ANGULAR DIFFERENTIAL CROSS SECTIONS IN LOW ENERGY CHARGE EXCHANGE COLLISIONS

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ANGULAR DIFFERENTIAL CROSS SECTIONS IN

LOW ENERGY CHARGE EXCHANGE COLLISIONS

C. Cocke

To cite this version:

C. Cocke.

ANGULAR DIFFERENTIAL CROSS SECTIONS IN LOW ENERGY CHARGE

JOURNAL DE PHYSIQUE

C o l l o q u e C l , suppl6ment au n o l , Tome 50, janvier 1 9 8 9

ANGULAR DIFFERENTIAL CROSS SECTIONS IN LOW ENERGY CHARGE EXCHANGE COLLISIONS( )

C . L . COCKE

J.R. Macdonald Laboratory, Physics Department, Kansas State

University, Manhattan, KS 66506, U.S.A.

Abstract - When a slow multiply charged ion captures electrons from a neutral target the angular distribution of the products is sensitive to the shape and participation of the potential curves involved. Models which provide adequate descriptions of total cross section data and of the final state populations in such collisions are generally less successful in dealing with the angular distributions. Using both recoil ion sources at KSU and the Oak Ridge ECR source, we have carried out a number of experiments on such angular distributions in recent The systems studied include partially stripped first-row elements on He, Ar+'ziIe, 012 on He and lri5 on D2. In this paper we review some of the results of these experiments.

I. INTRODUCTION

The subject of the capture of electrons from neutral targets by multiply charged projectiles has seen intense activity over the past d e ~ a d e . l - ~ If the projectile velocity is slow compared to that of the electrons in the target's outer shell, and if the projectile charge is high, it is common to assume that the following major characteristics of the capture process hold: 1) For projectiles with energies above a few eV, the Born-Oppenheimer separation is valid and the heavy particle motion can be treated classically. 2) The capture takes place at large internuclear distances where the potential curves are dominated by the asymptotic Coulomb energies of the post-collision products. 3) The transitions occur at localized crossings between incoming and outgoing potential curves, and the mediating coupling matrix element increases exponentially with decreasing internuclear distance4 so that the adiabaticity condition for optimum transition probability occurs over a very restricted range in R , giving rise to a "reaction window" and a very selective population of final states. Quantitative models based on Landau-Zener treatments of the transitions have been quite successful in accounting for total capture cross sections and for the location of the reaction ~ i n d o w . ~ - ~ Similar success has been achieved with the classical "over barrier" model and its sophistications .9'12

It is only a slight overstatement to claim that these models really only provide prescriptions for the determination of a single parameter for any given collision system, namely the radius at which the transfer occurs. Both the total cross section and the location of the reaction window follow from this parameter, the former determined geometrically and the latter from Coulomb energies. Thus the question arises as to whether the simple curve crossing model with Coulomb energies can deal with more subtle aspects of the capture process. Translational energy-gain spectroscopy and total cross sections test whether it gets the radius right, but not much more. The angular distributions of the

his

work was supported by the Division of Chemical Sciences. Office of Basic Energy Sciences. U.S. Department of Energy.

Cl-20 JOURNAL

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reaction products, on the other hand, are sensitive to the trajectory of the projectile over its entire encounter with the target, and probe what happens inside as well as outside the crossing radius. Over the past few years, our program in low energy collisions has concentrated on measuring the angular distributions of these products, and this paper discusses some examples of the results. As a point of departure we use the simple Coulomb curve crossing picture as a framework for discussion. However, as will become apparent, the model has shortcomings in dealing with the angular deflections.

We chose the semi-classical deflection function picture as a framework within which to discuss the experimental results. Starting with a fully quantal treatment of potential scattering, Ford and Wheeler13 showed that the deflection angle of a.projectile moving through a well defined potential can be calculated classically if the wavelength is small, if a stationary phase approximation is valid for the evaluation of the scattering amplitude and if the product of the scattering angle (9) and angular momentum divided by fi is much greater than unity. For the cases discussed here, at least the first and last assumptions are expected to be well justified. The resulting differential cross section is given by the classical expression

where b is the impact parameter. If the deflection function 9(b) is multi-valued, an additional interference appears between amplitudes for scattering to the same angle but with different impact parameters. For example, the two amplitude expression is

If the deflection function has an extremum for which db/d9 goes to zero with a positive second derivative, a rainbow will occur at this angle. In this case, the phase angle #(g)

is given, to within a fixed additive phase, by the area enclosed within the deflection function between the rainbow angle and the observation angle. Interferences between the two amplitudes in Eq. 2 can give rise to Stueckelberg oscillations.

Numerous authors have generalized this result to the case of reaction scattering.14-l7 Particularly relevant to the present discussion is the investigation by Danared et a1.18 of the validity of the semi-classical treatment for the on He case. They found that the semi-classical treatment was qualitatively correct, although not entirely satisfactory quantitatively. For the case of a flat incoming potential curve and a Coulomb outgoing potential the deflection functions are uninterestingly simple, as shown in Fig. 1. There are two branches to the deflection function which meet at an angle 9, which is one half the angle of scattering which would occur for Rutherford scattering in the final potential for an impact parameter equal to the crossing radius. The upper branch corresponds to capture at the crossing on the way in, and the lower one to capture on the way out. For this case, there is no rainbow, no double valued deflection function and no Stueckelberg oscillations are possible. However, this potential curve is rarely relevant to the real world, because there are commonly capture channels more exoergic than the active one whose behavior at the crossing with the incoming channel is adiabatic, and thus the incident potential is not flat but is strongly promoted somewhat inside the crossing. This case is shown schematically also in Fig. 2, where it is apparent that a minimum scattering angle Or now appears giving rise to a rainbow and Stueckelberg oscillations are now possible. In this simple two-channel picture, one can expect to see both a rainbow near the position of Or, which carries information on the behavior of the promoting channel, and gross structure in the angular distribution associated with the dependence of db/d9 on B , with a minimum at BC. In addition, one may expect Stueckelberg oscillations due to the interfering amplitudes of Eq.

POTENTIAL VS. I M P A C T PARAMETER

POTENTIAL VS. IMPACT P A R A M E T E R

2 1 7

DEFLECTION ANGLE V S , IMPACT PARAMETER OEFLECTlON ANGLE V S I M P A C T P A R A M E T E R

Fig. 1 Potentials and deflection function for Coulomb unpromoted case (for 1200 eV 0+6 on He with a Q-value of 30 eV).

Fig. 2 Similar to Fig. 1, but for a case where the incoming channel is strongly promoted just inside the crossing.

111. EXPERIMENTS

A. First row projectiles on He: Promotion of the incident channel

This experiment illustrates the qualitative difference between a case where the incident channel is strongly promoted inside the crossing (Fig.2) and one where no such promotion occurs (Fig. 1). The experiments were carried out in collaboration with R. A.

Phaneuf, F. W. Meyer and C. C. Havener of Oak Ridge National Laboratory. A schematic of the apparatus is shown in Fig. 3. Beams of C, N, 0, F and Ne in charge states between 5 and 8

were delivered by the Oak Ridge National Laboratory ECR source. The beam was tightly collimated and passed through a short gas cell containing He as a target. The exiting ions then proceeded 1.7 m onto the face of a channel plate chevron backed by a one-dimensional position sensitive resistive anode. The acceleration voltage was between 1.2 and 2.0 kV. This rather low extraction voltage resulted in weak beams, but had the advantages that it produced a good resolution in E-8 product and that it allowed the use of a simple retarding grid before the channelplates to block the direct beam, letting only the charge exchanged components pass. The detector was collimated with a bow-tie shaped diaphragm which projected the radially symmetric distribution on the plate onto the position sensitive axis of the anode with a negligible loss in resolution.19 The overall angular resolution of the system was 0.5 mrad (FWHM). By various settings of the grid, it was possible to distinguish single capture from double capture.

Adlustable Target 4

-

Jaw Slits P.S.D.

*

From E.C.R.

-1

Pump Grid Drives

System +"Bow ti$ Mask

C-22 JOURNAL

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In pioneering measurements with higher charge states performed here at the Grenoble ECR source, Roncin et a1 .20 made both energy and angle selection simultaneously. They found that the transfer ionization (TI), which here really means double capture to autoionizing states, is associated with larger scattering angles than is single capture. In our experiment we have given up all but a the very crude energy resolution obtainable with the retarding grid system but have obtained higher angular resolution. We rely on earlier measurements at Nagoya21 for the final state populations, which show only very weak population of TI for our charge states and low bombarding energies for the He target.

The experimental angular distributions were found to be very similar for the same incident charge state, independent of the particular species. That is, ~ e + ~ ,

e7

and 0+7

all give similar angular distributions for single capture. Thus we direct our attention to how the angular distributions vary with the charge state of the projectile, choosing for examination the cases of N + ~ ,

o + ~ ,

e7

and Ne+* on He. The energy gain spectra for these systems show that the major populations are of the 3s, 3d, 4s, and 4p,d orbits on the

projectile,respectively. Unlike the case for bare projectiles, the subshell splitting is

appreciable and the separation of different

B

within a single n manifold is sufficient that very selective population of not only a single n but also a single

B

is possible. Schematic level diagrams for three of these systems are shown in Fig. 4, with the crossing with the level which receives the major population being indicated with a circle.

The experimental angular distributions are shown for these cases in Fig. 5. The most remarkable feature is that the 0+6 case shows much wider angle scattering than do the other cases. For all other cases, the major population lies centered around BC, suggesting that the Coulomb deflection function models of Fig. 1 without the strong promotion give the correct picture. Especially for the +5 and +7 cases, where S states are populated and no

lower-lying promoting orbital is immediately available, the angular distribution is forward peaked as would be expected for the case of Fig. 1. The 0+' case appears anomalous because the active crossing, with the 3d level, is at rather small internuclear distances where the coupling matrix element with the 3p and 3s levels are expected to be so large that adiabatic behavior of the incident channel at these crossings occurs. Thus the incident channel is strongly promoted just inside the crossing, and the promoted case of Fig. 2 obtains. Thus it appears that the potential curve path followed by the collision system inside the crossing is crucial in determining the angular distribution of the reaction products. No total cross section or energy gain measurement can probe this region of the potential curves.

Fig. 4 Coulomb potential curves for various projectiles on He.

N + ~ + He V,,, = 1.478 kV o+= + He V, ,, = 1.478 kV

. .

.

.

F+'+ H e V, , , = 1.478 k V ~e+' + He V,,, = 2.000 kV

8

( rnrad)

Fig. 5 Angular distributions for capture from He by 1.2 kV

If one takes the model that the 3p serves as the promoter, and the 3d is populated, the resulting deflection function is of the type of Fig. 2, and encloses an area which varies slowly with theta because the 3p and 3d potential curves are so close together. Thus one might expect Stueckelberg oscillations to be low enough in frequency to give rise to observable oscillations in the angular distributions. Whether this is indeed the source of the oscillations seen for the case has not been verified by any theoretical cal.culation. It is noteworthy that no such oscillations occur for any of the other "unpromoted" systems, as would be expected.

B. ~ r on He: Test of the simple "promoted" model + ~

In order to examine how well the "promoted" Coulomb model describes the data, it is useful to choose a case for which energy gain data exist and for which a single .lvalue is populated, with the next lower 2 implicated as the promoter. Such is the case for ~ r on + ~ He. Energy gain spectra,21 shown in Fig. 6 , show interesting structure which was attributed by Andersen and ~ d r l n ~ ~ ~ not to the population of different final states but to oscillations in the angular distribution for the single capture which is reflected in the energy gain spectrum via the angle dependent energy given to the recoiling ~ e + ion. Andersen and Bardny used the promoted Coulomb model with a Landau-Zener model for the transition probabilities to predict that the population should overwhelmingly favor the 4p final state, with negligible population of 4s and 4d states for projectile energies of a few hundred eV. They were able to qualitatively reproduce with this model the double structure in the energy gain spectrum. This appeared to be a good case to use to test the promoted Coulomb model and deflection functions, and we decided to have a direct look at the angular distributions for this system.

Energy Gain (eV)

Fig. 6 Energy gain spectra for ~ r + ~

on He. The lowest energy spectrum is from the present work; the others are from Ref. 22.

Recoil Ion Source

C

1-24

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This experiment, and all succeeding ones described in this paper, were performed using a secondary ion recoil source (SIRS) pumped by Cu beams from the KSU tandem. The SIRS is a weak source of multiply charged ions, but is competitive for this kind of work because it produces ions with extremely low energy and with a very good transverse emittance. Both characteristics make possible working with good E-8 resolution without catastrophic losses in beam intensity. The experimental apparatus is shown in Fig. 7 and is similar to that described in Ref. 19 except that the scattered particle detector has a two-dimensional position-sensitive anode. From the X-y location of each event on this detector, the scattering angle is calculated and the distribution is presented as &/do. The absolute cross sections are determined in the experiment from knowledge of the gas cell length and cell pressure.

An angular distribution for 523 eV ~ r on He single capture is shown in Fig. 8. + ~ There is evidence for a double structure with maxima near 13 and 32 mrad., but the valley between the humps is filled in. The angular resolution measured on the direct beam was 3.5

mrad (FWHM) so that this filling in of the structure is not instrumental. The Coulomb deflection function for this system, with the 4p level being populated and the 4s level serving as promoter, are shown in Fig. 9 and the angular distributions calculated from this model, using Landau-Zener transition probabilities as described by Andersen and BdrAny, are shown in Fig. 8. The minimum in the calculation at 18 mrad is associated with the zero in db/dE which occurs at BC. Most of the events scattered inside this angle come from transitions on the "way out", while most events scattered outside this angle are from "way in" transitions.

Ar'+ + H e 523 .V

Experiment hr.+ -I- I l e

Pote~tiol C u r v e a

Fig. 8 Angular distributions for single Fig. 9 Promoted Coulomb potential curves capture from He by ~ r + ~ . The upper and deflection function for ~ r on He + ~ curve is the experimental data, and the for E = 296 eV. The potentials used for lower one is calculated from the model the deflection function calculation are potentials of Fig. 8. Expected shown as solid lines in the upper figure. locations of maxima in a Stueckelberg

oscillation pattern are shown as small circles along a line above the lower figure. A \

i

!

i

-9

4 p

-

-

\

-

, ?S

-

\ \ I

'-v

0 5 10 I5 20 1 0

-

:

a. k

.4

is

6 SF: \ - :L. P O d. M -

;

01

D " o D 0 D O " ~ o o o o o O 0 o o O 0 0 . 0 0 0 ' O - W I I . . e . e - - P Are+

+

H e 623 cV 4p R Co.".) 6 q

g m Total Dificre~~tial Crore Section

The calculation does not include the interference term in Eq. 2, but it is easy to see that the frequency expected for Stueckelberg oscillations is too high to be resolved in the experiment even if the oscillations wera present. Using the area enclosed within the deflection function of Fig. 9 , the locations of angles for which mv/fi times this area advances through 27t were calculated, and are shown by circles along a line above the model calculation of Fig. 8. The separation of maxima is too small to be resolved. The result that the Stueckelberg oscillation is too fast to observe is quite common for cases we have studied. The overall conclusion from this example is that the simple Coulomb model even in an apparently very favorable case does not do well at quantitatively describing the angular distributions, and probably is not reliable for more than qualitative arguments.

C. 0+2 on He: Stueckelberg Oscillations

One can expect to see Stuckelberg oscillations if one has a simple two-channel case and if the corresponding deflection function is "skinny". That is, the area enclosed between the two branches of the deflection function must vary slowly with deflection angle. Such is the case for double captJre by from He.24 Although no description in terms of semi-classical deflection functions has been presented in the literature, such is apparently the case for 'single capture by 0+2 on He. This case has been heavily studied theoretically for some years because of potential applications in astrophysics and atmospheric physics 25 Fully quantal treatments of the angular distributions are a~ailable*~ and show that at low energies population of the 2P final state dominates, a prediction con£ irmed by experiment. 27 The calculated adiabatic potential curves are shown in Fig. 10, where it is seen that one might expect the reaction to be dominated by the avoided crossing near 5 a.u. and interference structure due the quasi two-channel nature of the 337t and 23.rr states. The calculations, which include all three channels, confirm this expectation and predict strongly oscillating structure which should be resolvable in the laboratory with our system.

Our experimental angular distribution for this system is shown in Fig. 11 for an incident energy of 247 eV. Unfortunately, lack of beam at low energies and E-0 resolution

at high energies made it impossible for us to reach either the 50 or 500 eV bombarding energies for which the calculations exist. A compromise comparison between theory and data is made in Fig. 11, where the data are plotted versus E-0 to partially compensate for the fact that they do not correspond to the same bombarding energy. The experiment confirms nicely the oscillatory nature of the distribution and the observed frequency is near that predicted. A more quantitative test of the theory awaits calculations done at the experimental energies. It is clear that angular distributions are a very sensitive and feature-rich ground for testing any serious reaction calculation and easily reveal

shortcomings of oversimplified models. I I

Fi .l0 Adiabatic potential curves for

,+S

on He (from Ref. 25).

.

*

d++

lie W. + 7 1 . E = 247eV

..

+ + Experiment ( a ) +. +

..".

.* ,'

:

'.*.** *. 2 I ' I ' I

C 1-26 JOURNAL DE PHYSIQUE D. Angular distributions from the recoil products

If more than one final state is populated, measurements such as those described above are difficult to interpret. Even the measurements of Ref. 20 are not able to resolve structure within the true single capture or TI groups. Since two body kinematics are involved, it is sufficient to measure the angle and energy of either the projectile or the recoil. For the extremely low energy projectiles which the SIRS offers, detecting the recoil offers certain resolution advantages over the commonly used detection of the projectile.

We take the case of ~ r oh H2 as an example. The energy gain spectrum for this case, + ~ shown in Fig. 12, shows that both the 4p and 4d channels are appreciably populated in true single capture. The average Q values for this case are 18.5 and 12.5 eV respectively, and intensity considerations have not allowed us to be able to achieve adequate energy and angular resolution on the projectiles to obtain separate angular distributions for these channels. Our new approach is to measure the angle and energy of the

H ~ +

molecules produced in the collision instead of those of the projectile. Calculated kinematics for these channels are shown in Fig. 13, where the flight time of the recoil over a path length of 66 mm is shown rather than the energy. The recoil energies range from 0.5 to 8 eV for these cases. It is interesting to note that recoil angles corresponding to

BC

for the two cases are very similar although the BC themselves are quite different. This plot is very insensitive to the projectile energy, and thus good energy resolution on the projectile is not necessary.

ENERGY G A I N ( e V )

Fig.12 Energy gain spectrum for ~ r + ~ Fig. 13 Calculated recoil time of flight

on H2 (Ref. 7). versus recoil angle for

Q

values of

12.5(4d) and 18.5(4p) eV for ~ r on H2. + ~

The experimental apparatus is shown schematically in Fig. 14. A gas jet is generated

by a

lass

capillary array and crossed with the SIRS beam. The projectiles proceed into a channelplate detector where the direct beam is cut off by a biased grid but no angular information is obtained. The recoils are detected in a position sensitive channel plate detector located 66 mm away. This detector accepts a recoil angle range of thirty degrees at one setting. The flight time of the recoil is measured by timing on the arrival of the ~ rprojectile in the forward angle detector. + ~

DOUBLE FOCUSING MAGNET

JET

An example of the data obtained is shown in Fig. 15, where the spectrum of events is shown in a two dimensional plot of recoil angle versus recoil flight time. The major population seen in the spectrum is of the 4p state, whose intrinsic width (there is considerable multiplet splitting of this configuration) contributes to the width of the line seen. The intense group located at a flighe time near 1.4 usec is due to H+ ions which come from TI and are products of the Coulomb explosion of the ~ 2 - molecule. Projections taken over two different angular ranges from this spectrum are shown in Fig. 16, where the contribution of the 4d state is seen to increase as the recoil angle increases. Since small projectile scattering angles correspond to large recoil angles, this indicates that the 4d projectile angular distribution is much more forward peaked than is that for the 4p state. Further analysis of this data is underway.

Reccil Angle (degrees)

'2O 1 3 0 1a 6 0

o-!

4

! e L o ~ . D ~ M m M m

Positian Channel

Fig. 15 Experimental spectrum of flight times versus recoil scattering angles for ~ r on + Hg at 925 eV. ~

Time

Channel

Fig. 16 Projections of Fig. 15 on fli ht time axis for different recoil

5

(H2 ) scattering angle ranges.

This technique is most promising for heavy projectiles on light targets, and at very low bombarding energies. For symmetric cases and higher energies the recoil energies quickly become so low that the thermal energy spread of the target washes out the energy resolution.

IV. Conclusions

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