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Inner and outer shell contributions to the charge state distribution in heavy ion collisions
Volume 74A, number 3,4
PHYSICS LETFERS
12 November 1979
INNER AND OUTER SHELL CONTRIBUTIONS TO THE CHARGE STATE DISTRIBUTION IN HEAVY ION COLLISIONS M. MERON, D. MAOR and B. ROSNER Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel Received 28 May 1979 Revised manuscript received 6 September 1979 The charge distributions of ~+q ions after small impact parameter collisions in the medium energy range —~50 keV/amu, were studied. For symmetric and nearly symmetric systems they display a simple convex structure as a function of the impact parameter. This structure is interpreted as a result of an inner shell promotion effect superimposed on a purely statistical, impact parameter independent distribution. Good agreement with the shape predicted by the rotational coupling model allows the separation of the inner and outer shell contributions to the charge distribution.
Charge exchange processes in heavy ion collisions,in the medium energy range, I
ed to be impact parameter dependent according to the MO couplings [5] In such a case it can be identified as a structure on the flat background of the statistical interaction. In an experiment intended to check these predictions, the charge distributions of N ions emerging from small impact parameter collisions with N2, Ne and Ar
be visualized as taking place inside a unified electron cloud with all details concerning initial origin and level occupation wiped out. Therefore we expect the resulting charge distributions to be governed by statistical processes, and to depend only weakly on the incoming charge state. They should be practically independent of the impact as long asThose it remains small compared with parameter, atomic dimensions. predictions were indeed experimentally confirmed [2]. In addition to statistical interaction there is a possibility of a contribution to charge exchange processes from inner shell interactions [3]. As the collision is almost adiabatic for the inner electrons, in the velocity range mentioned above, their interactions can be well described in terms of the molecular orbital model [4]. Under certain conditions, especially for symmetric and nearly symmetric collisions, these interactions create inner shell vacancies which affect the resulting charge distributions, both directly and through the subsequent Auger emission. This contribution is almost independent of the outer shell processes, and is expect-
atoms were measured under single collision conditions, as a function of angle, energy and incoming charge state. ~ beams up to charge state 4+, in the energy range 0.5—1 MeV, were obtained from the 1 MV Van de Graaf accelerator at the Technion using a post-acceleration gas stripper and magnetic analyzer. A neutral 1~beam by means beam was also produced from thethe Nanalyzing magnet, of an additional gas cell beyond and an electrostatic deflector which removed the charged particles from the beam. The target gas was contained in a differentially pumped windowless gas cell. A narrow movable slit defined the scattering angle to 0.10. The outgoing charge states were electrostatically analyzed and recorded by a position sensitive detector. The beam purity, as determined by an additional electrostatic analyzer was better than 99% for 0, 1 + and 2+ charge states, and not worse than 90% even for the 4~beam. The single collision condition was checked by target pressure measurement and independently by an analysis of the neutral beam passing
.
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PHYSICS LETTERS
at 00 angle through the target. It was found that multiple collision events amounted to less than 5% of all the scattering events. More details of the experimental setup and its performance will soon be published. Charge state spectra of N projectiles scattered between 0.4°and 100 corresponding to impact parameters in the range 0.3—0.03 au were taken at 500, 700 and 1000 keV, for different incoming charges. The scattering angle was converted to the impact parameter, assuming an exponentially screened Coulomb p0tential. Fig. 1 displays typical results for the values of the average charge states of the scattered ions, for the N—N and N—Ar systems, as a function of the impact parameter. As can be seen, the results for the asymmetric system N—Ar, are impact parameter independent. On the other hand, for the symmetric N—N system a convex structure can be seen in the impact parameter dependence, whose amplitude, although small, is well beyond the experimental error. In view of the previous discussion we tried to relate this structure to inner shell excitation processes, of which only the 2pa—2pir promotion contributes significantly in our case [5] A semiquantitative analysis of the experimental results was performed, using the theoretical results of Taulbjerg and Briggs [6] This theory was previously applied mainly in the analysis of experimental results concerning measurements of X-rays and Auger .
.
12 November 1979
Table 1 Comparison of the location of the maximum of the K-vacancy production predicted by the rotational coupling model with the maximum experimental average charge. Colliding system
Velocity (au)
N—N NN N—N NNe N—Ne
1.20 1.41 1.60 1.41 1.60
Theoretical [6] impact parameter of maximal ~ex
Experimental impact parameter of maximal
(au)
average charge (au)
0.144 0.155 0.163 0.114 0.121
0.14 0.14 0.15 0.11 0.11
±0.01 ±0.01 ±0.01 ±0.01 ±0.01
electrons emitted after heavy ion collisions [7]. On the other hand, the present study analyses the effect of the creation of inner shell vacancies on the atomic charge distributions which are predominantly due to outer shell interactions. Secondly, we tried to separate the contributions of the statistical interaction of the outer shells and of the promotion effects of the K-shell, as follows: The average number of K-vacancies produced in the collision is N~TF~X where 1’ex is the 2pa—2pir K-excitation probability, and N,r is the average number of vacancies available in the 2p7r~orbital. Assuming complete independence of inner and outer shell processes, the final average charge state, obtained for an incoming charge state n is given by: (1) where c~denotes the average charge state resulting from the outer shell statistical interaction alone. The coefficient a depends on the collision partners and is equal to the average charge increase per vacancy creaqn—qn+aN,~l’ex,
N— Ar
3.0
N
-
-~________ 21 ~
2.5
2n
Ft
3
—~
________ ~ _________
o
-
0
As the fluorescence yield in our case is very low, each K-vacancy causes the emission of an Auger election. tron. In a symmetric collision the vacancy created has a probability of 1/2 to remain in the projectile K-shell after separation, therefore we obtain for the N—N system a = 1/2. On the other hand, for the N—Ne system,
2
I
0.1
0.2
0.3
0
b (a.u.)
0.1
I
02
I
0.3
Fig. 1. Average charge states of N ions after a close single collision with N 2 and Ar at 700 keV (velocity of 1.41 au). The numbers 0—3 denote the incoming charge state.
202
the vacancy is created in the nitrogen’s K-shell and the promoted electron is transferred to the Ne atom. This can be verified from the correlation diagram of this system [5] The N charge state is therefore raised by two units per promotion, if vacancy sharing is neglect.
Volume 74A, number 3,4
PHYSICS LETFERS
12 November 1979
INNER AND OUTER SHELL CONTRIBUTIONS TO THE CHARGE STATE DISTRIBUTION IN HEAVY ION COLLISIONS M. MERON, D. MAOR and B. ROSNER Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel Received 28 May 1979 Revised manuscript received 6 September 1979 The charge distributions of ~+q ions after small impact parameter collisions in the medium energy range —~50 keV/amu, were studied. For symmetric and nearly symmetric systems they display a simple convex structure as a function of the impact parameter. This structure is interpreted as a result of an inner shell promotion effect superimposed on a purely statistical, impact parameter independent distribution. Good agreement with the shape predicted by the rotational coupling model allows the separation of the inner and outer shell contributions to the charge distribution.
Charge exchange processes in heavy ion collisions,in the medium energy range, I
ed to be impact parameter dependent according to the MO couplings [5] In such a case it can be identified as a structure on the flat background of the statistical interaction. In an experiment intended to check these predictions, the charge distributions of N ions emerging from small impact parameter collisions with N2, Ne and Ar
be visualized as taking place inside a unified electron cloud with all details concerning initial origin and level occupation wiped out. Therefore we expect the resulting charge distributions to be governed by statistical processes, and to depend only weakly on the incoming charge state. They should be practically independent of the impact as long asThose it remains small compared with parameter, atomic dimensions. predictions were indeed experimentally confirmed [2]. In addition to statistical interaction there is a possibility of a contribution to charge exchange processes from inner shell interactions [3]. As the collision is almost adiabatic for the inner electrons, in the velocity range mentioned above, their interactions can be well described in terms of the molecular orbital model [4]. Under certain conditions, especially for symmetric and nearly symmetric collisions, these interactions create inner shell vacancies which affect the resulting charge distributions, both directly and through the subsequent Auger emission. This contribution is almost independent of the outer shell processes, and is expect-
atoms were measured under single collision conditions, as a function of angle, energy and incoming charge state. ~ beams up to charge state 4+, in the energy range 0.5—1 MeV, were obtained from the 1 MV Van de Graaf accelerator at the Technion using a post-acceleration gas stripper and magnetic analyzer. A neutral 1~beam by means beam was also produced from thethe Nanalyzing magnet, of an additional gas cell beyond and an electrostatic deflector which removed the charged particles from the beam. The target gas was contained in a differentially pumped windowless gas cell. A narrow movable slit defined the scattering angle to 0.10. The outgoing charge states were electrostatically analyzed and recorded by a position sensitive detector. The beam purity, as determined by an additional electrostatic analyzer was better than 99% for 0, 1 + and 2+ charge states, and not worse than 90% even for the 4~beam. The single collision condition was checked by target pressure measurement and independently by an analysis of the neutral beam passing
.
201
Volume 74A, number 3,4
PHYSICS LETTERS
at 00 angle through the target. It was found that multiple collision events amounted to less than 5% of all the scattering events. More details of the experimental setup and its performance will soon be published. Charge state spectra of N projectiles scattered between 0.4°and 100 corresponding to impact parameters in the range 0.3—0.03 au were taken at 500, 700 and 1000 keV, for different incoming charges. The scattering angle was converted to the impact parameter, assuming an exponentially screened Coulomb p0tential. Fig. 1 displays typical results for the values of the average charge states of the scattered ions, for the N—N and N—Ar systems, as a function of the impact parameter. As can be seen, the results for the asymmetric system N—Ar, are impact parameter independent. On the other hand, for the symmetric N—N system a convex structure can be seen in the impact parameter dependence, whose amplitude, although small, is well beyond the experimental error. In view of the previous discussion we tried to relate this structure to inner shell excitation processes, of which only the 2pa—2pir promotion contributes significantly in our case [5] A semiquantitative analysis of the experimental results was performed, using the theoretical results of Taulbjerg and Briggs [6] This theory was previously applied mainly in the analysis of experimental results concerning measurements of X-rays and Auger .
.
12 November 1979
Table 1 Comparison of the location of the maximum of the K-vacancy production predicted by the rotational coupling model with the maximum experimental average charge. Colliding system
Velocity (au)
N—N NN N—N NNe N—Ne
1.20 1.41 1.60 1.41 1.60
Theoretical [6] impact parameter of maximal ~ex
Experimental impact parameter of maximal
(au)
average charge (au)
0.144 0.155 0.163 0.114 0.121
0.14 0.14 0.15 0.11 0.11
±0.01 ±0.01 ±0.01 ±0.01 ±0.01
electrons emitted after heavy ion collisions [7]. On the other hand, the present study analyses the effect of the creation of inner shell vacancies on the atomic charge distributions which are predominantly due to outer shell interactions. Secondly, we tried to separate the contributions of the statistical interaction of the outer shells and of the promotion effects of the K-shell, as follows: The average number of K-vacancies produced in the collision is N~TF~X where 1’ex is the 2pa—2pir K-excitation probability, and N,r is the average number of vacancies available in the 2p7r~orbital. Assuming complete independence of inner and outer shell processes, the final average charge state, obtained for an incoming charge state n is given by: (1) where c~denotes the average charge state resulting from the outer shell statistical interaction alone. The coefficient a depends on the collision partners and is equal to the average charge increase per vacancy creaqn—qn+aN,~l’ex,
N— Ar
3.0
N
-
-~________ 21 ~
2.5
2n
Ft
3
—~
________ ~ _________
o
-
0
As the fluorescence yield in our case is very low, each K-vacancy causes the emission of an Auger election. tron. In a symmetric collision the vacancy created has a probability of 1/2 to remain in the projectile K-shell after separation, therefore we obtain for the N—N system a = 1/2. On the other hand, for the N—Ne system,
2
I
0.1
0.2
0.3
0
b (a.u.)
0.1
I
02
I
0.3
Fig. 1. Average charge states of N ions after a close single collision with N 2 and Ar at 700 keV (velocity of 1.41 au). The numbers 0—3 denote the incoming charge state.
202
the vacancy is created in the nitrogen’s K-shell and the promoted electron is transferred to the Ne atom. This can be verified from the correlation diagram of this system [5] The N charge state is therefore raised by two units per promotion, if vacancy sharing is neglect.
Volume 74A, number 3,4
PHYSICS LETTERS
12 November 1979
i
~
3b
2.5
Pex
—-—-—~—~—-—ld
Fig. 2. Average charge states of N ions after a close single collision with N 2, as a function of P~at u = 1.41 au. The crosses are experimental data points from fig. 1. The solid lines are linear fits according to eq. (1). The numbers 0—3 denote the incoming charge state.
ed. This means a(N—Ne) = 2. The factor N~cannot be reliably estimated from the initial conditions, as at our collision velocities it contains a dynamical contribution which is not well known [6]. However, its value is not vital for the analysis. As can be seen from eq. (2) at any given velocity c~ depends linearly on ~ex• Therefore a linear fit to the experimental t~ values according to eq. (1) gives us both 4~and alV~,thus performing the desired separation of inner and outer shell contributions. The results of such a fit for a specific set of data, N—N at v = 1.41 1’ex au,clearly are shown fig.it 2. The linear dependence on asis seen,inand verifies the soundness of the sumptions which led to eq. (1). In addition, the knowledge of a enables us to extract N~from the a1V~values obtained by the fit. Thus we get for the N—N system N~values between 0.6—0.8 depending on the incoming charge state. For the N~—Ne system, where the 2pir~electrons come from the Ne atom, we get N~ = 0.07 in reasonable agreement with ref. [6]. The errors of these values are about 20%. The experimental N—N data at u = 1.41 au, and the curves obtained after the subtraction of the promotion contribution, are compared in fig. 3 with the N—Ar data at the same velocity. It can be seen that the N—N promotion subtracted line lies rather close to the N—Ar results, where no promotion effect is expected. The lowest set of lines displays the computed results
2.0
—
1.5
I
0
0.1
0.2 b(a.u.)
I
0.3
Fig.
3. Comparison of experimental average charge states of N ions after a close single collision with N2 (a) and Ar (b),
with the promotion subtracted curves for the N—N system (c) andforwith the predictions of the dynamical screening model (d) the same system. The velocity is 1.41 au. The numbers 1 and 3 denote the incoming charge states.
of the the dynamic screening modelbelonging [8]. It seems that while spacing of the curves to different incoming charge states is correctly predicted by this model, their absolute values are lower by about 0.5 charge unit than the experimental values. This discrepancy can be related to additional outer shell electron emission which takes place after the collision [3]. We conclude that for small parameter collisions in the medium energy range the resulting charge state distributions are governed mainly by a statistical interaction of the outer electrons which gives rise to an impact parameter independent contribution. Under proper conditions, especially in symmetric collisions, a small promotion contribution is superimposed on the statistical one. A more quantitative analysis with a full account for the statistical part will be possible when a good estimate of the residual outer electrons’ excitation energy will be available. 203
Volume 74A, number 3,4
PHYSICS LETTERS
12 November 1979
The authors are grateful to Dr. I. Tserruya for many fruitful discussions.
[3] D. Maor and B. Rosner, Phys. Lett. 69A (1978) 100. [4] C. Kessel and B. Fastrup, Case Stud. At. Phys. 3 (1973) 137.
References
[5] J.S. Briggs and K. Taulbjerg, J. Phys. B8 (1975) 1909. [6] K. Taulbjerg, J.S. Briggs and J. Vaaben, 1. Phys. B9 (1976) 1351.
[1] N. Bohr, K. Dan. Vidensk. Seisk. Mat. Phys. Medd. 18 (1948)no.8. [2] B. Rosner and D. Gur, Phys. Rev. A15 (1977) 70.
[7] N. Luz, S. Sackmann and H.O. Lutz, J. Phys. B12 (1979) 1973. [8] B. Rosner and W. Brandt, Phys. Lett. 61A (1977) 97.
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