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The importance of projectile ionisation in studies of forward electron ejection from solid targets
Nuclear Instruments and Methods 194 (1982) 419-422 North-Holland Publishing Company
419
T H E I M P O R T A N C E O F P R O J E C T I L E I O N I S A T I O N IN S T U D I E S O F F O R W A R D E L E C T R O N EJECTION FROM SOLID TARGETS R i c h a r d W. C R A N A G E , Walter S T E C K E L M A C H E R a n d Michael W. L U C A S School of Mathematical and Physical Sciences, Universi(v of Sussex, Falmer, Brighton, Su.s'sex. BN1 OQH, England
The velocity spectra of electrons ejected in the forward direction in ion-atom collisions with gas or solid targets are discussed in terms of charge exchange to the continuum (CEC) and of projectile ionisation. Measurements of the absolute cross sections for electron ejection during H~- (160-985 keV/amu) collisions with hydrogen gas show that projectile ionisation is the dominant source of vc ~vion electrons over this energy range. The cusps observed show a width which is independent of projectile velocity unlike those for CEC. The significance of these results for collisions involving heavy ions and solid targets is discussed.
1. Introduction The presence of a sharp cusp shaped peak in the velocity distribution of electrons ejected when an ion beam traverses a gas or solid target is now well established [1,2]. For a proton, or other fully stripped projectile, interacting with a gas under single collision conditions it is clear that charge exchange to continuum states of the projectile [3,4] must be the mechanism (CEC). The cusps measured under these conditions [5-7] exhibit a width proportional to the projectile velocity as predicted by theory [8] but also show an asymmetry not present in early theories. Higher order terms can be incorporated in the theory to give an asymmetry but it is difficult to do this consistently and this part of the phenomenon is currently of some theoretical interest [9-11]. Suffice it to say that, experimentally, the asymmetry is not an effect confined to high velocity, high Z projectiles. One can also define and measure a cross section for the CEC process and compare this with theory. For protons incident at velocities around vion = 10 a.u. (I a.u. = 2.2 × 10 6 m / s ) the predicted Vio n-l0 dependence of this cross section is just becoming apparent [7,12] although the absolute magnitude of the theoretical and experimental cross sections are often rather different. When heavier ions of comparable or even higher velocity are used [13] to examine both the Zion and vion behaviour the theory is not well obeyed. This is almost certainly due to the high velocity criteria implicit in the theories and in fairness it must be pointed out that the situation is much the same for charge exchange to bound states. Broadly speaking then, existing theories describe the basic process for gas targets but there is much room for improvement particularly at modest impact velocities or when the effective velocity is low because high Z are involved. 0029-554X/82/0000-0000/$02.75 © 1982 North-Holland
For projectiles incident on solid targets the interpretation has been confused by different experimental resuits from different laboratories. Meckbach et al. [14], using protons and carbon foils, measured cusp widths which were not proportional to projectile velocity and this led to suggestions by Brandt and Ritchie [16] and by Meckbach et al. [17] that a different mechanism, wake riding, was responsible for the peak in the case of solid targets. Steckelmacher et al. [15] pointed out that the widths taken in [14] were after subtraction of a background which was included in the charge exchange theory. The comparison between theory and experiment was therefore inconsistent and it was not necessarily true that a separate model was needed to explain the results from solid targets. Steckelmacher et al. showed results for protons on both carbon and gold foils which were consistent with charge exchange theory when the background was included. However at about that time Laubert et al. [6], using high velocity heavy ions and solid targets, again obtained cusps with widths substantially independent of projectile velocity. For these heavy ions the background was small so that its inclusion or subtraction did not markedly affect the interpretation. These results did not agree with either the wake riding or charge exchange prediction and Breinig et al. [25] show clear evidence that the competing mechanism of projectile ionisation or "electron loss to the continuum" is responsible for the cusp in these heavy ion collisions with solids. This mechanism, although well known [18-22], has only recently been studied in detail in the forward direction with gas targets [23-25]. In our earlier work with solids [8] we drew attention to the probable importance of projectile ionisation in situations when an appreciable neutral fraction was formed. Since a solid usually represents a "thick" target from the point of view of atomic collision cross sections a projectile will capture and lose VIII. ELECTRON EMISSION
420
R.W. Cranage et al. / Pr~?jectile ionisation
7.0
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I
i
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I
I
2.0
4.0
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0.0-0.0
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l
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4.0
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8.0
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Fig.'l. Differential cross section for electron ejection into a solid angle of (0. I )2 sr about the forward direction with (a) 160 keV/amu H~ incident on H 2 and (b) 985 keV/amu H~ on H 2. Electron velocity t¥ in atomic units.
electrons many times during its passage through a foil. Hence even an initially bare projectile can arrive near the exit surface of the target carrying one or more electrons with it. If projectile ionisation occurs so close to the exit surface that the electron leaves the solid without being scattered out of the forward direction it will have the same final sate as a continuum electron, i.e. a Coulomb wave centered on the projectile. Cusps produced by this mechanism were clearly seen by Menendez et al. (23) when they compared the effect of bombarding gases with both He + and He 2+ and it now seems that this is the dominant process in studies involving carbon, oxygen and heavier ions with solid targets. This seems very reasonable in that for carbon ions at 1 M e V / a m u the measured equilibrium fractions allow that 80% of the transmitted ions are carrying one or more electrons with them [26].
2. Experiments and discussion To examine the relative importance of projectile ionisation for light ions we measured the absolute cross section for ionisation of H ~ of energy 160-985 k e V / a m u in a target of hydrogen gas. We used the same apparatus as in previous CEC cross section measure-
merits [12]. This apparatus collects electrons ejected forwards into a cone of solid angle (0.1) 2 sr. We show a doubly differential curve for each end of our energy range for the H2+ ~ H 2 collision in figs. la and b. For direct comparison one of the original CEC curves for H ~ - ' H2 is reproduced fig. 2. The residual gas background has been subtracted in all cases and the raw data has been corrected for varying channeltron detector efficiency and spectrometer pass band. The differences are only too apparent. Notice first that the ordinate scales for the H_/ ~ H 2 data show that this signal can be more than ten times the CEC signal. N o w for a solid target one cannot readily measure a cross section so that the data presented has to be "normalised" or in "arbitrary units" and this feature is lost. While it is true that the CEC cusp would have shown up much more clearly at low energies and may even dominate the projectile ionisaton below about 60 k e V / a m u * [27] it is also true that, in the previous study, we found the CEC cusp too small to identify above about 600 keV: a very different situation from the large nearly symmetric peak standing clear of a small back-
* It is likely that the data of fig. la contains a small but significant contribution from CEC
421
R.W. Cranage et al. / Projectile ionisation
3.0
height; the gas target data with all fully stripped projectiles also shows it. The solid target data [6] for oxygen and heavier ions does not show it. Recent experiments [25] using gas targets with beams of partially stripped heavy ions produced a fwhm which at 0.26-+ 0.04 a.u. was independent of ion velocity and of the same value, 0.25-+ 0.02 a.u., as for solid targets in the same apparatus. Our data here for H f ~ H z also show no dependence on ion velocity and a fwhm of 0.65 -+ 0.15 a.u. For our apparatus 00 = 5 × 10 -2 rad. F r o m the experimental point of view then it is clear that one of the major discrepancies between the light and heavy ion data from solids is resolved. There is no difference between gas and solid targets as such but a difference which depends on whether CEC or projectile ionisation dominates the observations. Such a difference is supprising in view of the expectation that the final state wavefunctions are the same. One may now take curves of the type shown in Figs. l a and b and integrate them over some limited velocity range for the purpose of making a direct comparison with CEC. We have done this in fig. 3, restricting the velocity interval to -+ ¼ a.u. either side of the peak. This is quite arbitrary but facilitates a direct comparison with fig. 5 of [12]. We note that these cross sections for forward electron ejection during H ~ ~ H 2 collisions are not only very much larger than the CEC cross section for H + --, H 2 but are much less dependent on energy. For example at 300 k e V / a m u [(o) H f --, H 2 ] / [ ( o ) H---'H2]--~35 while at 500 k e V / a m u the same ratio is nearly 200 so that even with these values we see that the contributions to the electron signal would be equal at a ratio of H~- to H + in the projectile
2.0-
do' x1(~ecmsec
dye
1.0
O.O
l
0.0
l
2.0
I
4.0
6.0
8.0
ve Fig. 2. As fig. 1 but for 367 keV/amu H + onto H 2.
ground in fig. lb. Indeed the peak of fig. lb bears a strong similarity to much of the data obtained from carbon and heavier ions with solid targets. The skewness, raising the low velocity wing, is present in all our curves for H2 ~ --, H 2 but is less marked than in our pure C E C data. For these light projectiles (H~-, He +) and gas targets the skewness so far as it is identifiable, is in the same sense for both projectile ionisation and CEC [28]. It could, of course, be the small underlying contribution of CEC that is responsible for the skewness in all cases. In the past much has been made of the failure of some of the data obtained from solid targets to show the simple relationship. (Ave)fwhm---- a2vion 00 predicted in our early theory [8]. Our p r o t o n - s o l i d data has always shown this relationship provided the direct ionisation background was included in the measurement of
5,0
~E
I
I
]
I
I
I
I
I
I
I 0,2
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I 0.6
I
I 0.8
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--
4.0--
'2 x g
3,0--
~
2.0--
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1.0-0.0 0.0
Impact Energy x103keVlamu Fig. 3. Cross secuon for electron ejection in H ~-~ H 2 collisions into (0. I)2 sr about the forward direction and integrated over electron velocities ] a.u. either side of the peaks. The error bars do not include systematic errors. VIII. ELECTRON EMISSION
422
R. W. Cranage et al. / Pro/ectile ionis'ation
b e a m of a b o u t 3% and 0.5%, respectively. Of course we are not concerned with H ~ itself since it will not survive passage through a foil in sufficient fraction b u t w h e n we extend these arguments to c a r b o n ions, a b o u t 80% of which m a y not be fully stripped and hence able to suffer ionisation, it is clear that the electrons from projectile ionisation must massively d o m i n a t e any signal from CEC electrons. Finally there is the interesting question of the relation of these projectile ionisation cross sections to theory. The data giving rise to fig. 3 can be integrated over slightly wider velocity limits so that it can be plotted with our He + ~ He d a t a o n fig. 1 of Briggs a n d D r e p p e r [29]. The effect of these increased velocity limits is to raise each p o i n t on fig. 3 by a b o u t 20%. Reference to the Briggs a n d D r e p p e r p a p e r then shows that near the higher i m p a c t energies our data will agree well with their predictions as did our He + ~ He data. It therefore appears that their theory gives reasonable values for the cross-section for b o t h H f and He ~ impact. This, in spite of the fact that implicit in their theory is the expectation that the cusp widths should increase with ion velocity in the same way as CEC cusps, a feature not actually b o r n out by the experiment. Breinig et al. [25] recognise that the Born criterion is only marginally satisfied for their heavy ions b u t such a n explanation is not so easily sustained for our results a n d it seems to us that this difficulty merits further study. In fact it is k n o w n that only two r a t h e r simple a s s u m p t i o n s are needed to provide a cusp whose width increases with projectile velocity. These are (a) that the ejection is isotropic in the projectile frame and (b) that the flux is inversely p r o p o r t i o n a l to the electron velocity again in the projectile frame. Variations on the former have recently been examined by D a y [30] a n d by Briggs a n d Day [31] with some success. This work was s u p p o r t e d by the Science Research Council. We are grateful to Messrs. Farmery, Hole a n d Priestley for their c o n t i n u e d technical support.
References [1] C.B. Crooks and M.E. Rudd, Phys. Rev. Lett. 25 (1970) 1599. [2] K.G. Harrison and M.W. gucas, Phys. Lett. 33A (1970) 142.
[3] A. Salin, J. Phys. B2 (1969) 631: J. Phys. B2 (1969) 1255: J. Phys. B5 (1972) 979. [4] J. Macek, Phys. Rev. AI (1970) 235. [5] K.C.R. Chiu, J. W m McGowan and J.B.A. Mitchell, J. Phys. BII (1978)L 117. [61 R. Laubert, I.A. Sellin, C.R. Vane, S.B. Elston, G.D. Alton and R.S. Thoe, Phys. Rev. Left. 41 (1978) 712. [7] M. Rgdbro and F.D. Andersen, J. Phys. B12 (1979) 2883. [8] K. Dettmann, KG. Harrison and M.W. Lucas, J. Phys. B7 (1974) 269. [9] R. Shakeshaft and L. Spruch, Phys. Rev. Lett. 41 (1978) 1037: Phys, Rev. A20 (1979) 376. [10] F.T. Chan and J. Eichler, Phys. Rev. AI9 (1979) 367. [I 1] C.R. Garibotti and J.E. Miraglia, J. Phys. BI4 (1981) 863. [12] R.W. Cranage and M.W. Lucas, J. Phys. B9 (1976) 445. [13] C.R. Vane, I.A. Sellin. M. Sutter. (i.D. Alton, P.M. Griffin and R.S. Thoe, Phys. Rev. Lett. 40 (1978) 1020. [14] W. Menckbach, K.C.R. Chiu, H.H. Brongersma and J. Wm. McGowan, J. Phys. BI0 (1977) 3255. [I 5] W. Steckelmacher, R. Strong, M.N. Khan and M.W. Lucas, J. Phys. BI1 (1978) 2711: see also K.C.R. Chiu, W. Meckbach, G. Sanchez Sarmiento and J. Win. McGowan, J. Phys. BI2 (1979) L 147 and W. Steckelmacher and M.W. Lucas, J. Phys. BI2 (1979) L 152. [16] W. Brandt and R.H. Ritchie, Phys. Lett. 62A (1977) 374. [17] W. Meckbach, N. Arista and W. Brandt, Phys. Lett. 65A (1978) 113. [18] W.E. Wilson and L.M. Toburen, Phys. Rev. A7 (1973) 1535. [19] D. Burch, H. Wieman and W.B. Ingalls, Phys. Rev. Lett. 30 (1973) 823. [20] N. Stolterfoht, D. Schneider, D. Burch, H. Wieman and J.S. Risley, Phys. Rev. Lett. 33 (1974) 59. [21] M.E. Rudd, J.S. Risley, J. F ~ a r and R.G. Rolfes, Phys. Rev. A21 (1980) 506. [22] F. Drepper and J.S. Briggs, J. Phys. B9 (1976) 2063. [23] M.G. Menendez, M.M. Duncan, F.L. Eisele, B.R. Junker, Phys. Rev. AI5 (1977) 80. [24] M.M. Duncan and M.G. Menendez, Phys. Rev. AI6 (1977) 1799: Phys. Rev. AI9 (1979) 49: Phys. Rev. A23 (1981) 1085. [25] M. Breinig, M.M. Schauer, I.A. Sellin, S.B. Elston, C.R. Vane, R.S. Thoe and M. Suter,. Phys. BI4 (1981) L 291. [26] N.E.B. Cowern, Atomic Energy Research Establishment, tfarwell, Report AERE R 9500 (August 1979). [27] R. Shakeshaft, Phys. Re,,'. AI8 (1978) 1930. [28] S.B. Elston, I.A. Sellin, M. Breinig, S. Huldt, L. Liljcby, R.S. Thoe, S. Datz, S. Overbury and R. Laubert, Phys. Rev. Lett. 46 (1981) 321. [29] J.S. Briggs and F. Drepper, J. Phys. BII (1978)4033. [301 M.H. Day. J. Phys. BI3 (1980) L 65. [31] J.S. Briggs and M.H. Day, J. Phys. BI3 (1980) 4797.
419
T H E I M P O R T A N C E O F P R O J E C T I L E I O N I S A T I O N IN S T U D I E S O F F O R W A R D E L E C T R O N EJECTION FROM SOLID TARGETS R i c h a r d W. C R A N A G E , Walter S T E C K E L M A C H E R a n d Michael W. L U C A S School of Mathematical and Physical Sciences, Universi(v of Sussex, Falmer, Brighton, Su.s'sex. BN1 OQH, England
The velocity spectra of electrons ejected in the forward direction in ion-atom collisions with gas or solid targets are discussed in terms of charge exchange to the continuum (CEC) and of projectile ionisation. Measurements of the absolute cross sections for electron ejection during H~- (160-985 keV/amu) collisions with hydrogen gas show that projectile ionisation is the dominant source of vc ~vion electrons over this energy range. The cusps observed show a width which is independent of projectile velocity unlike those for CEC. The significance of these results for collisions involving heavy ions and solid targets is discussed.
1. Introduction The presence of a sharp cusp shaped peak in the velocity distribution of electrons ejected when an ion beam traverses a gas or solid target is now well established [1,2]. For a proton, or other fully stripped projectile, interacting with a gas under single collision conditions it is clear that charge exchange to continuum states of the projectile [3,4] must be the mechanism (CEC). The cusps measured under these conditions [5-7] exhibit a width proportional to the projectile velocity as predicted by theory [8] but also show an asymmetry not present in early theories. Higher order terms can be incorporated in the theory to give an asymmetry but it is difficult to do this consistently and this part of the phenomenon is currently of some theoretical interest [9-11]. Suffice it to say that, experimentally, the asymmetry is not an effect confined to high velocity, high Z projectiles. One can also define and measure a cross section for the CEC process and compare this with theory. For protons incident at velocities around vion = 10 a.u. (I a.u. = 2.2 × 10 6 m / s ) the predicted Vio n-l0 dependence of this cross section is just becoming apparent [7,12] although the absolute magnitude of the theoretical and experimental cross sections are often rather different. When heavier ions of comparable or even higher velocity are used [13] to examine both the Zion and vion behaviour the theory is not well obeyed. This is almost certainly due to the high velocity criteria implicit in the theories and in fairness it must be pointed out that the situation is much the same for charge exchange to bound states. Broadly speaking then, existing theories describe the basic process for gas targets but there is much room for improvement particularly at modest impact velocities or when the effective velocity is low because high Z are involved. 0029-554X/82/0000-0000/$02.75 © 1982 North-Holland
For projectiles incident on solid targets the interpretation has been confused by different experimental resuits from different laboratories. Meckbach et al. [14], using protons and carbon foils, measured cusp widths which were not proportional to projectile velocity and this led to suggestions by Brandt and Ritchie [16] and by Meckbach et al. [17] that a different mechanism, wake riding, was responsible for the peak in the case of solid targets. Steckelmacher et al. [15] pointed out that the widths taken in [14] were after subtraction of a background which was included in the charge exchange theory. The comparison between theory and experiment was therefore inconsistent and it was not necessarily true that a separate model was needed to explain the results from solid targets. Steckelmacher et al. showed results for protons on both carbon and gold foils which were consistent with charge exchange theory when the background was included. However at about that time Laubert et al. [6], using high velocity heavy ions and solid targets, again obtained cusps with widths substantially independent of projectile velocity. For these heavy ions the background was small so that its inclusion or subtraction did not markedly affect the interpretation. These results did not agree with either the wake riding or charge exchange prediction and Breinig et al. [25] show clear evidence that the competing mechanism of projectile ionisation or "electron loss to the continuum" is responsible for the cusp in these heavy ion collisions with solids. This mechanism, although well known [18-22], has only recently been studied in detail in the forward direction with gas targets [23-25]. In our earlier work with solids [8] we drew attention to the probable importance of projectile ionisation in situations when an appreciable neutral fraction was formed. Since a solid usually represents a "thick" target from the point of view of atomic collision cross sections a projectile will capture and lose VIII. ELECTRON EMISSION
420
R.W. Cranage et al. / Pr~?jectile ionisation
7.0
f
I
I
i
]
a
I
I
I
2.0
4.0
6.0
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0.0-0.0
l
l
2.0
4.0
__l
6.0
I
I.~
8.0
0.0
v,
80
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Fig.'l. Differential cross section for electron ejection into a solid angle of (0. I )2 sr about the forward direction with (a) 160 keV/amu H~ incident on H 2 and (b) 985 keV/amu H~ on H 2. Electron velocity t¥ in atomic units.
electrons many times during its passage through a foil. Hence even an initially bare projectile can arrive near the exit surface of the target carrying one or more electrons with it. If projectile ionisation occurs so close to the exit surface that the electron leaves the solid without being scattered out of the forward direction it will have the same final sate as a continuum electron, i.e. a Coulomb wave centered on the projectile. Cusps produced by this mechanism were clearly seen by Menendez et al. (23) when they compared the effect of bombarding gases with both He + and He 2+ and it now seems that this is the dominant process in studies involving carbon, oxygen and heavier ions with solid targets. This seems very reasonable in that for carbon ions at 1 M e V / a m u the measured equilibrium fractions allow that 80% of the transmitted ions are carrying one or more electrons with them [26].
2. Experiments and discussion To examine the relative importance of projectile ionisation for light ions we measured the absolute cross section for ionisation of H ~ of energy 160-985 k e V / a m u in a target of hydrogen gas. We used the same apparatus as in previous CEC cross section measure-
merits [12]. This apparatus collects electrons ejected forwards into a cone of solid angle (0.1) 2 sr. We show a doubly differential curve for each end of our energy range for the H2+ ~ H 2 collision in figs. la and b. For direct comparison one of the original CEC curves for H ~ - ' H2 is reproduced fig. 2. The residual gas background has been subtracted in all cases and the raw data has been corrected for varying channeltron detector efficiency and spectrometer pass band. The differences are only too apparent. Notice first that the ordinate scales for the H_/ ~ H 2 data show that this signal can be more than ten times the CEC signal. N o w for a solid target one cannot readily measure a cross section so that the data presented has to be "normalised" or in "arbitrary units" and this feature is lost. While it is true that the CEC cusp would have shown up much more clearly at low energies and may even dominate the projectile ionisaton below about 60 k e V / a m u * [27] it is also true that, in the previous study, we found the CEC cusp too small to identify above about 600 keV: a very different situation from the large nearly symmetric peak standing clear of a small back-
* It is likely that the data of fig. la contains a small but significant contribution from CEC
421
R.W. Cranage et al. / Projectile ionisation
3.0
height; the gas target data with all fully stripped projectiles also shows it. The solid target data [6] for oxygen and heavier ions does not show it. Recent experiments [25] using gas targets with beams of partially stripped heavy ions produced a fwhm which at 0.26-+ 0.04 a.u. was independent of ion velocity and of the same value, 0.25-+ 0.02 a.u., as for solid targets in the same apparatus. Our data here for H f ~ H z also show no dependence on ion velocity and a fwhm of 0.65 -+ 0.15 a.u. For our apparatus 00 = 5 × 10 -2 rad. F r o m the experimental point of view then it is clear that one of the major discrepancies between the light and heavy ion data from solids is resolved. There is no difference between gas and solid targets as such but a difference which depends on whether CEC or projectile ionisation dominates the observations. Such a difference is supprising in view of the expectation that the final state wavefunctions are the same. One may now take curves of the type shown in Figs. l a and b and integrate them over some limited velocity range for the purpose of making a direct comparison with CEC. We have done this in fig. 3, restricting the velocity interval to -+ ¼ a.u. either side of the peak. This is quite arbitrary but facilitates a direct comparison with fig. 5 of [12]. We note that these cross sections for forward electron ejection during H ~ ~ H 2 collisions are not only very much larger than the CEC cross section for H + --, H 2 but are much less dependent on energy. For example at 300 k e V / a m u [(o) H f --, H 2 ] / [ ( o ) H---'H2]--~35 while at 500 k e V / a m u the same ratio is nearly 200 so that even with these values we see that the contributions to the electron signal would be equal at a ratio of H~- to H + in the projectile
2.0-
do' x1(~ecmsec
dye
1.0
O.O
l
0.0
l
2.0
I
4.0
6.0
8.0
ve Fig. 2. As fig. 1 but for 367 keV/amu H + onto H 2.
ground in fig. lb. Indeed the peak of fig. lb bears a strong similarity to much of the data obtained from carbon and heavier ions with solid targets. The skewness, raising the low velocity wing, is present in all our curves for H2 ~ --, H 2 but is less marked than in our pure C E C data. For these light projectiles (H~-, He +) and gas targets the skewness so far as it is identifiable, is in the same sense for both projectile ionisation and CEC [28]. It could, of course, be the small underlying contribution of CEC that is responsible for the skewness in all cases. In the past much has been made of the failure of some of the data obtained from solid targets to show the simple relationship. (Ave)fwhm---- a2vion 00 predicted in our early theory [8]. Our p r o t o n - s o l i d data has always shown this relationship provided the direct ionisation background was included in the measurement of
5,0
~E
I
I
]
I
I
I
I
I
I
I 0,2
I
I 40
I
I 0.6
I
I 0.8
I
I 1.0
--
4.0--
'2 x g
3,0--
~
2.0--
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1.0-0.0 0.0
Impact Energy x103keVlamu Fig. 3. Cross secuon for electron ejection in H ~-~ H 2 collisions into (0. I)2 sr about the forward direction and integrated over electron velocities ] a.u. either side of the peaks. The error bars do not include systematic errors. VIII. ELECTRON EMISSION
422
R. W. Cranage et al. / Pro/ectile ionis'ation
b e a m of a b o u t 3% and 0.5%, respectively. Of course we are not concerned with H ~ itself since it will not survive passage through a foil in sufficient fraction b u t w h e n we extend these arguments to c a r b o n ions, a b o u t 80% of which m a y not be fully stripped and hence able to suffer ionisation, it is clear that the electrons from projectile ionisation must massively d o m i n a t e any signal from CEC electrons. Finally there is the interesting question of the relation of these projectile ionisation cross sections to theory. The data giving rise to fig. 3 can be integrated over slightly wider velocity limits so that it can be plotted with our He + ~ He d a t a o n fig. 1 of Briggs a n d D r e p p e r [29]. The effect of these increased velocity limits is to raise each p o i n t on fig. 3 by a b o u t 20%. Reference to the Briggs a n d D r e p p e r p a p e r then shows that near the higher i m p a c t energies our data will agree well with their predictions as did our He + ~ He data. It therefore appears that their theory gives reasonable values for the cross-section for b o t h H f and He ~ impact. This, in spite of the fact that implicit in their theory is the expectation that the cusp widths should increase with ion velocity in the same way as CEC cusps, a feature not actually b o r n out by the experiment. Breinig et al. [25] recognise that the Born criterion is only marginally satisfied for their heavy ions b u t such a n explanation is not so easily sustained for our results a n d it seems to us that this difficulty merits further study. In fact it is k n o w n that only two r a t h e r simple a s s u m p t i o n s are needed to provide a cusp whose width increases with projectile velocity. These are (a) that the ejection is isotropic in the projectile frame and (b) that the flux is inversely p r o p o r t i o n a l to the electron velocity again in the projectile frame. Variations on the former have recently been examined by D a y [30] a n d by Briggs a n d Day [31] with some success. This work was s u p p o r t e d by the Science Research Council. We are grateful to Messrs. Farmery, Hole a n d Priestley for their c o n t i n u e d technical support.
References [1] C.B. Crooks and M.E. Rudd, Phys. Rev. Lett. 25 (1970) 1599. [2] K.G. Harrison and M.W. gucas, Phys. Lett. 33A (1970) 142.
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