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Statistical treatment of the inner M-shell excitation in heavy ion-atom collisions
Volume 96A, number 4
PHYSICS LETTERS
27 June 1983
STATISTICAL TREATMENT OF THE INNER M-SHELL EXCITATION IN HEAVY ION-ATOM COLLISIONS R. SHANKER Fakult~t fftr Physik, UniversitiitBielefeld, 4800-Bielefeld 1, West Germany Received 14 April 1983
A statistical treatment has been applied to interpret the experimental data on the Xe M-shellvacancy production in slow 1.05 MeV Xe-Xe collisions and is shown to give better agreement with experiment than that of the molecularorbital models.
A large body of data on experimental and theoret. ical investigations has been accumulated for the Kand I_,shell excitations in slow heavy i o n - a t o m collisions [ 1 - 3 ] . The experimental data of these studies have been generally interpred in terms of the molecular- orbital (MO) model of atomic collisions [4]. The excitation mechanism for the inner M shells in slow heavy i o n - a t o m collisions is, however, particularly complex since a large number of strongly coupled MOs are involved. The impact parameter dependence of the Xe M-shell excitation in 1.05 MeV X e - X e collisions has been studied by Shanker et al. [5] and the experimental data were interpreted in terms of the MO promotion of Fano and Lichten [4] in the Kessel model [6]. As a complement to the Fano-Lichten electron promotion through single non-interacting level crossings in light atoms, a statistical treatment of electron promotion in collision systems of large Z, with very complex and densely spaced level crossings under dynamic conditions, may offer a basis for a comprehensive description of Pauli excitation [7] leading to inner-shell ionization in heavy elements. Such a treatment was originally developed by Mittleman and Wilets [8] for treating outer-shell ionization problems. Later this approach was applied to interpret the innershell vacancy productions, e.g., the K-shell excitation by Brandt and Jones [9] and the K- and L-shell excitations by Johnson et al. [ 10]. As a matter of fact, this model is expected to be more appropriate for 188
treating higher inner shells, for example, the M.sheU excitation of high-Z elements in heavy i o n - a t o m collisions. In this letter we report on the application of the statistical model for the first time to interpret the inner M-shell excitation in heavy i o n - a t o m collisions. Predictions of the statistical model and those of the MO theories are compared with the data of Shanker et al. [5] and discussed. Heavy i o n - a t o m collisions are in general expected to be characterized by a distribution of charge and electronic states in a transiently formed quasimolecule with complex and densely spaced level crossings. Inner-shell vacancy production in such collisions may be viewed as the diffusion in energy space of a vacancy from an unoccupied level through a number of interacting level crossings of transient MOs to some inner shell of the united atom. The effect of various electronic configurations and the complexity of the collision are incorporated in one adjustable parameter, the so-called "diffusion constant" of the model. In the diffusion model, the impact parameter dependent excitation probability in the n shell for an electron to reach the ionization edge e n while leaving a vacancy in the n shell is given by [9] 2 ~ 0 (-1)v e x p [ - ( v + ½)27r2Sn(b)] , (1) =
where
0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
Volume 96A, number 4
PHYSICS LETTERS
27 June 1983 ,
Sn(b ) = (2R 0 V / D n ) F ( b / R O) = W n F ( x ) ,
with F ( x ) = (1 - x 2 ) 1/2 - x arccos x for x = b / R 0 ~< 1 and F ( x ) "~ 0 for x > 1. W n = 2R 0 V/D n, D n = e2n/C, C being an empirical constant, R 0 is the length of the strong interaction during the collision and V is the projectile velocity. D n is the diffusion constant which contains in principle all the quantummechanical information about electron promotion between interacting level crossings in the molecularorbital picture. In particular, D n changes with the energy gap from the level n in the united atom to unoccupied states. The latter ones could, indeed, be affected by the degree of ionization and by vacancies in the core of the projectiles as they are prepared prior to the collisions during the time of strong interaction. The extreme assumption about the density of MOs is in fact not necessary to first order [11 ]. In the present case, the internuclear radius R 0 has been chosen as the sum of the radii of M shells of the Xe atoms, This choice o f R 0 seems to be physical and meaningful for interpreting the data in the picture of Pauli excitation [7]. The diffusion constant for the M-shell excitation D M has been obtained by fitting eq. (1) to the experimental data of Shanker et al. [5]. Employing two parameters D M and R0, a curve is calculated using eq. (1) for the impact parameter dependent Xe M-shell vacancy production in slow 1.05 MeV X e - X e collisions and is compared with the experimental data in fig. 1. Since the electron data directly reflect the M-shell vacancy production, the X-ray data of Shanker et al. have been omitted for the present comparison. Theoretical predictions of the Fano-Lichten electron promotion in the Kessel model and that of 4f¢-4f6-4fTr and 5 f ¢ - 5 f o rotational couplings for the impact parameter dependent Xe M-shell vacancy production are also shown in fig. I. A comparison between experiment and the MO theories shows that the gross features of the Xe M-shell vacancy production can be explained by applying a generalized Kessel model (shown by the dashed curve in fig. 1). However, the step-functional structure which is an inherent property of the Kessel model is not reflected in the experimental data. Further, a large discrepancy is seen between experiment and MO theories in the impact parameter range 0.18 ~< b ~< 0.3 au (see fig. 1). More satisfactory agreement is obtained if the experiment is compared with the predictions of the statis-
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Fig. I. Comparison of the impact parameter dependent Xe M-shell vacancy production in 1.05 MeV Xe-Xe collisions with the predictions of the molecular orbital and the statistical model; • experimental data from ref. [5], - - - generalized Kessel model [5 ].... rotational couplings 4f¢-4f6 -4frr and 5f¢-5fo [5], - - present calculations based on the statistical model. tical model (shown by a solid curve in fig. 1) with the parametersD M = 1.6 cm2/s andR 0 = 3.7 X 10 - 9 cm. In order to make a direct comparison between the predictions of the statistical model and experiment, the impact parameter dependence of the Xe M excitation probabilities were first calculated by using eq. (1) with parameter D M obtained by fitting the experimental data and were then multiplied by 18, the total number of electrons in the M shell. The particular choice o f R 0 does not affect the calculated ionization probabilities sensitively in the region of small impact parameters where they are large. However, in the present case, if we take the interaction length R 0 = 3.7 X 10- 9 cm which is about 15% larger than the diameter of the neutral Xe atom, the agreement between the predictions of the statistical model and the exper. iment is found to be very good in the whole range of impact parameters considered. The above large value for the apparent radius of Xe could be attributed to the resonant interaction of the Xe M shells with resulting enhanced interaction volume. It is seen. from fig. 1 that the shape and the magnitude of the Xe M.shell ionization probability is more nicely reproduced by the statistical model than by the MO theo. des. The statistical treatment seems therefore to be adequate to describe the inner M-shell excitation in slow heavy i o n - a t o m collisions and illustrates the 189
Volume 96A, number 4
PHYSICS LETTERS
unique power and effective basis for the prediction of inner-shell vacancy production probabilities. The author wishes to thank Professor H.O. Lutz, Dr. R. Hippler and S. Jetzke for their useful discussions and comments. This work was supported by the Deutsche Forschungsgemeinschaft (DFG).
References [1] N. Luz, S. Sackmann and H.O. Lutz, J. Phys. B12 (1979) 1973. [2] W.E. Meyerhof and K. Taulbjerg, Ann. Rev. Nucl. Sci. 27 (1977) 279. [3] R. Shanker, R. Bilau, R. Hippler, U. Wille and H.O. Lutz, J. Phys. B14 (1981) 997.
190
27 June 1983
[4] U. Fano and W. Lichten, Phys. Rev. Lett. 14 (1965) 627. [5] R. Shanker, R. Hippler, U. Wille and H.O. Lutz, J. Phys. B15 (1982) 2041. [6] Q.C. Kessel, in: Case studies in atomic physics, Vol. 1, eds. E.W. McDaniel and M.R.C. McDowell (North Holland, Amsterdam, 1969) p. 399. [7] W. Brandt and R. Laubert, Phys. Rev. Lett. 24 (1970) 1037. [8] M.H. Mittleman and L. Wilets, Phys. Rev. 154 (1967) 12. [9] W. Brandt and K.W. Jones, Phys. Lett. 57A (1976) 35. [10] B.M. Johnson et al., Phys. Rev. 19A (1979) 81. [11] L. Wilets, Proc. Second Intern. Conf. on The physics of electronic and atomic collisions (Benjamin, New York, 1961) p. 47.
PHYSICS LETTERS
27 June 1983
STATISTICAL TREATMENT OF THE INNER M-SHELL EXCITATION IN HEAVY ION-ATOM COLLISIONS R. SHANKER Fakult~t fftr Physik, UniversitiitBielefeld, 4800-Bielefeld 1, West Germany Received 14 April 1983
A statistical treatment has been applied to interpret the experimental data on the Xe M-shellvacancy production in slow 1.05 MeV Xe-Xe collisions and is shown to give better agreement with experiment than that of the molecularorbital models.
A large body of data on experimental and theoret. ical investigations has been accumulated for the Kand I_,shell excitations in slow heavy i o n - a t o m collisions [ 1 - 3 ] . The experimental data of these studies have been generally interpred in terms of the molecular- orbital (MO) model of atomic collisions [4]. The excitation mechanism for the inner M shells in slow heavy i o n - a t o m collisions is, however, particularly complex since a large number of strongly coupled MOs are involved. The impact parameter dependence of the Xe M-shell excitation in 1.05 MeV X e - X e collisions has been studied by Shanker et al. [5] and the experimental data were interpreted in terms of the MO promotion of Fano and Lichten [4] in the Kessel model [6]. As a complement to the Fano-Lichten electron promotion through single non-interacting level crossings in light atoms, a statistical treatment of electron promotion in collision systems of large Z, with very complex and densely spaced level crossings under dynamic conditions, may offer a basis for a comprehensive description of Pauli excitation [7] leading to inner-shell ionization in heavy elements. Such a treatment was originally developed by Mittleman and Wilets [8] for treating outer-shell ionization problems. Later this approach was applied to interpret the innershell vacancy productions, e.g., the K-shell excitation by Brandt and Jones [9] and the K- and L-shell excitations by Johnson et al. [ 10]. As a matter of fact, this model is expected to be more appropriate for 188
treating higher inner shells, for example, the M.sheU excitation of high-Z elements in heavy i o n - a t o m collisions. In this letter we report on the application of the statistical model for the first time to interpret the inner M-shell excitation in heavy i o n - a t o m collisions. Predictions of the statistical model and those of the MO theories are compared with the data of Shanker et al. [5] and discussed. Heavy i o n - a t o m collisions are in general expected to be characterized by a distribution of charge and electronic states in a transiently formed quasimolecule with complex and densely spaced level crossings. Inner-shell vacancy production in such collisions may be viewed as the diffusion in energy space of a vacancy from an unoccupied level through a number of interacting level crossings of transient MOs to some inner shell of the united atom. The effect of various electronic configurations and the complexity of the collision are incorporated in one adjustable parameter, the so-called "diffusion constant" of the model. In the diffusion model, the impact parameter dependent excitation probability in the n shell for an electron to reach the ionization edge e n while leaving a vacancy in the n shell is given by [9] 2 ~ 0 (-1)v e x p [ - ( v + ½)27r2Sn(b)] , (1) =
where
0 031-9163/83/0000-0000/$ 03.00 © 1983 North-Holland
Volume 96A, number 4
PHYSICS LETTERS
27 June 1983 ,
Sn(b ) = (2R 0 V / D n ) F ( b / R O) = W n F ( x ) ,
with F ( x ) = (1 - x 2 ) 1/2 - x arccos x for x = b / R 0 ~< 1 and F ( x ) "~ 0 for x > 1. W n = 2R 0 V/D n, D n = e2n/C, C being an empirical constant, R 0 is the length of the strong interaction during the collision and V is the projectile velocity. D n is the diffusion constant which contains in principle all the quantummechanical information about electron promotion between interacting level crossings in the molecularorbital picture. In particular, D n changes with the energy gap from the level n in the united atom to unoccupied states. The latter ones could, indeed, be affected by the degree of ionization and by vacancies in the core of the projectiles as they are prepared prior to the collisions during the time of strong interaction. The extreme assumption about the density of MOs is in fact not necessary to first order [11 ]. In the present case, the internuclear radius R 0 has been chosen as the sum of the radii of M shells of the Xe atoms, This choice o f R 0 seems to be physical and meaningful for interpreting the data in the picture of Pauli excitation [7]. The diffusion constant for the M-shell excitation D M has been obtained by fitting eq. (1) to the experimental data of Shanker et al. [5]. Employing two parameters D M and R0, a curve is calculated using eq. (1) for the impact parameter dependent Xe M-shell vacancy production in slow 1.05 MeV X e - X e collisions and is compared with the experimental data in fig. 1. Since the electron data directly reflect the M-shell vacancy production, the X-ray data of Shanker et al. have been omitted for the present comparison. Theoretical predictions of the Fano-Lichten electron promotion in the Kessel model and that of 4f¢-4f6-4fTr and 5 f ¢ - 5 f o rotational couplings for the impact parameter dependent Xe M-shell vacancy production are also shown in fig. I. A comparison between experiment and the MO theories shows that the gross features of the Xe M-shell vacancy production can be explained by applying a generalized Kessel model (shown by the dashed curve in fig. 1). However, the step-functional structure which is an inherent property of the Kessel model is not reflected in the experimental data. Further, a large discrepancy is seen between experiment and MO theories in the impact parameter range 0.18 ~< b ~< 0.3 au (see fig. 1). More satisfactory agreement is obtained if the experiment is compared with the predictions of the statis-
,
,I,,,I
I
,
'
, ,,ll,
15
s % .~
......
-q
I
L__ O(
0.1
1.0
lmpoct Porometer (o.u.)
Fig. I. Comparison of the impact parameter dependent Xe M-shell vacancy production in 1.05 MeV Xe-Xe collisions with the predictions of the molecular orbital and the statistical model; • experimental data from ref. [5], - - - generalized Kessel model [5 ].... rotational couplings 4f¢-4f6 -4frr and 5f¢-5fo [5], - - present calculations based on the statistical model. tical model (shown by a solid curve in fig. 1) with the parametersD M = 1.6 cm2/s andR 0 = 3.7 X 10 - 9 cm. In order to make a direct comparison between the predictions of the statistical model and experiment, the impact parameter dependence of the Xe M excitation probabilities were first calculated by using eq. (1) with parameter D M obtained by fitting the experimental data and were then multiplied by 18, the total number of electrons in the M shell. The particular choice o f R 0 does not affect the calculated ionization probabilities sensitively in the region of small impact parameters where they are large. However, in the present case, if we take the interaction length R 0 = 3.7 X 10- 9 cm which is about 15% larger than the diameter of the neutral Xe atom, the agreement between the predictions of the statistical model and the exper. iment is found to be very good in the whole range of impact parameters considered. The above large value for the apparent radius of Xe could be attributed to the resonant interaction of the Xe M shells with resulting enhanced interaction volume. It is seen. from fig. 1 that the shape and the magnitude of the Xe M.shell ionization probability is more nicely reproduced by the statistical model than by the MO theo. des. The statistical treatment seems therefore to be adequate to describe the inner M-shell excitation in slow heavy i o n - a t o m collisions and illustrates the 189
Volume 96A, number 4
PHYSICS LETTERS
unique power and effective basis for the prediction of inner-shell vacancy production probabilities. The author wishes to thank Professor H.O. Lutz, Dr. R. Hippler and S. Jetzke for their useful discussions and comments. This work was supported by the Deutsche Forschungsgemeinschaft (DFG).
References [1] N. Luz, S. Sackmann and H.O. Lutz, J. Phys. B12 (1979) 1973. [2] W.E. Meyerhof and K. Taulbjerg, Ann. Rev. Nucl. Sci. 27 (1977) 279. [3] R. Shanker, R. Bilau, R. Hippler, U. Wille and H.O. Lutz, J. Phys. B14 (1981) 997.
190
27 June 1983
[4] U. Fano and W. Lichten, Phys. Rev. Lett. 14 (1965) 627. [5] R. Shanker, R. Hippler, U. Wille and H.O. Lutz, J. Phys. B15 (1982) 2041. [6] Q.C. Kessel, in: Case studies in atomic physics, Vol. 1, eds. E.W. McDaniel and M.R.C. McDowell (North Holland, Amsterdam, 1969) p. 399. [7] W. Brandt and R. Laubert, Phys. Rev. Lett. 24 (1970) 1037. [8] M.H. Mittleman and L. Wilets, Phys. Rev. 154 (1967) 12. [9] W. Brandt and K.W. Jones, Phys. Lett. 57A (1976) 35. [10] B.M. Johnson et al., Phys. Rev. 19A (1979) 81. [11] L. Wilets, Proc. Second Intern. Conf. on The physics of electronic and atomic collisions (Benjamin, New York, 1961) p. 47.