir
electron
prwesre;r
399
1 of target ions of charge state M in collisions Absolute crash sections em (in units of 10 lo cm’) for production 1.~ keV. E: Experiments (to be published). 7’: extended classical barrier model described in text and defined
Table
Q
4 5 6 7 8
#t=l E 32 26 39 57 53
m=2
of Arq’ with Ar at by eqs. (7) and (8).
m=S
m=3
nt = 4
‘I’
E
T
7 7 7 8
4 13
6 6
I
E
I-
E
T
E
25 29 32 36 40
15 17 22 28 26
16 18 20 23 25
4 13 14 13 21
13 15 17 19 21
1 7 12 11
Table 2 Absolute cross sections e$,^‘/’ (in units of 10 ” cm ’ ) for capture of k electrons and ionizatmn of n electrons in collisions of ArY’ with Ar a~ 1.8q kcV. E: Experiments (10 be published). T: statistical model of Muller et al. ]R]. normalized for each y and k to the total capturecross section nqyy_k. The value 0 is given to cross sections smaller than 0.5 and a dash signifies an endothermic reaction. 4
A
?I=0
n-1
E
T
E
n=2 T
n=3
E
‘I‘
4 4
1 2
32 13
34 I5
2 2
1 0
5 5 5
1 2 3
26 9 5
29 12 5
8 8 1
6 6 0
6 6 6
1 2 3
39 5 4
46 9 6
17 10 6
11 7 4
1 1
0 0 0
7 7 7 7
1 2 3 4
57 4 2 1
27 2 1 1
24 10 8 3
51 11 9 3
1 2 1
4 3
8 x 8 8
1 2 3 4
53 3 2 1
11 1 0 0
23 I6 5 4
53 16 7 3
3 5 5
16 9 5 2
electron processes is possible and leads to fair predictions for the absolute cross sections in low energy collisions of ArVf-Ar with q = 4-8. The model treats the transfer of m electrons from the target to the projectile while not distinguishing as to the further fate of these electrons (autoionization or radiative stabilization). We have also compared our results with a statistical model which gives very specific predictions as to the fate of all electrons. For the capture of two or more electrons this model. properly normalised. also gives good results. References
[l] H.W. Drawin, Phys. Scripta 4 (1981) 622. [2] C.L. Cocke. R. Dubois. T.J. Gray. E. Justiniano and C. Can, Phys. Rev. Lett. 46 (1981) 1671. [3] G. Astner, A. Bar&y. H. Cederquist, H. Danared. P. Hyelplund. A. Johnson. H. Knudsen, L. Liljeby and L. Lundin. Phys. Scripta T3 (1983) 163.
E
T
._
2 0
2
0 0
[4] L. Liljeby. H. Cederyuist, H. Danared. G. Astner. A. Bhrhny and A. Johnson, in : Proc. 13th Conf. on the Physics of Electronic and Atomic Collisions, Berlin (1983). eds.. J. Eichler et al., Abstracts, p. 711. [5] R.K. Janev and L.P. Presnyakov. Phys. Reports 70 (1981) 1. [6] H. Ryufuku. K. Sasaki and T. Watanabe. Phys. Rev. A21 (1980) 745. [7] R. Mann, F. Folkmann and H.F. Bcyer. J. Phys. B 14 (1981) 1161. (81 A. Miiller, W. Groh and E. Salzborn. Phys. Rev. Lett. 51 (1983) 107. [9] T. Aberg. A. Blomberg, J. Tulkki and 0. Goscinski. Phys. Rev. Lett. 52 (1984) 1207. [IO] F. Folkmann. R. Mann and H.F. Beyer, Phys. Scripta T3 (1983) 88. [ll] M.R.C. McDowell and R.K. Janev. J. Phys. B 17 (1984) 2295. 1121 E.H. Nielsen, L.H. Andersen, A. B&any, H. Cederquist. P. Hvelplund, H. Knudsen, K.B. MacAdam and J. Sorensen, J. Phys. B 17 (1984) L 139.