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Scaling properties of target excitation cross sections in collisions between atoms and multiply charged ions
Volume 126, number 1
PHYSICSLETTERSA
14 December 1987
SCALING PROPERTIES OF TARGET EXCITATION CROSS SECTIONS IN C O L L I S I O N S BETWEEN ATOMS AND MULTIPLY CHARGED IONS Wolfgang FRITSCH Bereich Kern- u nd Strahlenphysik, Hahn-Meitner-lnstitut Berlin, D-I O00 Berlin 39, Germany
and
K.-H. SCHARTNER L Physikalisches lnstitut, Universit?it Giessen, D-6300 Giessen, FRG
Received 1 September 1987:revised manuscript received22 October 1987;accepted for publication 26 October 1987 Communicatedby B. Fricke
The scalingproperties of one-electrontarget excitation crosssectionsin collisionsbetween atoms and multiplychargedions are investigated. For the example of bare-ion(Z)-hydrogencollisions with various charge numbers Z it is shown that, in many-state calculations for Z>I2 and energiesE/Z.~ 15-100keV/amu, calculated 2p excitationcrosssectionslie approximatelyon a universal curve. This curve deviates from the one which has been derived earlier by Janev and Presnyakov for all Z on the basis of a simplified three-state model, and in fact results from a consistent three-state treatment showno scaling. The scalingproperties of the excitation cross sectionsare easily understood in a purelyclassical modelof distant collisions.
Electronic transitions in collisions between atoms and multiply charged ions have been studied extensively in recent years. While these investigations have mainly concentrated on electron transfer and ionization, see, e.g., refs. [1-3] and references therein, little is known about target excitation in these systems. Ryufuku [4] has applied the UDWA in calculations of total excitation cross sections for some bare-ion(A z+ )-hydrogen systems. Janev and Presnyakov [ 5 ] have determined H ( n p ) excitation cross sections in AZ++ H collisions with a three-state close-coupling dipole approximation. Due to a scaling relation which holds in this approximation the results derived in ref. [ 5 ] may be applied for a wide range of projectile charge numbers Z. Other theoretical work is available for a few systems, see refs. [ 6-8 ] and references therein. Unfortunately there exist no experimental excitation cross sections for hydrogenic targets to date except for proton projectiles [ 9 ]. The excitation of He targets by highly-charged ions has been investigated [ 10] only recently for the first time. On the
other hand, cross sections for excitation of hydrogen by ion impact have, besides their fundamental aspect, an important application: the neutral-beam stopping cross section in fusion plasmas may be substantially increased due to ionization of that fraction of hydrogen atoms which, after injection, has been excited in collisions with impurity ions [ 11 ]. Though presently neutral beam injection heating occurs at 60-80 keV, energies around 300 keV may be used in future fusion experiments. In this Letter we present and discuss calculated 2p excitation cross sections in A z+ + H collisions, which are derived in a many-state close-coupling formalism. We show that the resulting cross sections do approximately scale for Z~>2 in some energy range although the calculated quasi-universal cross section curve deviates from the curve given by Janev and Presnyakov. In their pioneering investigation [ 5 ] on H (np) excitation in A Z + + H collisions, Janev and Presnyakov start from the customary coupled equations of the semiclassical close-coupling formalism. By intro-
0375-9601/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
17
Volume 126, number 1
PHYSICS LETTERS A
ducing a n u m b e r o f approximations they arrive at an analytic expression for the excitation cross sections. In particular, (i) the number of states which are considered is restricted to three, i.e. the initial ls and the final npo and np~ target states; (ii) all diagonal interactions are neglected; (iii) the interaction between npo and np~ states is neglected; (iv) the remaining interactions are approximated by an analytical dipole expression; (v) the coupled equations are solved by an approximate method. An important result o f ref. [5] is that the excitation cross sections a lie on a universal curve, a l Z = f ( g- IZ) ,
(1)
where v denotes the collision velocity and the funct i o n f c a n be found in eq. (22) of ref. [5]. As is discussed in ref. [5] the scaling relation (1) does no longer hold once the approximations ( i ) - ( v ) are lifted. Other than in the early 1980s the exact numerical integration of the coupled equations with large basis sets is now c o m m o n practice in investigations o f electron transfer [2]. In particular, the exact treatment o f three collisionally coupled atomic orbitals is very easily done. In fig. 1 we show calculated 2p excitation cross sections in A z+ + H collisions for Z = 1, 2, 4, 8 and 16, where the calculations are performed in a three-state model (cf. approximation (i) above) but with approximations ( ii ) - ( v ) lifted. Clearly these results do not scale as in eq. (1), rather they deviate strongly from the universal curve of ref. [ 5]. From the results o f fig. 1 we conclude that at least one o f the approximations ( i i ) - ( v ) is very severe at low-tointermediate collisions energies. The importance of including the diagonal interactions (cf. approximation (ii)) even at high energies has been specifically discussed in the past [ 12]. In passing we note that in the energy region covered in fig. 1, the first Born approximation would also not be appropriate as its results would follow scaling relation (1) as long as its logarithmic term can be considered constant. While the results presented in fig. 1 demonstrate the problems associated with approximations ( i i ) - ( v ) to the close-coupling scheme, they still can18
I0-15
14 December 1987 I
I
i
i
i i i I!
I
i
T~711
I1~
E ~J N c~_ t~
g aJ t~
10-16
g 4--
3-state
closecoupting
lO
lOO
impact energy/Z (keV/clmu) Fig. la. Theoretical 2p excitation cross sections in A/+ +H collisions from three-state models. Full curves: results from closecoupling calculations for various charge numbers Z, this work; short-dashed line (labelled JP): universal curve derived [ 5 ] with additional approximations, see text. Note that the close-coupling results in this figure are not considered predictions of experiment. not be regarded reliable predictions o f experimental cross sections. Clearly the three-state approximation (cf. (i) above) is very much unsatisfactory as particularly the 2s and the n = 3 excitation channels are expected to couple strongly to the former three states. For a better assessment o f 2p excitation cross sections, calculations have therefore been performed with larger basis sets consisting o f all n = 1-3 target atomic states and 13 other target-centered pseudostates which have been used earlier [ 13] in order to represent the ionization channels in hydrogen. At lower energies where electron transfer becomes important the projectile states nolm have also been included in the basis for Z = 1-8 (no denotes the single most important projectile shell in electron transfer, no= I, 2, 3, 5 for respectively Z = 1, 2, 4, 8 [ 14]). Details of the calculations can be found in earlier work [ 13,14]. The calculated 2p excitation cross sections from the many-state close-coupling scheme are shown in fig. 2 (low energy results for Z = 1 are taken from ref. [ 13 ]). They clearly are quite different from the results derived in the three-state approximation, cf. fig. 1, and hence demonstrate that also approximation
Volume 126, number 1
f
t-~
E t.d
I
PHYSICS LETTERS A
I
I
I [ III
[
I
I
I
l
I II
t
AZ'+H
S
2p excitofion 10 -16 .4--
I
. . . - . . . . . . . . x ;'~'~'-'~'--.~ ~•
mony-stafe close -coupling
.-'" ]P .-"
~,o'~ ,'~
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Fig. 2. Theoretical predictions of 2p excitation cross sections in Az+ + H collisions.Symbolsdenote results from many-stateclosecoupling calculations with Z= 16 (.), 8 ( o ), 4 ( × ), 2 ( A) and 1 (full line), this work; the long-dashed line indicates a quasiuniversal curve for the systemswith Z>~2 at higher energies; the short-dashed line (JP) denotes the universal curve from ref. [5 ]. (i) should be avoided. At low energies where electron transfer plays some role and where comparatively small impact parameters are involved, the cross sections turn out to be quite different for each projectile Z with no apparent regularity. For higher collision energies, however, we find the striking fact that the calculated excitation cross sections do lie approximately on a common curve, i.e. they scale like in eq. (1), except for proton projectiles. This approximate "universal" curve is distinctively shifted in energy from the curve given in ref. [5] although it turns out to have similar magnitude. In quantummechanical terms the quasi-scaling of cross sections for Z>~2 at higher energies, cf. fig. 2, is not easy to understand particularly since it occurs not in a consistent few-state description (cf. fig. 1 ) but rather in a "quasi-complete" description of the collisions or else in few(2-3)-state descriptions involving doubtful approximations. For example, the direct off-diagonal excitation matrix elements in the three-state description do scale at large internuclear separations with charge number Z, (lslHl2p) ~-constxZ/R 2 ,
(2)
such as to give rise to scaling relation (1) in distant collisions. The important diagonal matrix elements,
14 December 1987
however, do not scale the same way and approach only rather slowly their limiting value - Z / R at large separations (where then they can be removed by unitary transformation). It also turns out that relation (2) is only rather poorly observed by actual matrix elements in the relevant range of internuclear separations. Therefore, in a consistent close-coupling formulation there is no obvious indication for scaling of the results as there is in the aforementioned simplified theoretical models (whose scaling also includes Z=I). On the other hand, in a purely classical description of the collision process, the scaling relation (1) is almost trivial. At internuclear separations R which are large in comparison to the orbit dimensions of the electron in its initial state, the projectile exerts a force F at the electron, which is of magnitude F ~- Z / R 2. Clearly the electron feels the same time-dependent force F(t) by all projectiles Z passing by at a distance R v / Z with a velocity vv/Z on a straight-line path. Since the excitation cross section depends on the square of the dimension of impact parameters relation (1) follows right away. In fact the calculated impact-parameter (b) dependent excitation probabilities (which underlie the results shown in fig. 2 but are not shown here) do show approximate scaling P( b, v, Z ) = g ( b / v / Z
, v/x/Z ) .
(3)
Since excitation in H ÷ + H collisions occurs at comparatively small impact parameters (not large against the radius of the electronic ls orbit) it comes as no surprise that the excitation curve for Z = 1 deviates from the near-universal curve even at its high-energy end in fig. 2. The increasing contributions from small impact-parameter collisions to the integrated excitation cross sections with decreasing energy also explains that the cross sections cease to scale at low energies. At present there are no experimental 2p excitation cross sections available for the collision systems considered here except for the H + + H system at E ~ 30 keV [ 15,16 ] for which the data lie well on the calculated curve (cf. the discussion in ref. [13]). Also the measured excitation cross sections to the n = 2 manifold at higher energies [9] are in very good agreement with the results shown in fig. 2 for H + + H if corrected for the small contribution of the 2s excitation channel. 19
Volume 126, number 1
PHYSICS LETTERSA
In conclusion, the scaling relation (1) for excitation cross sections in A z+ + H collisions (which follows from simplified two-state or three-state models) is shown to be severely violated in a consistent threestate description. This scaling relation has been, however, recovered in a more realistic many-state description of collisions at energies E/Z>~ 15 keV/ ainu a n d is shown to follow from a classical picture of distant collisions. This classical picture is well known empirically to be appropriate at these energies (for recent work in the classical picture, see refs. [ 17,18 ] a n d references therein). At lower energies, excitation cross sections have to be d e t e r m i n e d for each charge n u m b e r Z separately. At much higher energies, certainly at E/Z>I 1 MeV/amu, the scaling property (1) is also expected to break down as the classical picture ceases to be adequate for optically allowed transitions [ 18]. Similarly, at these high energies the appropriate first Born a p p r o x i m a t i o n would no longer predict a scaling of results according to eq. (1). Finally it is noted that the qualitative discussion of this paper is expected to apply also to other excitation channels. In fact, in a yet unfinished investigation on 3 JP excitation in A z+ 4- He collisions we find relation (1) largely confirmed for charge n u m b e r s Z > I. We also find that, for the population of higher-excited states, scaling relation (1) is progressively less satisfied, in agreement with the classical picture given above, which requires the electronic orbital radii to be small in comparison with the collision impact parameters.
20
14 December 1987
References [ 1] R.K. Janev and H. Winter. Phys. Rep. 117 (1985) 265. [2] W. Fritsch, Nucl. Instrum. Methods B 23 (1987) 9. [3] J.H. McGuire, A. Miiller, B. Schuch, W. Groh and E. Salzborn, Phys. Rev. A 35 (1987) 2479. [4] H. Ryufuku, Phys. Rev. A 25 (1982) 720. [ 5 ] R.K. Janev and L.P. Presnyakov,J. Phys. B 13 (1980) 4233. [6] R. McCarroll and A. Salin, Ann. Phys. (Paris) 1 (1966) 283. [7] B. Brendlr, R. Gayet, J.P. Rozet and K. Wohrer, Phys. Rev. Lett. 54 (1985) 2007. [ 81 A. Salop and J. Eichler, in: Electronicand atomic collisions, Abstracts of contributed papers from 14th Int. Conf. on Physics of electronic and atomic collisions, eds. M.J. Coggiola, D.L. Huestis and R.P. Saxon (North-Holland, Amsterdam, 1986) p. 462. [9] J.T. Park, J.E. Aldag, J.M. George, J.L. Preacher and J.H. McGuire, Phys. Rev. A 15 (1977) 508. [10]K. Reymann, K.-H. Schartner and B. Sommer, Nucl. Instrum. Methods B 23 (1987) 157. [ 11 ] C.D. Boley, R.K. Janev and D.E. Post, Phys. Rev. Lett. 52 (1984) 534. [ 12] D.R. Bates, Proc. Phys. Soc. 73 ( 1959) 227. [ 13] W. Fritsch and C.D. Lin, Phys. Rev. A 27 (1983) 3361. [ 14] W. Fritsch and C.D. Lin, Phys. Rev. A 29 (1984) 3039. [15] T.J. Morgan, J. Geddes and H.B. Gilbody, J. Phys. B 6 (1973) 21t8. [ 16] T. Kondow, R.J. Grinius, T.P. Chong and W.L. Fite, Phys. Rev. A 10 (1974) 1167. [ 17] R.E. Olson, T.J. Gay, H.G. Berry, E.B. Hale and V.D. Irby, Phys. Rev. Lett. 59 (1987) 36. [ 18] G. Schiwietzand W. Fritsch, J. Phys. B, to be published.
PHYSICSLETTERSA
14 December 1987
SCALING PROPERTIES OF TARGET EXCITATION CROSS SECTIONS IN C O L L I S I O N S BETWEEN ATOMS AND MULTIPLY CHARGED IONS Wolfgang FRITSCH Bereich Kern- u nd Strahlenphysik, Hahn-Meitner-lnstitut Berlin, D-I O00 Berlin 39, Germany
and
K.-H. SCHARTNER L Physikalisches lnstitut, Universit?it Giessen, D-6300 Giessen, FRG
Received 1 September 1987:revised manuscript received22 October 1987;accepted for publication 26 October 1987 Communicatedby B. Fricke
The scalingproperties of one-electrontarget excitation crosssectionsin collisionsbetween atoms and multiplychargedions are investigated. For the example of bare-ion(Z)-hydrogencollisions with various charge numbers Z it is shown that, in many-state calculations for Z>I2 and energiesE/Z.~ 15-100keV/amu, calculated 2p excitationcrosssectionslie approximatelyon a universal curve. This curve deviates from the one which has been derived earlier by Janev and Presnyakov for all Z on the basis of a simplified three-state model, and in fact results from a consistent three-state treatment showno scaling. The scalingproperties of the excitation cross sectionsare easily understood in a purelyclassical modelof distant collisions.
Electronic transitions in collisions between atoms and multiply charged ions have been studied extensively in recent years. While these investigations have mainly concentrated on electron transfer and ionization, see, e.g., refs. [1-3] and references therein, little is known about target excitation in these systems. Ryufuku [4] has applied the UDWA in calculations of total excitation cross sections for some bare-ion(A z+ )-hydrogen systems. Janev and Presnyakov [ 5 ] have determined H ( n p ) excitation cross sections in AZ++ H collisions with a three-state close-coupling dipole approximation. Due to a scaling relation which holds in this approximation the results derived in ref. [ 5 ] may be applied for a wide range of projectile charge numbers Z. Other theoretical work is available for a few systems, see refs. [ 6-8 ] and references therein. Unfortunately there exist no experimental excitation cross sections for hydrogenic targets to date except for proton projectiles [ 9 ]. The excitation of He targets by highly-charged ions has been investigated [ 10] only recently for the first time. On the
other hand, cross sections for excitation of hydrogen by ion impact have, besides their fundamental aspect, an important application: the neutral-beam stopping cross section in fusion plasmas may be substantially increased due to ionization of that fraction of hydrogen atoms which, after injection, has been excited in collisions with impurity ions [ 11 ]. Though presently neutral beam injection heating occurs at 60-80 keV, energies around 300 keV may be used in future fusion experiments. In this Letter we present and discuss calculated 2p excitation cross sections in A z+ + H collisions, which are derived in a many-state close-coupling formalism. We show that the resulting cross sections do approximately scale for Z~>2 in some energy range although the calculated quasi-universal cross section curve deviates from the curve given by Janev and Presnyakov. In their pioneering investigation [ 5 ] on H (np) excitation in A Z + + H collisions, Janev and Presnyakov start from the customary coupled equations of the semiclassical close-coupling formalism. By intro-
0375-9601/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
17
Volume 126, number 1
PHYSICS LETTERS A
ducing a n u m b e r o f approximations they arrive at an analytic expression for the excitation cross sections. In particular, (i) the number of states which are considered is restricted to three, i.e. the initial ls and the final npo and np~ target states; (ii) all diagonal interactions are neglected; (iii) the interaction between npo and np~ states is neglected; (iv) the remaining interactions are approximated by an analytical dipole expression; (v) the coupled equations are solved by an approximate method. An important result o f ref. [5] is that the excitation cross sections a lie on a universal curve, a l Z = f ( g- IZ) ,
(1)
where v denotes the collision velocity and the funct i o n f c a n be found in eq. (22) of ref. [5]. As is discussed in ref. [5] the scaling relation (1) does no longer hold once the approximations ( i ) - ( v ) are lifted. Other than in the early 1980s the exact numerical integration of the coupled equations with large basis sets is now c o m m o n practice in investigations o f electron transfer [2]. In particular, the exact treatment o f three collisionally coupled atomic orbitals is very easily done. In fig. 1 we show calculated 2p excitation cross sections in A z+ + H collisions for Z = 1, 2, 4, 8 and 16, where the calculations are performed in a three-state model (cf. approximation (i) above) but with approximations ( ii ) - ( v ) lifted. Clearly these results do not scale as in eq. (1), rather they deviate strongly from the universal curve of ref. [ 5]. From the results o f fig. 1 we conclude that at least one o f the approximations ( i i ) - ( v ) is very severe at low-tointermediate collisions energies. The importance of including the diagonal interactions (cf. approximation (ii)) even at high energies has been specifically discussed in the past [ 12]. In passing we note that in the energy region covered in fig. 1, the first Born approximation would also not be appropriate as its results would follow scaling relation (1) as long as its logarithmic term can be considered constant. While the results presented in fig. 1 demonstrate the problems associated with approximations ( i i ) - ( v ) to the close-coupling scheme, they still can18
I0-15
14 December 1987 I
I
i
i
i i i I!
I
i
T~711
I1~
E ~J N c~_ t~
g aJ t~
10-16
g 4--
3-state
closecoupting
lO
lOO
impact energy/Z (keV/clmu) Fig. la. Theoretical 2p excitation cross sections in A/+ +H collisions from three-state models. Full curves: results from closecoupling calculations for various charge numbers Z, this work; short-dashed line (labelled JP): universal curve derived [ 5 ] with additional approximations, see text. Note that the close-coupling results in this figure are not considered predictions of experiment. not be regarded reliable predictions o f experimental cross sections. Clearly the three-state approximation (cf. (i) above) is very much unsatisfactory as particularly the 2s and the n = 3 excitation channels are expected to couple strongly to the former three states. For a better assessment o f 2p excitation cross sections, calculations have therefore been performed with larger basis sets consisting o f all n = 1-3 target atomic states and 13 other target-centered pseudostates which have been used earlier [ 13] in order to represent the ionization channels in hydrogen. At lower energies where electron transfer becomes important the projectile states nolm have also been included in the basis for Z = 1-8 (no denotes the single most important projectile shell in electron transfer, no= I, 2, 3, 5 for respectively Z = 1, 2, 4, 8 [ 14]). Details of the calculations can be found in earlier work [ 13,14]. The calculated 2p excitation cross sections from the many-state close-coupling scheme are shown in fig. 2 (low energy results for Z = 1 are taken from ref. [ 13 ]). They clearly are quite different from the results derived in the three-state approximation, cf. fig. 1, and hence demonstrate that also approximation
Volume 126, number 1
f
t-~
E t.d
I
PHYSICS LETTERS A
I
I
I [ III
[
I
I
I
l
I II
t
AZ'+H
S
2p excitofion 10 -16 .4--
I
. . . - . . . . . . . . x ;'~'~'-'~'--.~ ~•
mony-stafe close -coupling
.-'" ]P .-"
~,o'~ ,'~
"
~'I
"--
r 0
X ~
10-17
[
I
I
L
I IIII
I
I
I
10 imporf energy/Z (keV/nmu)
t
I I I
100
Fig. 2. Theoretical predictions of 2p excitation cross sections in Az+ + H collisions.Symbolsdenote results from many-stateclosecoupling calculations with Z= 16 (.), 8 ( o ), 4 ( × ), 2 ( A) and 1 (full line), this work; the long-dashed line indicates a quasiuniversal curve for the systemswith Z>~2 at higher energies; the short-dashed line (JP) denotes the universal curve from ref. [5 ]. (i) should be avoided. At low energies where electron transfer plays some role and where comparatively small impact parameters are involved, the cross sections turn out to be quite different for each projectile Z with no apparent regularity. For higher collision energies, however, we find the striking fact that the calculated excitation cross sections do lie approximately on a common curve, i.e. they scale like in eq. (1), except for proton projectiles. This approximate "universal" curve is distinctively shifted in energy from the curve given in ref. [5] although it turns out to have similar magnitude. In quantummechanical terms the quasi-scaling of cross sections for Z>~2 at higher energies, cf. fig. 2, is not easy to understand particularly since it occurs not in a consistent few-state description (cf. fig. 1 ) but rather in a "quasi-complete" description of the collisions or else in few(2-3)-state descriptions involving doubtful approximations. For example, the direct off-diagonal excitation matrix elements in the three-state description do scale at large internuclear separations with charge number Z, (lslHl2p) ~-constxZ/R 2 ,
(2)
such as to give rise to scaling relation (1) in distant collisions. The important diagonal matrix elements,
14 December 1987
however, do not scale the same way and approach only rather slowly their limiting value - Z / R at large separations (where then they can be removed by unitary transformation). It also turns out that relation (2) is only rather poorly observed by actual matrix elements in the relevant range of internuclear separations. Therefore, in a consistent close-coupling formulation there is no obvious indication for scaling of the results as there is in the aforementioned simplified theoretical models (whose scaling also includes Z=I). On the other hand, in a purely classical description of the collision process, the scaling relation (1) is almost trivial. At internuclear separations R which are large in comparison to the orbit dimensions of the electron in its initial state, the projectile exerts a force F at the electron, which is of magnitude F ~- Z / R 2. Clearly the electron feels the same time-dependent force F(t) by all projectiles Z passing by at a distance R v / Z with a velocity vv/Z on a straight-line path. Since the excitation cross section depends on the square of the dimension of impact parameters relation (1) follows right away. In fact the calculated impact-parameter (b) dependent excitation probabilities (which underlie the results shown in fig. 2 but are not shown here) do show approximate scaling P( b, v, Z ) = g ( b / v / Z
, v/x/Z ) .
(3)
Since excitation in H ÷ + H collisions occurs at comparatively small impact parameters (not large against the radius of the electronic ls orbit) it comes as no surprise that the excitation curve for Z = 1 deviates from the near-universal curve even at its high-energy end in fig. 2. The increasing contributions from small impact-parameter collisions to the integrated excitation cross sections with decreasing energy also explains that the cross sections cease to scale at low energies. At present there are no experimental 2p excitation cross sections available for the collision systems considered here except for the H + + H system at E ~ 30 keV [ 15,16 ] for which the data lie well on the calculated curve (cf. the discussion in ref. [13]). Also the measured excitation cross sections to the n = 2 manifold at higher energies [9] are in very good agreement with the results shown in fig. 2 for H + + H if corrected for the small contribution of the 2s excitation channel. 19
Volume 126, number 1
PHYSICS LETTERSA
In conclusion, the scaling relation (1) for excitation cross sections in A z+ + H collisions (which follows from simplified two-state or three-state models) is shown to be severely violated in a consistent threestate description. This scaling relation has been, however, recovered in a more realistic many-state description of collisions at energies E/Z>~ 15 keV/ ainu a n d is shown to follow from a classical picture of distant collisions. This classical picture is well known empirically to be appropriate at these energies (for recent work in the classical picture, see refs. [ 17,18 ] a n d references therein). At lower energies, excitation cross sections have to be d e t e r m i n e d for each charge n u m b e r Z separately. At much higher energies, certainly at E/Z>I 1 MeV/amu, the scaling property (1) is also expected to break down as the classical picture ceases to be adequate for optically allowed transitions [ 18]. Similarly, at these high energies the appropriate first Born a p p r o x i m a t i o n would no longer predict a scaling of results according to eq. (1). Finally it is noted that the qualitative discussion of this paper is expected to apply also to other excitation channels. In fact, in a yet unfinished investigation on 3 JP excitation in A z+ 4- He collisions we find relation (1) largely confirmed for charge n u m b e r s Z > I. We also find that, for the population of higher-excited states, scaling relation (1) is progressively less satisfied, in agreement with the classical picture given above, which requires the electronic orbital radii to be small in comparison with the collision impact parameters.
20
14 December 1987
References [ 1] R.K. Janev and H. Winter. Phys. Rep. 117 (1985) 265. [2] W. Fritsch, Nucl. Instrum. Methods B 23 (1987) 9. [3] J.H. McGuire, A. Miiller, B. Schuch, W. Groh and E. Salzborn, Phys. Rev. A 35 (1987) 2479. [4] H. Ryufuku, Phys. Rev. A 25 (1982) 720. [ 5 ] R.K. Janev and L.P. Presnyakov,J. Phys. B 13 (1980) 4233. [6] R. McCarroll and A. Salin, Ann. Phys. (Paris) 1 (1966) 283. [7] B. Brendlr, R. Gayet, J.P. Rozet and K. Wohrer, Phys. Rev. Lett. 54 (1985) 2007. [ 81 A. Salop and J. Eichler, in: Electronicand atomic collisions, Abstracts of contributed papers from 14th Int. Conf. on Physics of electronic and atomic collisions, eds. M.J. Coggiola, D.L. Huestis and R.P. Saxon (North-Holland, Amsterdam, 1986) p. 462. [9] J.T. Park, J.E. Aldag, J.M. George, J.L. Preacher and J.H. McGuire, Phys. Rev. A 15 (1977) 508. [10]K. Reymann, K.-H. Schartner and B. Sommer, Nucl. Instrum. Methods B 23 (1987) 157. [ 11 ] C.D. Boley, R.K. Janev and D.E. Post, Phys. Rev. Lett. 52 (1984) 534. [ 12] D.R. Bates, Proc. Phys. Soc. 73 ( 1959) 227. [ 13] W. Fritsch and C.D. Lin, Phys. Rev. A 27 (1983) 3361. [ 14] W. Fritsch and C.D. Lin, Phys. Rev. A 29 (1984) 3039. [15] T.J. Morgan, J. Geddes and H.B. Gilbody, J. Phys. B 6 (1973) 21t8. [ 16] T. Kondow, R.J. Grinius, T.P. Chong and W.L. Fite, Phys. Rev. A 10 (1974) 1167. [ 17] R.E. Olson, T.J. Gay, H.G. Berry, E.B. Hale and V.D. Irby, Phys. Rev. Lett. 59 (1987) 36. [ 18] G. Schiwietzand W. Fritsch, J. Phys. B, to be published.