Energy distribution of protons following electron capture in
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collisions of N ions with H2 at sub keV impact energies
P. Sobocinski, G. Allio, D. Martina, O. James, S. Dubois, J. Rangama, G. Laurent,
J.-Y. Chesnel, L. Adoui, A. Cassimi, D. Hennecart and F. Frémont,
Centre Interdisciplinaire de Recherche Ions Lasers, Unité Mixte CEA-CNRS-ISMRA-Université de Caen BasseNormandie, 6 Bd du Maréchal Juin, F-14050 Caen Cedex, France
J. Caillat and A. Dubois
Laboratoire de Chimie Physique-Matière et Rayonnement, 11 rue P. et M. Curie, F-75231 Paris Cedex, France
J.-H. Bremer, Z. Pesic, B. Sulik and N. Stolterfoht
Hahn-Meitner Institut, Bereich Festkörperphysik, Glienicker Strasse 100, D-14109 Berlin, Germany
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Abstract. The energy distributions of H fragments produced in N + H2 collisions at projectile energies ranging from
1.4 keV down to 32 eV have been investigated experimentally as a function of the detection angle. At 1.4 keV, two
groups of peaks are clearly visible, especially at forward angles. The structure centered at energies lower than ∼ 20 eV,
corresponds to a double capture at relatively large impact parameters, whereas the highly energetic protons result from
capture events at very small impact parameters. The results from a quasiclassical calculation method show a good
agreement with our experimental data for the fragment energy distributions. At the lowest projectile energy, the
fragment energy is found to be independent on the detection angle.
velocity has a strong influence on the fragment energy
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distributions. For the specific case of O + H2
collisions, three impact velocity regions can be
distinguished :
INTRODUCTION
The study of collisions between slow multicharged
ions and molecules is of fundamental interest [1-4],
since it gives information on both the primary
processes (i.e. electron capture) that occur during the
collision and on the dynamics of the molecular
dissociation after the removal of target electrons. In
particular, much work has been devoted to simple
molecular targets such as H2 or D2 [3-7].
(i) At relatively high projectile velocities
v p (> 0.5 a.u.), the fragmentation is found to be
isotropic [3], and the energy distribution is given by a
sharp peak centered at ∼ 9.5 eV, which corresponds to
a free fragmentation.
During the last few years, experimental [3,4,8] and
theoretical works [9,10] have shown that the projectile
(ii) For impact velocities ranging from ∼ 0.1 a.u. to
0.5 a.u., the fragments are found to be emitted in the
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
40
backward direction with respect to the incident beam
direction, suggesting the emergence of the role of
Coulomb forces induced by the projectile field [3, 4].
SPECTRA ANALYSIS
Figure 1 shows typical ion spectra for the system
N + H2 at an energy of 1.4 keV and for detection
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(iii) At very low impact velocities (< 0.1 a.u.), the
number of detected protons at forward (resp.
backward) angles increases (resp. decreases) with
decreasing the projectile velocity [4]. This surprising
effect was understood by investigating theoretically
the energy distributions as a function of the impact
parameter. While, at projectile velocities of the order
of 0.5 a.u., the capture occurs predominantly at large
impact parameters (soft collisions), the contribution of
small impact parameters (hard collisions) increases
and becomes dominant at projectile velocities smaller
than 0.1 a.u. Hence, soft collisions are responsible of
the ejection of protons in the backward direction, and
hard collisions give rise to protons which are emitted
mainly at forward angles [4].
o
o
o
angles of 20 , 90 and 130 . As shown previously for
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the collision system O + H2 [4] two groups of peaks
are observed at forward angles. The peaks located at
fragment energies lower than 30 eV originate from the
Coulomb explosion of the ionized target following the
double capture at relatively large impact parameters
(∼ 7 a.u.) while hard collisions are responsible for the
o
highly energetic protons. At 20 , the contribution of
soft collisions is strongly reduced, due to the Coulomb
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repulsion of the slow N outgoing projectile. At this
projectile energy, the contribution of hard collisions is
seen to be small compared with that of soft collisions.
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In the present work, the collision system N + H2
is analyzed, at projectile energies Ep ranging from 1.4
keV down to 32 eV, corresponding to velocities v p
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between 0.06 and 0.009 a.u. The choice of N ion as a
projectile is motivated by the fact that multiple
processes such as the excitation of the projectile is
avoided. Furthermore, calculations are expected to be
simpler using a bare projectile.
EXPERIMENTAL SET-UP
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The N ions were produced by the 14.5 GHz
electron cyclotron resonance (ECR) sources of the
Hahn-Meitner Institut (HMI) in Berlin. The low beam
energies were achieved by means of an electrostatic
deceleration of the 70 keV ions before entering the
scattering chamber. The ions were collimated to a
diameter of ∼ 2 mm. Typical currents of about 10 pA
and 10 nA were obtained for beams of 32 eV and
1.4 keV, respectively, and were used to normalize the
spectra after collection in a Faraday cup. In the
chamber, the beam was colliding an effusive H2-gas
FIGURE 1 : Energy distributions of fragments following
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electron capture in 1.4 keV N + H2 collisions at
observation angles of 20°, 90° and 130°. The solid line is the
result of quasiclassical calculations.
-4
jet. The average pressure, estimated to be ∼ 10 mbar,
was kept low enough to reduce multiple collisions for
the incident ions.
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Calculations using a quasiclassical description have
been performed for the present system at 1.4 keV. This
approach has the advantage to describe simultaneously
the electronic and nuclear motions. It is based on the
numerical resolution of Hamilton's equations for the
usual many-body Hamiltonian augmented by some
effective potentials [12].
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The resulting H and H 2 ions were detected using
the ion-spectroscopy apparatus from HMI [11], at
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detection angles in the range 10 – 130 , with respect
to the incident beam direction. The ion-spectrometer
consists of parallel plates in which an homogeneous
electric field is applied. By varying this field, a range
of selected ion energies can be explored, giving rise to
an energy-distribution spectrum.
The results of the model calculation are presented
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in Figure 1 (solid line). At 90 the calculated
o
distribution is normalized to the experiment. At 90 ,
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the calculation reproduces nicely the experimental
o
mean energy and the width of the distribution. At 20 ,
a qualitative agreement between experiment and
o
calculations is observed. For example, at 20 , the
positions in energy are well reproduced for the
energetic fragments. However, while the experimental
and calculated contributions of large impact
parameters are very similar, the contributions of small
impact parameters is overestimated by the present
model.
In this relation, m and M are proton and projectile
masses, respectively, and ψ r is the detection angle.
The quantity f (ψ r ) is defined by :
2
f (ψ r ) = 2 cos ψ +
r
m+M Q
m E
(2)
p
The quantity Q is the difference between the initial and
final potential energies and, thus, represents the
inelasticity of the collision.
70
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The Q value can be estimated by measuring Auger
spectra following the double capture giving rise to
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doubly excited states of the N projectile. At very low
impact velocities, the population of the 3l6l'
configurations is dominant, corresponding to an
average Q value of ~ 40 eV.
32 eV N + H2
Mean energy of a fragment (eV)
60
50
40
The result of this simple formula is given in
Figure 2. The agreement between experiment and
calculation is only qualitative, since the angular
dependence of the calculated energy is more
pronounced than that observed experimentally by a
factor of 2. This discrepancy is due to the fact that, at
32 eV, the collision has to be treated as a true threebody problem.
30
20
10
0
0
20
40
60
80
The weak dependence of the mean fragment energy
Er on ψ r can be easily explained by relations (1) and
(2). At high projectile energies the second term of
relation (2) vanishes, and the fragment energy is found
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Detection angle (deg.)
2
to be dependent on cos ψ
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FIGURE 2 : Mean energy of a fragment for the system N
+ H2 at a projectile energy of 32 eV. The solid line is the
result of calculation using relation (1).
r
[4]. In contrast, when Q
is much larger than Ep, the second term in relation (2)
2
is large compared with cos ψ . Hence the recoil
At the lowest projectile energy of 32 eV, the
spectra are somewhat different, since the mean energy
of a fragment is of the order of 30 eV whatever the
detection angle, as seen in Figure 2. Since relatively
large fragment energies are involved, compared to the
energy of 9.5 eV resulting from a free fragmentation,
the collision can be treated as a two-body collision
between the projectile and one of the protons.
Applying the energy and momentum conservation
rules, one obtains for the energy Er of the ejected
proton :
Er =
mM
(m + M )2
E
p
(f (ψ ) + 2 cosψ
r
r
f (ψ )
r
r
energy is nearly equal to the Q value. Consequently, at
very low impact velocities, the energy of a fragment
does not depend on the projectile energy.
Experimental energy distributions were used to
extract cross section for the detection of a proton. This
was done by integration of the spectra over the
fragment energy. The results for 1.4 keV and 32 eV
are shown in Figure 3.
At the highest energy, the protons are mainly
emitted at backward angles, due to the Coulomb
repulsion induced by the projectile after the capture.
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As shown previously for the system O + H2 at 2.5
keV [4], hard collisions involving impact parameters
smaller than 1 a.u. compete with soft collisions at
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detection angles close to 90 . At forward and
) (1)
42
detected in the direction of the incident projectile, due
to collisions at small impact parameters, while
fragments whose energy is of the order of 10 eV are
detected all the directions. These latter fragments
originate from capture at large impact parameters (~ 7
a.u.). Calculations using a quasiclassical method are in
good agreement with the experimental energy
distributions and cross sections.
backward angles, the role of soft collisions is
predominant. The calculated cross section using the
quasiclassical method is in rather good agreement with
our cross sections, since the difference does not exceed
a factor of 2.
In contrast, for the lowest projectile energy (bottom
of Figure 3), the protons are seen to be emitted mainly
at forward angles, indicating the important role of
small impact parameters. This observation is similar to
the results of previous calculations performed for the
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collision system Xe + H2 at a projectile energy of
1 eV / amu [13].
At the projectile energy of 32 eV, the fragments are
emitted with nearly the same energy. This could be
explained with a simple formula derived from
conservation laws. This formula indicates that, at very
low impact velocities, the energy given to a fragment
is of the order of the Q-value and is independent on the
collision energy. Hence, the fragment energy is
expected to originate mainly from the capture process.
3
10
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N + H2
Differential cross section dσ / dΩ (arb. unit)
1.4 keV
REFERENCES
2
10
1. Shah, M. B., and Gilbody, H. B., J. Phys. B 23,
1491 (1990).
2. M. Tarisien, L. Adoui, F. Frémont, D. Lelièvre, L.
Guillaume, J.-Y. Chesnel, H. Zhang, A. Dubois, D.
Mathur, S. Kumar, M. Krishnamurthy and A.
Cassimi, J. Phys. B Lett,. 33 L11 (2000).
3. Frémont, F., Bedouet, C., Chesnel, J.-Y., Adoui, L.,
Cassimi, A., and Tarisien, M., J. Phys. B, 33, L249
(2000).
4. Sobocinski, P., Rangama J., Laurent, G., Adoui, L.,
Cassimi, A., Chesnel, J.-Y., Dubois, A., Hennecart,
D., Husson, X., and Frémont, F., J. Phys. B, 35, 1353
(2002).
5. Meng, L., Olson, R. E., Folkerts, H. O. and
Hoekstra, R., J. Phys. B 27, 2269 (1994).
6. Kravis, S., Saitoh, H., Okuno, K., Soejima, K.,
Kimura, M., Shimamura, I., Awaya, Y., Kaneko, Y.,
Oura, M., and Shimakura, N., Phys. Rev. A 52, 1206
(1995).
7. Errea, L. F., Gorfinkiel, J. D., Macias, A., Mendez,
L., and Riera, A., J. Phys. B 30, 3855 (1997).
8. Ali, I., DuBois, R. D., Cocke, C. L., Feeler, C. R.,
and Olson, R. E., Phys. Rev. A 64, 022712 (2001).
9. Wood, C. J., and Olson, R. E., Phys. Rev. A 59,
1317 (1999).
10. Feeler, C. R., Olson, R. E., DuBois, R. D.,
Schlathölter, T., Hadjar, O., Hoekstra, R., and
Morgenstern, R., Phys. Rev. A 60, 2112 (1999).
11. Stolterfoht N., 1971 Z. Phys. 248, 81 ; 248, 92.
12. Cohen, J. S., Phys. Rev. A 56, 3583 (1997).
13. Olson, R. E., and Feeler, C. R., J. Phys. B 34, 1163
(2001).
32 eV
1
10
0
20
40
60
80
100
120
140
Detection angle (deg.)
FIGURE 3 : Cross sections for detecting one proton as a
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function of detection angle, for the system N + H2 at
projectile energies of 1.4 keV and 32 eV. The solid line is
the result of the quasi classical calculation, and the dashed
line is a guide for the eye.
CONCLUSION
The fragmentation of H2 following electron capture
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by sub keV N projectiles has been investigated
experimentally. The fragments were detected at angles
o
o
in the range 10 – 130 .
At the highest energies, two major contributions
are clearly observed. Highly energetic fragments are
43