- Email: [email protected]
Electron capture by O8+ from aligned molecular deuterium
78
Nuclear
Instruments
and Methods
in Physics Research
B56/57
(1991) 7X-81 North-trolled
Electron S. Cheng, J. R.
capture
by 0”
C.L. Cocke, V. Frohne,
Mucdonald
Laborafoql,
Physzcs Department,
from aligned molecular E.Y. Kamber
1 and S.L. Varghese
Kansas State Univemty,
Manhattan,
deuterium 2
KS 66506-1601,
USA
Velocity space dist~butions of deuterons from electron capture and ionization by 10 MeV oxygen ions in collision with molecular deuterium targets were measured. The experiment was performed by applying an extraction electric field perpendicular to the b&m axis to project the whole velocity distribution of the recoil ions onto a two-dimensional position sensitive detector. By additional measurement of the time-of-flight of these recoil ions, we are able to reconstruct the three-dimensional velocity distribution. From the reconstructed results, the dependence of the cross sections on the alignment of the molecular axis with respect to the beam axis was determined.
1. Introduction The fact that the electron capture cross sections from molecular hydrogen are not simply twice as much as those from atomic hydrogen has been known for a long time. Tuan and Gerjuoy [l] first pointed out that for high energies the assumption that one hydrogen molecule is equivalent to two hydrogen atoms is generally not valid. They suggested that the interference between the two capture amplitudes from the two atomic centers might be responsible for this invalidity, They also noticed that the interference after averaging over the molecular orientation angle generally does not cancel out. Knudsen et al. [2] examined all experimental data available at the time for electron capture by various projectiles from molecular and atomic hydrogen and got an empirical formula for the ratio of a,(H,)/o,(H) as a function of projectile energy and charge state. According to this formula, the ratio of a,(Hz)/u,(H) can vary from < 1 to - 4. Although part of this ratio change may be explained by the interference from the two atomic centers [l], theoretical investigations into this phenomenon are rare due to the complexity of the calculation. Recently, Wang et al. [3] reported the calculation of electron capture cross sections for high energy protons incident on molecular hydrogen. By adapting the interference idea from Tuan and Gerjuoy, they calculated the dependence of the cross section on the molecular alignment angle. They predicted that the electron capture cross sections from H, molecules change
’ Present address: Department of Physics, Western Michigan University, Kalamazoo, Michigan 49008-3899, USA. ’ Present address: Department of Physics. University of Alabama, Mobile, Alabama 36688, USA. 0168-583X/91/$03.50
0 1991 - Elsevier Science Publishers
as a function of the longitudinal momentum transferred and the molecular orientation with respect to the incident projectile beam direction at given energies. In order to allow the theory to be compared with experiment in a more direct way. we used high energy bare oxygen ions to bombard molecular deuterium. We looked for a dependence of the cross section on the molecular orientation, without averaging over the orientation of the molecules.
2. Experiment According to our previous experimental results [4], when 10 MeV 0” ions collide with D, molecules and capture one electron from the molecule, there is a 46% probability that the projectile will eject the other one into the continuum, leaving the molecular ions in the doubly ionized state (Df+ D+ channel in fig. 1). There is a 21% probability that the molecular ions are left in one of the electronically excited states (2~0,. 2~7, and 2p~, channels in fig. 1). The molecular ions in such states are not stable and subsequently dissociate into ion-ion or neutral-ion pairs either because of Coulomb repulsion (DC+ DC) or because of they have excess energy. (The probability for true single capture, leaving a ground state D,’ molecular ion, is - 33%). The dissociated ions carry the information about their molecular orientation when the collision happened. Since the collision time is on the order of lo-” s and the typical rotation time of small molecules is on the order of lo-l2 s, the molecules can be considered “frozen” at the moment of collision. The postcollision interaction between the projectile and the dissociated ions has little effect on the trajectory of the dissociated ions. With our experimental setup, we are able to de-
B.V. (North-Holland)
S Cheng
et al. / Electron
D++ D(ls)
I
'0
I
I
2
INTERNUCLEAR
I
4
,
I
I
6
DISTANCE (au)
Fig. 1. The potential curves of a D, molecular ion. The mean released kinetic energy E, is shown for the 2~0” and Dt + Df channels.
termine the orientation of the molecule at the time of the collision. Although most of the theoretical calculations are carried out for molecular hydrogen targets, we chose theoretically equivalent molecular deuterium gas as a target to avoid contamination from the background gases in the beamline. The experimental apparatus is shown in fig. 2. A 10 MeV oxygen beam from the 6 MeV tandem Van de Graaff accelerator at Kansas State University was poststripped by a carbon foil to get bare oxygen ions. Before the ion beam collides with the target, an upstream magnet (Ml) was used to clean the beam so that the 07+ Ions produced along the beamline by capture of an electron from the background gas were deflected away from the entrance slits. A turbomolecu-
capture bv O8 +
79
lar pump was mounted immediately after this cleaning magnet to maintain a good vacuum in order to reduce the charge impurity. These are necessary because the ionization cross section for 07+ ions on D, molecules is several orders of magnitude larger than that for the capture process at this collision energy and thus the 07+ component of the beam has to be minimized. In the target region, D, gas was blown perpendicular to and - 1 mm away from the beam from a multicapillary jet collimated by a glass capillary array in order to provide a gas flow with good directionality and enough target density. After the collision the projectiles were charge-state-separated by magnet M2 and collected by a one-dimensional position sensitive detector (PSD). The recoil ions produced during the collisions were extracted by applying an electric field. The extracted ions then were allowed to travel in a field-free region before they were collected by a two-dimensional position sensitive detector (2DPSD). An aperture of 6 mm diameter was placed between the beam and the detector to restrict the view of the detector to only the central collision region. Timing pulses from the PSD and 2DPSD were used, respectively, to start and stop the TAC which measured the time-of-flight of the recoil ions. A coincidence between the projectiles and recoils was used to select the desired events. In order to determine the cross section dependence on each molecular orientation in one single run. two important parameters, the extraction voltage applied and the distance between the detector and the beam, have to be considered. First, all of the recoil ions which were produced during the collision must be collected. Since the dissociated ions have an energy of several eV, an extraction voltage high enough to turn around the ions flying away from the detector has to be applied. At the same time, this voltage has to accelerate the ions which originally have only a longitudinal velocity component (parallel to the beam) so that these ions will be
TARGET
GAS
Fig. 2. (From ref. [4]). Schematic of the apparatus. S denotes adjustable shts, EF is the extraction field, 2-DPSD is a two-dimensional position sensitive detector, Ml, M2 are magnets, Pl is the turbomolecular pump, and P2 IS a cryogenic pump. The shown Cartesian coordinates xyz are assigned to the collision center. I. ATOMIC/MOLECULAR
PHYSICS
S. Cheng
80
et al. / Electron
capture by 0’ +
by the 2DPSD which is 40 mm in diameter. Too high a voltage will cause the recoil ions to hit only in the central area of the 2DPSD and reduce the spatial resolution. Secondly, the time-of-flight of the recoil ions is proportional to the distance from the detector to the beam and inversely proportional to fi, where V is the voltage applied. There is a time spread due to the ions either flying towards the detector or flying away and then turning around in the electric field. We would like to maximize the time spread, but this is in conflict with the maximization of the spatial resolution on the 2DPSD. Tradeoff is needed to get the best results. In our case the 2DPSD was mounted 41 mm away from the beam. The extraction region, to which 500 V was applied, was 20 mm long. By measuring the 2-D position information of the recoil ions and their time-offlight, we are able to reconstruct the three-dimensional velocity distribution of the recoil ions. The molecular orientation information of the molecules at the moment of collision can thus be determined. collected
3. Results
and discussions
The position spectrum and the time-of-flight (TOF) spectrum of the recoil D+ ions in coincidence with O’+ ions are shown in fig. 3. The recoil molecular ions were also detected but only served as a reference and are not shown in fig. 3. The curve to the left of the marked point t, in the TAC spectrum (fig. 3b) represents recoils of smaller TOF, thus faster, and corresponds to the recoils flying towards the 2DPSD. The curve to the right is the signature of slow recoils flying away from the 2DPSD. The marked point t, is the TOF for recoils of V, = 0. Notice that TOF spectrum is not totally symmetrical about tO, due to the nonlinear transformation from velocity space to time space. Among the dissociative channels which produce recoil ions, the Df + D+ channel results in two deuteron ions‘ for one Coulomb explosion. If both D+ ions are detected by the 2DPSD, electronics and data acquisition system are not fast enough to tell them apart. As a result, the two position signals add up and we get false position information. In order to avoid this problem, a shield was placed between the extraction region and the detector in such a way that the cutting edge of the shield is at the same height with and parallel to the beam so that only one ion from the Coulomb exploded ion pair will be detected. The shield will cut the position spectrum by half (fig. 3a) but no information is lost since the collision system is symmetrical about the yz plane. Through a straightforward transformation, V, for each event was obtained from the TOF spectrum, and V,, V, from both the TOF and the position information from the ZDPSD (refer to fig. 2 for the coordinate
360
360
400
420
440
TOF (ns) Fig. 3. (a) A density plot of the position spectrum of the recoil deuteron ions. The horizontal axis is the z axis and the vertical is the x axis. The negative x part is not present as a result of placing a shield between the extraction region and the detector. (b) Time-of-flight spectrum of the recoil deuteron ions. The marked pomt to is the time corresponding to recods which have no VYcomponent.
system). Each is characterized by V,, I$, V, or their equivalence V, 8, +, where 6’ is the angle between V and the z axis and + is the angle between the projection of V on the xz plane and the z axis. Thus a three-dimensional velocity distribution was constructed. To display this distribution, slices parallel to the V,-V, plane for different values of FY were made, and are shown in fig. 4. We see a strong + angle dependence in the sliced displays. There are more events around I#J= 90” and less at 0 o and 180 O. This means that when the collision happens, the deuterium molecules are more likely to be in the states of orientation perpendicular to the incident beam than parallel to the beam. Fig. 5, in which dN/d(cos 8) was plotted as a function of the polar angle 0, shows this feature more clearly. A qualitative explanation of this feature is possible in terms of interference. When the molecular orientation is perpendicular to the beam, the phase difference between amplitudes originating on the two scattering centers of the molecule is minimum resulting in a constructive interference. When the angle between the
S. Cheng et al. / Electron capture by 08+
81
\ ;.-.:‘.... _..
;, _ _ .
..I.
45
.:
._ ,_ ._
L.
_i_
0
: : ..
‘*_ .,
._
_’
I
‘.
.._
.’
90
135
180
8
Fig. 5. Electron capture cross section dependence on the polar angle 0 for 10 MeV oxygen bare ions in collision with deuterium molecules. 4. Summary We have measured the dependence of the velocity space distribution of deuterons on their molecular orientation for collisions of 10 MeV oxygen bare ions with deuterium molecules. The result of peaking in the direction perpendicular to the beam can be qualitatively interpreted by the interference of capture amplitudes from the two atomic centers. Acknowledgements
Fig. 4. Sliced velocity drstributions along the Vy axis. The horizontal 1s the z axis and the vertrcalis the x axis. From top to bottom: 0 I Vy5 0.2Va; 0.2VaI y 5 0.4Va; 0.4V, I Vy 5 0.6V,; 0.6V, 2 vvI V,. V0 is the full speed of the deuteron ions after then Coulomb explosion. molecular orientation and the beam becomes smaller, the phase difference increases and constructive interference decreases. Further comparison with theory is under way.
The authors would like to thank Y. Wang, Professor McGuire and Dr. R. Shingal for their invaluable discussions and theoretical supports. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U.S. Department of Energy.
[l] T.F. Tuan and E. Gerjuoy, Phys. Rev. 117 (1960) 756. [2] H. Knudsen, H.K. Haugen and P. Hvelplund, Phys. Rev. A24 (1981) 2287. [3] Y.D. Wang, J.H. McGuire and R.D. Rivarola, Phys. Rev. A40 (1989) 3673. [4] S. Cheng, CL. Cocke, E.Y. Kamber, C.C. Hsu and S.L. Varghese, Phys. Rev. A42 (1990) 214.
I. ATOMIC/MOLECULAR
PHYSICS
Nuclear
Instruments
and Methods
in Physics Research
B56/57
(1991) 7X-81 North-trolled
Electron S. Cheng, J. R.
capture
by 0”
C.L. Cocke, V. Frohne,
Mucdonald
Laborafoql,
Physzcs Department,
from aligned molecular E.Y. Kamber
1 and S.L. Varghese
Kansas State Univemty,
Manhattan,
deuterium 2
KS 66506-1601,
USA
Velocity space dist~butions of deuterons from electron capture and ionization by 10 MeV oxygen ions in collision with molecular deuterium targets were measured. The experiment was performed by applying an extraction electric field perpendicular to the b&m axis to project the whole velocity distribution of the recoil ions onto a two-dimensional position sensitive detector. By additional measurement of the time-of-flight of these recoil ions, we are able to reconstruct the three-dimensional velocity distribution. From the reconstructed results, the dependence of the cross sections on the alignment of the molecular axis with respect to the beam axis was determined.
1. Introduction The fact that the electron capture cross sections from molecular hydrogen are not simply twice as much as those from atomic hydrogen has been known for a long time. Tuan and Gerjuoy [l] first pointed out that for high energies the assumption that one hydrogen molecule is equivalent to two hydrogen atoms is generally not valid. They suggested that the interference between the two capture amplitudes from the two atomic centers might be responsible for this invalidity, They also noticed that the interference after averaging over the molecular orientation angle generally does not cancel out. Knudsen et al. [2] examined all experimental data available at the time for electron capture by various projectiles from molecular and atomic hydrogen and got an empirical formula for the ratio of a,(H,)/o,(H) as a function of projectile energy and charge state. According to this formula, the ratio of a,(Hz)/u,(H) can vary from < 1 to - 4. Although part of this ratio change may be explained by the interference from the two atomic centers [l], theoretical investigations into this phenomenon are rare due to the complexity of the calculation. Recently, Wang et al. [3] reported the calculation of electron capture cross sections for high energy protons incident on molecular hydrogen. By adapting the interference idea from Tuan and Gerjuoy, they calculated the dependence of the cross section on the molecular alignment angle. They predicted that the electron capture cross sections from H, molecules change
’ Present address: Department of Physics, Western Michigan University, Kalamazoo, Michigan 49008-3899, USA. ’ Present address: Department of Physics. University of Alabama, Mobile, Alabama 36688, USA. 0168-583X/91/$03.50
0 1991 - Elsevier Science Publishers
as a function of the longitudinal momentum transferred and the molecular orientation with respect to the incident projectile beam direction at given energies. In order to allow the theory to be compared with experiment in a more direct way. we used high energy bare oxygen ions to bombard molecular deuterium. We looked for a dependence of the cross section on the molecular orientation, without averaging over the orientation of the molecules.
2. Experiment According to our previous experimental results [4], when 10 MeV 0” ions collide with D, molecules and capture one electron from the molecule, there is a 46% probability that the projectile will eject the other one into the continuum, leaving the molecular ions in the doubly ionized state (Df+ D+ channel in fig. 1). There is a 21% probability that the molecular ions are left in one of the electronically excited states (2~0,. 2~7, and 2p~, channels in fig. 1). The molecular ions in such states are not stable and subsequently dissociate into ion-ion or neutral-ion pairs either because of Coulomb repulsion (DC+ DC) or because of they have excess energy. (The probability for true single capture, leaving a ground state D,’ molecular ion, is - 33%). The dissociated ions carry the information about their molecular orientation when the collision happened. Since the collision time is on the order of lo-” s and the typical rotation time of small molecules is on the order of lo-l2 s, the molecules can be considered “frozen” at the moment of collision. The postcollision interaction between the projectile and the dissociated ions has little effect on the trajectory of the dissociated ions. With our experimental setup, we are able to de-
B.V. (North-Holland)
S Cheng
et al. / Electron
D++ D(ls)
I
'0
I
I
2
INTERNUCLEAR
I
4
,
I
I
6
DISTANCE (au)
Fig. 1. The potential curves of a D, molecular ion. The mean released kinetic energy E, is shown for the 2~0” and Dt + Df channels.
termine the orientation of the molecule at the time of the collision. Although most of the theoretical calculations are carried out for molecular hydrogen targets, we chose theoretically equivalent molecular deuterium gas as a target to avoid contamination from the background gases in the beamline. The experimental apparatus is shown in fig. 2. A 10 MeV oxygen beam from the 6 MeV tandem Van de Graaff accelerator at Kansas State University was poststripped by a carbon foil to get bare oxygen ions. Before the ion beam collides with the target, an upstream magnet (Ml) was used to clean the beam so that the 07+ Ions produced along the beamline by capture of an electron from the background gas were deflected away from the entrance slits. A turbomolecu-
capture bv O8 +
79
lar pump was mounted immediately after this cleaning magnet to maintain a good vacuum in order to reduce the charge impurity. These are necessary because the ionization cross section for 07+ ions on D, molecules is several orders of magnitude larger than that for the capture process at this collision energy and thus the 07+ component of the beam has to be minimized. In the target region, D, gas was blown perpendicular to and - 1 mm away from the beam from a multicapillary jet collimated by a glass capillary array in order to provide a gas flow with good directionality and enough target density. After the collision the projectiles were charge-state-separated by magnet M2 and collected by a one-dimensional position sensitive detector (PSD). The recoil ions produced during the collisions were extracted by applying an electric field. The extracted ions then were allowed to travel in a field-free region before they were collected by a two-dimensional position sensitive detector (2DPSD). An aperture of 6 mm diameter was placed between the beam and the detector to restrict the view of the detector to only the central collision region. Timing pulses from the PSD and 2DPSD were used, respectively, to start and stop the TAC which measured the time-of-flight of the recoil ions. A coincidence between the projectiles and recoils was used to select the desired events. In order to determine the cross section dependence on each molecular orientation in one single run. two important parameters, the extraction voltage applied and the distance between the detector and the beam, have to be considered. First, all of the recoil ions which were produced during the collision must be collected. Since the dissociated ions have an energy of several eV, an extraction voltage high enough to turn around the ions flying away from the detector has to be applied. At the same time, this voltage has to accelerate the ions which originally have only a longitudinal velocity component (parallel to the beam) so that these ions will be
TARGET
GAS
Fig. 2. (From ref. [4]). Schematic of the apparatus. S denotes adjustable shts, EF is the extraction field, 2-DPSD is a two-dimensional position sensitive detector, Ml, M2 are magnets, Pl is the turbomolecular pump, and P2 IS a cryogenic pump. The shown Cartesian coordinates xyz are assigned to the collision center. I. ATOMIC/MOLECULAR
PHYSICS
S. Cheng
80
et al. / Electron
capture by 0’ +
by the 2DPSD which is 40 mm in diameter. Too high a voltage will cause the recoil ions to hit only in the central area of the 2DPSD and reduce the spatial resolution. Secondly, the time-of-flight of the recoil ions is proportional to the distance from the detector to the beam and inversely proportional to fi, where V is the voltage applied. There is a time spread due to the ions either flying towards the detector or flying away and then turning around in the electric field. We would like to maximize the time spread, but this is in conflict with the maximization of the spatial resolution on the 2DPSD. Tradeoff is needed to get the best results. In our case the 2DPSD was mounted 41 mm away from the beam. The extraction region, to which 500 V was applied, was 20 mm long. By measuring the 2-D position information of the recoil ions and their time-offlight, we are able to reconstruct the three-dimensional velocity distribution of the recoil ions. The molecular orientation information of the molecules at the moment of collision can thus be determined. collected
3. Results
and discussions
The position spectrum and the time-of-flight (TOF) spectrum of the recoil D+ ions in coincidence with O’+ ions are shown in fig. 3. The recoil molecular ions were also detected but only served as a reference and are not shown in fig. 3. The curve to the left of the marked point t, in the TAC spectrum (fig. 3b) represents recoils of smaller TOF, thus faster, and corresponds to the recoils flying towards the 2DPSD. The curve to the right is the signature of slow recoils flying away from the 2DPSD. The marked point t, is the TOF for recoils of V, = 0. Notice that TOF spectrum is not totally symmetrical about tO, due to the nonlinear transformation from velocity space to time space. Among the dissociative channels which produce recoil ions, the Df + D+ channel results in two deuteron ions‘ for one Coulomb explosion. If both D+ ions are detected by the 2DPSD, electronics and data acquisition system are not fast enough to tell them apart. As a result, the two position signals add up and we get false position information. In order to avoid this problem, a shield was placed between the extraction region and the detector in such a way that the cutting edge of the shield is at the same height with and parallel to the beam so that only one ion from the Coulomb exploded ion pair will be detected. The shield will cut the position spectrum by half (fig. 3a) but no information is lost since the collision system is symmetrical about the yz plane. Through a straightforward transformation, V, for each event was obtained from the TOF spectrum, and V,, V, from both the TOF and the position information from the ZDPSD (refer to fig. 2 for the coordinate
360
360
400
420
440
TOF (ns) Fig. 3. (a) A density plot of the position spectrum of the recoil deuteron ions. The horizontal axis is the z axis and the vertical is the x axis. The negative x part is not present as a result of placing a shield between the extraction region and the detector. (b) Time-of-flight spectrum of the recoil deuteron ions. The marked pomt to is the time corresponding to recods which have no VYcomponent.
system). Each is characterized by V,, I$, V, or their equivalence V, 8, +, where 6’ is the angle between V and the z axis and + is the angle between the projection of V on the xz plane and the z axis. Thus a three-dimensional velocity distribution was constructed. To display this distribution, slices parallel to the V,-V, plane for different values of FY were made, and are shown in fig. 4. We see a strong + angle dependence in the sliced displays. There are more events around I#J= 90” and less at 0 o and 180 O. This means that when the collision happens, the deuterium molecules are more likely to be in the states of orientation perpendicular to the incident beam than parallel to the beam. Fig. 5, in which dN/d(cos 8) was plotted as a function of the polar angle 0, shows this feature more clearly. A qualitative explanation of this feature is possible in terms of interference. When the molecular orientation is perpendicular to the beam, the phase difference between amplitudes originating on the two scattering centers of the molecule is minimum resulting in a constructive interference. When the angle between the
S. Cheng et al. / Electron capture by 08+
81
\ ;.-.:‘.... _..
;, _ _ .
..I.
45
.:
._ ,_ ._
L.
_i_
0
: : ..
‘*_ .,
._
_’
I
‘.
.._
.’
90
135
180
8
Fig. 5. Electron capture cross section dependence on the polar angle 0 for 10 MeV oxygen bare ions in collision with deuterium molecules. 4. Summary We have measured the dependence of the velocity space distribution of deuterons on their molecular orientation for collisions of 10 MeV oxygen bare ions with deuterium molecules. The result of peaking in the direction perpendicular to the beam can be qualitatively interpreted by the interference of capture amplitudes from the two atomic centers. Acknowledgements
Fig. 4. Sliced velocity drstributions along the Vy axis. The horizontal 1s the z axis and the vertrcalis the x axis. From top to bottom: 0 I Vy5 0.2Va; 0.2VaI y 5 0.4Va; 0.4V, I Vy 5 0.6V,; 0.6V, 2 vvI V,. V0 is the full speed of the deuteron ions after then Coulomb explosion. molecular orientation and the beam becomes smaller, the phase difference increases and constructive interference decreases. Further comparison with theory is under way.
The authors would like to thank Y. Wang, Professor McGuire and Dr. R. Shingal for their invaluable discussions and theoretical supports. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, U.S. Department of Energy.
[l] T.F. Tuan and E. Gerjuoy, Phys. Rev. 117 (1960) 756. [2] H. Knudsen, H.K. Haugen and P. Hvelplund, Phys. Rev. A24 (1981) 2287. [3] Y.D. Wang, J.H. McGuire and R.D. Rivarola, Phys. Rev. A40 (1989) 3673. [4] S. Cheng, CL. Cocke, E.Y. Kamber, C.C. Hsu and S.L. Varghese, Phys. Rev. A42 (1990) 214.
I. ATOMIC/MOLECULAR
PHYSICS