- Email: [email protected]
Angular distributions of slow multiply charged ions following capture
Nuclear Instruments and Methods in Physics Research B24/25 (1987) 97-100 North-Holland, Amsterdam
97
ANGULAR DISTRIBUTIONS OF SLOW MULTIPLY CHARGED IONS FOLLOWING CAPTURE
COCKE, L.N. TUNNELL, and J.O.K. PEDERSEN
CL.
J. R. Maedonald Laboratoq
W. WAGGONER,
Physics Qepartmeni,
J.P. GIESE, S.L. VARGHESE
*, E.Y. KAMBER
Kansas State University, Manhattan, KS 66.706, USA
When slow, multiply charged projectiles capture electrons from neutral targets, the angular distributions of the capturing particles are much more sensitive to the potential curves involved than are the total cross sections. We have constructed an apparatus suitable for measuring angular dist~butions of these capture products. A position sensitive channel plate chevron followed by a resistive anode is used to determine the scattering angle and a simple retarding grid system is used to select the final charge states. Multiply charged projectiles are obtained from recoil ion sources pumped by fast ion beams from the KSU tandem accelerator. Systems studied include Ne4+, C4+ and Arq+, with 4 lying between 3 and 8, on targets of He, D, and Ar at accelerating voltages between 40 and 350 V. Selected cases will be presented and discussed,
In recent years a great deal of experimental and theoretical work has appeared in the literature on the subject of capture of electrons from neutral targets from multiply charged projectiles [l]. At low velocities, the collision can be described in terms of time dependent curve-crossing pictures for which the nuclear motion is taken to follow classical trajectories while the electronic motion is treated quantum mechanically. While such treatments have had many successes in describing the capture process, it has become clear that much of the data on total cross sections and even state-selective capture do not really test in a very detailed way either the form of the treatment or the potential curves involved. This is the case because the matrix elements which couple the incident channel to the final one(s) increase so rapidly with decreasing internuclear distance that both the total cross section and the “reaction window” which determines the states which are fed are nearly determined geometrically, independent of the exact form of the coupling or the potential curves. The angle through which the projectile is scattered is, on the other hand, rather sensitive to the potential curve history experienced by the heavy particle throughout the entire collision, and thus angular dist~bution measurements stand to provide information on the reaction process not otherwise available. For the past few years we have been working on angular distributions for low energy capture by multiply charged projectiles, concentrating on initial charges sufficiently large that the capture goes into orbits entirely vacant on the projectile core. This paper summarizes some of our results.
* Permanent address: University of South Alabama, Mobile, AL, USA. 0168-583X/87/$03.50 0 Ekwier Science Pubfishers B.V. (North-Hol~~d Physics Publishing Division)
The apparatus we use is shown in fig. 1. For most experiments, the ions are created in a secondary ion recoil source pumped by a fast ion beam from the KSU tandem. This source, while having low intensities, produces a high quality beam such that even after severe angular collimation a rather good resolution in Et? (= T) product is obtained, where E and 6 are the laboratory energy and scattering angle, respectively. The ion charge state is magnetically selected and directed onto a 2.5 cm long ‘gas cell, exiting therefrom to a charmel plate assembly equipped with a one-dimensional resistive anode encoder. Since the angular distri-
PUMPBEAt$ -__ ---_-_
position
sensitive
anode
Fig. 1. Schematic of apparatus. I. ATOMIC PHYSICS / RELATJZD PHENOMENA
C. L. Cacke et ul. / Angulur distributions
98
bution has cylindrical symmetry about the beam axis, a bow-tie shaped collimator is used to project the distribution onto the position sensitive axis of the resistive anode. The half-tie angle is 22.5”, which means that the projection operation incurs only a 2.8% loss in radial resolution on the average. The apparatus records directly da/d6 rather than da/da. The collimators were set for the experiments discussed here so that the overall angular resolution of the system was typically 4.5 mrad FWHM.
Deflection function -
I.01 0.0
I
5.0
T
3. Results We select here two cases to present. Since we have discussed these in terms of semi-classical curve-crossing models, we summarize first the general features of this model as we have used it. The typical curve crossing situation for capture by a highly charged projectile from a neutral target involves an active crossing between an incident channel whose potential curve is nearly indepent of the internuclear distance R, since the target is neutral, and the exit channel which follows a nearly Coulomb potential curve because both systems bear charge. A sample of such a situation is shown in fig. 2 for Ne4+ on He, where the active crossing is with the 3s capture channel. A semi-classical treatment of the inelastic collision process in which only these two channels are considered can be done within the localized crossing approximation by calculating the classical deflection functions for scattering of the projectile along two paths leading to the final capture channel: the first path corresponds to capture on the way in, with adiabatic behavior at the crossing on the way in and diabatic behavior on the way out, and the second path involves diabatic behavior on the way in and adiabatic behavior on the way out. These potential histories produce two branches on the classical deflection function B(h), where b is the impact parameter. The first path produces larger scattering angles, or the upper branch of 6(b), and the second, the lower branch. The branches meet at a critical angle 6,, which is the scattering angle corresponding to b equal to the crossing radius R , and
05 -10 00
0 IO
-0.5 5
KJ
xt
R
5olmm5com
(a.u.1
Fig. 2. Energy level schematic
for Ne“+ on He.
1
15.0
t
20.0
I
I
25.0
30.0
( eV - rad 1
Fig. 3. Deflection functions for various model potentials Ne4+ on He. See text for description of models A-C.
for
which for small angles is given by the surprisingly simple and general expression 0, = Q/2 E, where Q is the exoergicity of the collision. If the incoming curve is flat right in to R = 0, then the lower branch of 19(b) decreases monotonically to zero at zero b (label C on fig. 3), and interference between scatterings along the two branches does not occur since only one b contributes to a given 0. In real life, the incoming potential is always promoted either by interaction with other more exoergic capture channels or by electron cloud interpenetrations, the lower branch of B(b) is promoted at small b and 8(b) becomes double values at a given @ and displays a rainbow at some minimum angle 8, (label A on fig. 3). Stuckelberg oscillations can then be seen due to interference between the two branches. The relative phase of the two amplitudes can be shown [2] to be proportional to the area enclosed by B(b) between the rainbow angle and the angle of observation. Thus once the deflection function is known, the location of all major features of the angular distribution can be calculated, including location of 0, and the frequency of Stuckelberg oscillations. Olson and Smith [3] describe in detail how this formalism can be coupled with a Landau-Zener treatment of the transition probability to yield differential cross sections. 3.1. Ne*+
2
I
10.0
on He
From ref. [4] we know the main population is of a 3s orbit on the projectile core. The measured angular distributions for Ne4+ on He are shown in fig. 4, plotted as a function r, which is a function of b but not of E for small angles. The critical angle 0, is shown also and it is immediately seen that much of the distribution lies inside 8,. This behavior is characteristic of cases where the incoming channel is not strongly promoted inside the crossing radius, as is the case when the active crossing populates an n s orbit on the projectile. In such a case the next crossing inside R, is with the next lower
C. L. Cocke et al. / An&w
n, and lies so far in that it plays little role in the collision. Thus the lower branch of B(b) extends in to very small scattering angles and small 6. In fig. 3 we show an example of a calculated deflection function (A) for Ne4+ on Ne, for which a screened Coulomb potential was used to represent the incoming channel and a pure Coulomb potential was used for the outgoing channel. The rainbow angle is so far forward that is is nearly unresolvable from O* in the experiment, and we believe this is the reason why the experiment shows such forward peaking this case. The model calulation for da/d@ is not so forward peaked as the experiment, however, raising the question as to whether or not the semi-classical treatment is adequate. We note that this extreme forward peaking is the exception rather than the rule. In most other cases we have studied, such as Ne5’, Ne6+, N6+, 06+, and F6+ on He, the forward peaking does not occur. These are cases where the primary population is of 31, I > 0, for which the incoming channel is strongly promoted by interaction with nearby lower capture channels, and the corresponding
Ne+4+ He SINGLE CAPTURE
.6
E=BOeV
.6
E=220eV
E = 172 eV
t_
0
IO T
20
30
40
feV-rod)
Fig. 4. Ekperimental angular distributions for Ne4+ on He. The locations of rainbow angles and first interference maxima for model B are indicated by filled and open arrow heads, respectively. 0, is indicated by a dashed arrow.
99
deflection functions have rainbows at very finite and observable scattering angles. The apparent oscillations at r = 4.5 and about 8 eV rad look Stucketberg-like, but all attempts to interpret them in terms of the areas enclosed by the deflection function A fail. This deflection function is so open that the oscillation frequency is too high to be resolved experimentally. We believe that these features arise from the tree-ch~el nature of the problem. There are really two 3s states fed, the *P and 4P formed on the 3P projectile core, and the energy gain spectra from which these final state populations are deduced do not resolve them. We believe that the oscillation comes from interference between two amplitudes leading to the less exoergic ‘P pupation. Considering only the *P final state, the two interfering paths are those discussed above, except that the incoming chmel behaves adiabatically at the crossing with the 4P state, and is thus promoted strongly, leading to a lower branch on B(b) which is much closer to the upper one (model B in fig. 3). We have done a two-state calculation for this case, including only the 2P and “promoted 4P’7 incoming curves, and have shown the resulting locations of the rainbow angle and maximum of the first Stuckelberg oscillation on fig. 4. The agreement with the data is good. It is interesting to note that to observe the participation of both of these 3s channels would have required extremely high energy resolution in an energy gain spectrum, but the presence of both gives an obvious feature in the angular distributions. 3.2. A+
E= 284eV
.6
distributions
on Ar
Pig. 5 shows angular distributions for single capture bY Ar sc from H,. The upper part of this figure shows the energy gain spectrum for this case [S], where we may identify two major processes. The normal single capture (SC) populates primarily Sf and 5d states, with a little 6s. In addition there is substantial population of TI channels, which correspond here to the population by double capture of autoionizing states which emit electrons before detection and thus appear to have only single-captured. In the angular distribution measurements, we do not resolve energetically these two channels. It would be tempting to try to interpret the structure seen in fig. 5 in terms of Stuckelberg interference again However, the presence of two rather distinct processes in the energy gain spectrum led us to try to ascertain whether the two peaks could correspond to these two processes. In order to do this, we used the retarding grid shown in fig.1 as a crude energy analyzer and measured, for Ar*” on Ar, angular dist~butions for SC and TI separately. The energy resolution is poor but just adequate to be able to separately record angular distributions for the two energy-gain groups. We used I. ATOMIC
PHYSICS
/ RELATED
PHENOMENA
C. L. Co&
0
IO
20
ENERGY
30 GAIN
40
50
et 01. / Angulur distributions
60
(EV)
have modeled this case by taking the incident channel to be flat until it is promoted by an adiabatic crossing with the Sp state which is not populated but which should serve as the promotor as discussed above. The predicted mid point on the rise of the angular distribution is indicated by an open arrow in fig. 5. Since this is well inside the observed threshold angle, we also consider that TI might go by a two-step process, whereby two successive crossings, each involving a single electron transfer, occur. In this case, this would mean crossing to the Sdf channel on the way in, and then from this “incident” channel to the TI channel either on the way in or the way out. In fact, the two crossings occur nearly at the same location in R but can be considered as sequential for the model. The resulting model calculation shows a threshold behavior whose mid-rise point is indicated by a solid arrow on fig. 5. It is in much better agreement with the data, and indicates that TI is better throught of as two single electron transfers than by a single two-electron transfer. This is certainly a reasonable result, since the two-electron matrix element is expected to be much weaker than that for single electron transfer. A very similar conclusion on the TI mechanism was reached by Roncin et al. [6].
4. Summary
Ai’
+ Ar
T.I.
vacc = 166 v
8
(mradl
Fig. 5. Experimental angular distributions for Ars+ on (a) D, and H, and (b) Ar. The top figure shows the energy gain spectrum for D2. The open and filled arrow heads indicate threshold angles predicted for single-step and double-step TI. respectively, and the dashed arrows indicate 0,.
Ar instead of D, or H, here to avoid any complications due to kinematic shifts, since we had previously determined that the three targets yield nearly the same energy gain spectra. The results are clear: the forward peak is due to SC while the second peak is due to TI, and has nothing to do with interference structure. One can learn something about the nature of the TI mechanism from the location of the maximum in its angular distribution. If the two-electron transition goes in a single step, that is at the single crossing between the incident channel and the TI channel, then there will be a lower branch of B(b) which extends to small 8. We
We have presented two examples of experimental studies of angular distributions for capture from neutral targets by multi-charged projectiles which reveal surprises and features which total cross sections and energy-gain spectra conceal. Although some qualitative understanding of these results is claimed, many questions remain to be answered, with even major features in the angular distributions lacking quantitative understanding. It is demonstrated that usuful information concerning reaction mechanisms can be gained from such angular distributions. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, US Department of Energy.
References [l] R.K. Janev and H. Winter, Phys. Rep. 117 (1985) 265; R.K. Janev, Comm. Atomic Mol. Phys. 12 (1983) 277. [2] K.W. Ford and J.A. Wheeler, Ann. Phys. (NY) 7 (1959) 259. [3] C. Schmeissner. CL. Cocke, R. Mann and W. Meyerhof, Phys. Rev. A30 (1984) 1661. [4] R.E. Olson and F.T. Smith, Phys. Rev. A3 (1971) 1607. [5] J.P. Giese. CL. Cocke, W. Waggoner, S.L. Varghese and L.N. Tunnell, Phys. Rev. A, to be published. [6] P. Roncin, M.N. Gaboriaud. M. Barat and H. Laurent, Europhys. Lett. 1 (1986).
97
ANGULAR DISTRIBUTIONS OF SLOW MULTIPLY CHARGED IONS FOLLOWING CAPTURE
COCKE, L.N. TUNNELL, and J.O.K. PEDERSEN
CL.
J. R. Maedonald Laboratoq
W. WAGGONER,
Physics Qepartmeni,
J.P. GIESE, S.L. VARGHESE
*, E.Y. KAMBER
Kansas State University, Manhattan, KS 66.706, USA
When slow, multiply charged projectiles capture electrons from neutral targets, the angular distributions of the capturing particles are much more sensitive to the potential curves involved than are the total cross sections. We have constructed an apparatus suitable for measuring angular dist~butions of these capture products. A position sensitive channel plate chevron followed by a resistive anode is used to determine the scattering angle and a simple retarding grid system is used to select the final charge states. Multiply charged projectiles are obtained from recoil ion sources pumped by fast ion beams from the KSU tandem accelerator. Systems studied include Ne4+, C4+ and Arq+, with 4 lying between 3 and 8, on targets of He, D, and Ar at accelerating voltages between 40 and 350 V. Selected cases will be presented and discussed,
In recent years a great deal of experimental and theoretical work has appeared in the literature on the subject of capture of electrons from neutral targets from multiply charged projectiles [l]. At low velocities, the collision can be described in terms of time dependent curve-crossing pictures for which the nuclear motion is taken to follow classical trajectories while the electronic motion is treated quantum mechanically. While such treatments have had many successes in describing the capture process, it has become clear that much of the data on total cross sections and even state-selective capture do not really test in a very detailed way either the form of the treatment or the potential curves involved. This is the case because the matrix elements which couple the incident channel to the final one(s) increase so rapidly with decreasing internuclear distance that both the total cross section and the “reaction window” which determines the states which are fed are nearly determined geometrically, independent of the exact form of the coupling or the potential curves. The angle through which the projectile is scattered is, on the other hand, rather sensitive to the potential curve history experienced by the heavy particle throughout the entire collision, and thus angular dist~bution measurements stand to provide information on the reaction process not otherwise available. For the past few years we have been working on angular distributions for low energy capture by multiply charged projectiles, concentrating on initial charges sufficiently large that the capture goes into orbits entirely vacant on the projectile core. This paper summarizes some of our results.
* Permanent address: University of South Alabama, Mobile, AL, USA. 0168-583X/87/$03.50 0 Ekwier Science Pubfishers B.V. (North-Hol~~d Physics Publishing Division)
The apparatus we use is shown in fig. 1. For most experiments, the ions are created in a secondary ion recoil source pumped by a fast ion beam from the KSU tandem. This source, while having low intensities, produces a high quality beam such that even after severe angular collimation a rather good resolution in Et? (= T) product is obtained, where E and 6 are the laboratory energy and scattering angle, respectively. The ion charge state is magnetically selected and directed onto a 2.5 cm long ‘gas cell, exiting therefrom to a charmel plate assembly equipped with a one-dimensional resistive anode encoder. Since the angular distri-
PUMPBEAt$ -__ ---_-_
position
sensitive
anode
Fig. 1. Schematic of apparatus. I. ATOMIC PHYSICS / RELATJZD PHENOMENA
C. L. Cacke et ul. / Angulur distributions
98
bution has cylindrical symmetry about the beam axis, a bow-tie shaped collimator is used to project the distribution onto the position sensitive axis of the resistive anode. The half-tie angle is 22.5”, which means that the projection operation incurs only a 2.8% loss in radial resolution on the average. The apparatus records directly da/d6 rather than da/da. The collimators were set for the experiments discussed here so that the overall angular resolution of the system was typically 4.5 mrad FWHM.
Deflection function -
I.01 0.0
I
5.0
T
3. Results We select here two cases to present. Since we have discussed these in terms of semi-classical curve-crossing models, we summarize first the general features of this model as we have used it. The typical curve crossing situation for capture by a highly charged projectile from a neutral target involves an active crossing between an incident channel whose potential curve is nearly indepent of the internuclear distance R, since the target is neutral, and the exit channel which follows a nearly Coulomb potential curve because both systems bear charge. A sample of such a situation is shown in fig. 2 for Ne4+ on He, where the active crossing is with the 3s capture channel. A semi-classical treatment of the inelastic collision process in which only these two channels are considered can be done within the localized crossing approximation by calculating the classical deflection functions for scattering of the projectile along two paths leading to the final capture channel: the first path corresponds to capture on the way in, with adiabatic behavior at the crossing on the way in and diabatic behavior on the way out, and the second path involves diabatic behavior on the way in and adiabatic behavior on the way out. These potential histories produce two branches on the classical deflection function B(h), where b is the impact parameter. The first path produces larger scattering angles, or the upper branch of 6(b), and the second, the lower branch. The branches meet at a critical angle 6,, which is the scattering angle corresponding to b equal to the crossing radius R , and
05 -10 00
0 IO
-0.5 5
KJ
xt
R
5olmm5com
(a.u.1
Fig. 2. Energy level schematic
for Ne“+ on He.
1
15.0
t
20.0
I
I
25.0
30.0
( eV - rad 1
Fig. 3. Deflection functions for various model potentials Ne4+ on He. See text for description of models A-C.
for
which for small angles is given by the surprisingly simple and general expression 0, = Q/2 E, where Q is the exoergicity of the collision. If the incoming curve is flat right in to R = 0, then the lower branch of 19(b) decreases monotonically to zero at zero b (label C on fig. 3), and interference between scatterings along the two branches does not occur since only one b contributes to a given 0. In real life, the incoming potential is always promoted either by interaction with other more exoergic capture channels or by electron cloud interpenetrations, the lower branch of B(b) is promoted at small b and 8(b) becomes double values at a given @ and displays a rainbow at some minimum angle 8, (label A on fig. 3). Stuckelberg oscillations can then be seen due to interference between the two branches. The relative phase of the two amplitudes can be shown [2] to be proportional to the area enclosed by B(b) between the rainbow angle and the angle of observation. Thus once the deflection function is known, the location of all major features of the angular distribution can be calculated, including location of 0, and the frequency of Stuckelberg oscillations. Olson and Smith [3] describe in detail how this formalism can be coupled with a Landau-Zener treatment of the transition probability to yield differential cross sections. 3.1. Ne*+
2
I
10.0
on He
From ref. [4] we know the main population is of a 3s orbit on the projectile core. The measured angular distributions for Ne4+ on He are shown in fig. 4, plotted as a function r, which is a function of b but not of E for small angles. The critical angle 0, is shown also and it is immediately seen that much of the distribution lies inside 8,. This behavior is characteristic of cases where the incoming channel is not strongly promoted inside the crossing radius, as is the case when the active crossing populates an n s orbit on the projectile. In such a case the next crossing inside R, is with the next lower
C. L. Cocke et al. / An&w
n, and lies so far in that it plays little role in the collision. Thus the lower branch of B(b) extends in to very small scattering angles and small 6. In fig. 3 we show an example of a calculated deflection function (A) for Ne4+ on Ne, for which a screened Coulomb potential was used to represent the incoming channel and a pure Coulomb potential was used for the outgoing channel. The rainbow angle is so far forward that is is nearly unresolvable from O* in the experiment, and we believe this is the reason why the experiment shows such forward peaking this case. The model calulation for da/d@ is not so forward peaked as the experiment, however, raising the question as to whether or not the semi-classical treatment is adequate. We note that this extreme forward peaking is the exception rather than the rule. In most other cases we have studied, such as Ne5’, Ne6+, N6+, 06+, and F6+ on He, the forward peaking does not occur. These are cases where the primary population is of 31, I > 0, for which the incoming channel is strongly promoted by interaction with nearby lower capture channels, and the corresponding
Ne+4+ He SINGLE CAPTURE
.6
E=BOeV
.6
E=220eV
E = 172 eV
t_
0
IO T
20
30
40
feV-rod)
Fig. 4. Ekperimental angular distributions for Ne4+ on He. The locations of rainbow angles and first interference maxima for model B are indicated by filled and open arrow heads, respectively. 0, is indicated by a dashed arrow.
99
deflection functions have rainbows at very finite and observable scattering angles. The apparent oscillations at r = 4.5 and about 8 eV rad look Stucketberg-like, but all attempts to interpret them in terms of the areas enclosed by the deflection function A fail. This deflection function is so open that the oscillation frequency is too high to be resolved experimentally. We believe that these features arise from the tree-ch~el nature of the problem. There are really two 3s states fed, the *P and 4P formed on the 3P projectile core, and the energy gain spectra from which these final state populations are deduced do not resolve them. We believe that the oscillation comes from interference between two amplitudes leading to the less exoergic ‘P pupation. Considering only the *P final state, the two interfering paths are those discussed above, except that the incoming chmel behaves adiabatically at the crossing with the 4P state, and is thus promoted strongly, leading to a lower branch on B(b) which is much closer to the upper one (model B in fig. 3). We have done a two-state calculation for this case, including only the 2P and “promoted 4P’7 incoming curves, and have shown the resulting locations of the rainbow angle and maximum of the first Stuckelberg oscillation on fig. 4. The agreement with the data is good. It is interesting to note that to observe the participation of both of these 3s channels would have required extremely high energy resolution in an energy gain spectrum, but the presence of both gives an obvious feature in the angular distributions. 3.2. A+
E= 284eV
.6
distributions
on Ar
Pig. 5 shows angular distributions for single capture bY Ar sc from H,. The upper part of this figure shows the energy gain spectrum for this case [S], where we may identify two major processes. The normal single capture (SC) populates primarily Sf and 5d states, with a little 6s. In addition there is substantial population of TI channels, which correspond here to the population by double capture of autoionizing states which emit electrons before detection and thus appear to have only single-captured. In the angular distribution measurements, we do not resolve energetically these two channels. It would be tempting to try to interpret the structure seen in fig. 5 in terms of Stuckelberg interference again However, the presence of two rather distinct processes in the energy gain spectrum led us to try to ascertain whether the two peaks could correspond to these two processes. In order to do this, we used the retarding grid shown in fig.1 as a crude energy analyzer and measured, for Ar*” on Ar, angular dist~butions for SC and TI separately. The energy resolution is poor but just adequate to be able to separately record angular distributions for the two energy-gain groups. We used I. ATOMIC
PHYSICS
/ RELATED
PHENOMENA
C. L. Co&
0
IO
20
ENERGY
30 GAIN
40
50
et 01. / Angulur distributions
60
(EV)
have modeled this case by taking the incident channel to be flat until it is promoted by an adiabatic crossing with the Sp state which is not populated but which should serve as the promotor as discussed above. The predicted mid point on the rise of the angular distribution is indicated by an open arrow in fig. 5. Since this is well inside the observed threshold angle, we also consider that TI might go by a two-step process, whereby two successive crossings, each involving a single electron transfer, occur. In this case, this would mean crossing to the Sdf channel on the way in, and then from this “incident” channel to the TI channel either on the way in or the way out. In fact, the two crossings occur nearly at the same location in R but can be considered as sequential for the model. The resulting model calculation shows a threshold behavior whose mid-rise point is indicated by a solid arrow on fig. 5. It is in much better agreement with the data, and indicates that TI is better throught of as two single electron transfers than by a single two-electron transfer. This is certainly a reasonable result, since the two-electron matrix element is expected to be much weaker than that for single electron transfer. A very similar conclusion on the TI mechanism was reached by Roncin et al. [6].
4. Summary
Ai’
+ Ar
T.I.
vacc = 166 v
8
(mradl
Fig. 5. Experimental angular distributions for Ars+ on (a) D, and H, and (b) Ar. The top figure shows the energy gain spectrum for D2. The open and filled arrow heads indicate threshold angles predicted for single-step and double-step TI. respectively, and the dashed arrows indicate 0,.
Ar instead of D, or H, here to avoid any complications due to kinematic shifts, since we had previously determined that the three targets yield nearly the same energy gain spectra. The results are clear: the forward peak is due to SC while the second peak is due to TI, and has nothing to do with interference structure. One can learn something about the nature of the TI mechanism from the location of the maximum in its angular distribution. If the two-electron transition goes in a single step, that is at the single crossing between the incident channel and the TI channel, then there will be a lower branch of B(b) which extends to small 8. We
We have presented two examples of experimental studies of angular distributions for capture from neutral targets by multi-charged projectiles which reveal surprises and features which total cross sections and energy-gain spectra conceal. Although some qualitative understanding of these results is claimed, many questions remain to be answered, with even major features in the angular distributions lacking quantitative understanding. It is demonstrated that usuful information concerning reaction mechanisms can be gained from such angular distributions. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, US Department of Energy.
References [l] R.K. Janev and H. Winter, Phys. Rep. 117 (1985) 265; R.K. Janev, Comm. Atomic Mol. Phys. 12 (1983) 277. [2] K.W. Ford and J.A. Wheeler, Ann. Phys. (NY) 7 (1959) 259. [3] C. Schmeissner. CL. Cocke, R. Mann and W. Meyerhof, Phys. Rev. A30 (1984) 1661. [4] R.E. Olson and F.T. Smith, Phys. Rev. A3 (1971) 1607. [5] J.P. Giese. CL. Cocke, W. Waggoner, S.L. Varghese and L.N. Tunnell, Phys. Rev. A, to be published. [6] P. Roncin, M.N. Gaboriaud. M. Barat and H. Laurent, Europhys. Lett. 1 (1986).