Proton emission following multiple electron capture in slow N7+ +HCl collisions

Abstract

Collisions between 98-keV N7+ ions and a HCl target have been investigated experimentally. The kinetic-energy distribution of fragment H+ ions originating from multiple electron capture was detected at angles in the range 20°-160° with respect to the incident beam direction. Proton energies as large as 100 eV were observed, and calculations made in the simple Coulomb explosion model suggest that up to seven target electrons may be involved during the collision. Using the Landau-Zener model, we show that the N7+ projectile mainly captures outer-shell electrons from HCl. From the experimental data we derived multiple-capture cross sections which we compared with results from a model calculation made using the classical over-barrier model and also with a semiempirical scaling law. For the specific case of double capture, several structures appeared, which were assigned using ab initio calculations to states of HCl2+ .

Full text

Proton emission following multiple electron capture in slow N7++HCl collisions
F. Frémont, D. Martina, O. Kamalou, P. Sobocinski, and J.-Y. Chesnel
Centre Interdisciplinaire de Recherche Ions Lasers, Unité Mixte CEA-CNRS-EnsiCaen-Université de Caen Basse-Normandie, 6 boulevard
du Mal Juin, F-14050 Caen Cedex, France
I. R. McNab
Physics, School of Natural Sciences, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, United Kingdom
F. R. Bennett
CSIRO Minerals, P. O. Box 90, Bentley, Western Australia 6982, Australia
共Received 25 January 2005; published 12 April 2005兲
Collisions between 98-keV N7+ ions and a HCl target have been investigated experimentally. The kinetic-
energy distribution of fragment H+ions originating from multiple electron capture was detected at angles in the
range 20°–160° with respect to the incident beam direction. Proton energies as large as 100 eV were observed,
and calculations made in the simple Coulomb explosion model suggest that up to seven target electrons may be
involved during the collision. Using the Landau-Zener model, we show that the N7+ projectile mainly captures
outer-shell electrons from HCl. From the experimental data we derived multiple-capture cross sections which
we compared with results from a model calculation made using the classical over-barrier model and also with
a semiempirical scaling law. For the specific case of double capture, several structures appeared, which were
assigned using ab initio calculations to states of HCl2+.
DOI: 10.1103/PhysRevA.71.042706 PACS number共s兲: 34.50.Gb, 34.70.⫹e
I. INTRODUCTION
The study of collisions between slow highly charged ions
and molecular species has received much attention during
the past few years. The studies give detailed experimental
关1–6兴and theoretical 关7–9兴information both on electron cap-
ture that occurs during the collision, and on the fragmenta-
tion dynamics that take place after the removal of the elec-
trons from the target. Much effort has been focused on
understanding collisions between slow highly charged ions
and simple molecular targets such as H2or D2关4–9兴.
Very recently, some of us performed experimental and
theoretical studies of slow collisions between O5++H2and
N7++H2关4,6兴. We were able to analyze the influence of the
projectile on the fragment energy distributions following
double electron capture 共DC兲, as a function of the projectile
velocity. Three impact-velocity regions could be
distinguished: 共1兲isotropic fragmentation at high velocities
共⬎0.5 a.u.兲,共2兲strong backward fragmentation at projectile
velocities between 0.5 and 0.1 a.u., and 共3兲strong forward
fragmentation at velocities less than 0.1 a.u. We now give a
little more detail for each of these regimes.
共1兲At relatively high projectile velocities vP
共⬎0.5 a.u.兲, the fragmentation was found to be isotropic, and
the energy distributions were given, at each detection angle,
by a sharp peak centered at ⬃9.5 eV, which corresponds to a
free fragmentation 关4兴. At such velocities, our model calcu-
lations showed that the capture occurs mainly at large impact
parameters b共5–7 a.u.兲, and in the “way out” of the collision,
according to the notation of the over-barrier 共OB兲model
关10兴. It was concluded that, at such velocities, the influence
of the projectile charge on each fragment is negligible.
共2兲At impact velocities ranging from ⬃1 to 0.5 a.u., the
fragments were found to be emitted mainly in the backward
direction with respect to the incident beam direction 关4,6兴.
This effect, also reported for the system Xe26++D2关8兴,isdue
to the strong influence of the Coulomb forces induced by the
projectile which modify the fragment trajectories and ener-
gies, during and after the capture process. While the domi-
nant capture occurs at large impact parameter 共b⬇5 a.u.兲
and on the way out of the collision, a small fraction of highly
energetic fragments are also detected in the forward direc-
tion. These fragments were found to originate from electron
capture at very small impact parameter 共b⬍1 a.u.兲,inthe
“way in” of the collision.
共3兲At projectile velocities lower than 0.1 a.u., the frag-
ment protons were seen to be emitted preferentially at for-
ward angles, indicating that the capture process occurs pre-
dominantly at small impact parameters 共b⬍1 a.u.兲, on the
“way in” to the collision. This observation is consistent with
the results of previous calculations performed for the colli-
sion system Xe23++H2at a projectile energy of 1 eV/amu
关9兴. In addition, for this latter system as well as for the O5+
+H2and N7++H2systems, the double-electron-capture pro-
cess was found to give the major contribution to the total
cross section 关4,6,9兴.
Slow collisions involving multielectronic molecular tar-
gets have also been studied in the last ten years 关11–15兴. The
detailed analysis of such collisions requires data from
multiple-coincidence techniques. Using these techniques, in-
formation on the fragmentation of the residual target after the
capture process could be revealed. For example, in double
charge exchange following very slow Kr8++N2collisions
关14兴, many fragmentation channels involving highly charged
N2
q+共q艋5兲residual target ions were identified. The role of
the initial molecule orientation in the multiple ionization of
PHYSICAL REVIEW A 71, 042706 共2005兲
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N2and O2was also studied experimentally in collisions of
highly charged Xe ions at projectile velocities of ⬃0.2 a.u.
关13兴.
Apart from these works, the fragmentation studies have
given only minor information on the electron-capture process
itself. For example, as shown previously 关4,6兴, the impact-
parameter distributions, which can be derived from the
analysis of the fragmentation channels, are important to
know because they give insight into the nature of the cap-
tured electrons. Moreover, the final charge-state distribution
of the target may change with the projectile velocity, giving
information on the number of electrons involved in the cap-
ture process. For the case of molecular targets, many ques-
tions remain to be answered, because the electronic structure
of a molecule differs strongly from that of an atom and the
electron capture and subsequent fragmentation of molecules
depend upon the chemical bonding within each electronic
state of the molecule that contributes to the observations.
In the present work we studied the fragmentation of HCl
following multiple electron capture by N7+ projectile ions.
The use of HCl was motivated by the fact that in a fragmen-
tation process conservation of momentum leads to the H+
fragment 共of mass 1 a.u.兲having a kinetic energy which is
typically 35 times larger than that of the corresponding Clq+
fragment 共of mass 35 a.u.兲. Therefore, after the capture pro-
cess, the dissociation of HCl leads to fragments whose ener-
gies may easily be separated. The H+fragments were de-
tected as a function of their energy and for detection angles
varying from 20° to 160° with respect to the incident beam
direction. In the following analysis, the different reaction
pathways are discussed and the charge distributions are de-
duced. From the fragment kinetic-energy spectra, relative
cross sections for multiple electron capture are deduced, and
these are compared with results derived from both the clas-
sical over-barrier model 关10兴and the semiempirical scaling
law of Selberg et al. 关16兴.
II. EXPERIMENTAL SETUP
The experimental setup has been described in detail else-
where 关17兴, and so only a brief description is given here. The
experiments were conducted at the 14-GHz electron cyclo-
tron resonance 共ECR兲ion source of the LIMBE facility, at
the Grand Accélérateur National d’Ions Lourds 共GANIL兲in
Caen. The N7+ ions, extracted at an energy of 98 keV, were
magnetically analyzed and focused to a diameter of ⬃2 mm.
Typical ion currents of ⬃50 nA were collected in a Faraday
cup and these were used to normalize the spectra. In the
scattering chamber, a base pressure smaller than 10−6 mbar
was achieved. In the center of the scattering chamber, the
N7+ beam was colliding with a gas-beam target of HCl that
was created by an effusive gas jet. The average HCl target
pressure was determined to be ⬃10−4 mbar, corresponding to
a residual pressure of ⬃10−5 mbar in the chamber. These
pressures were sufficiently low to ensure the predominance
of single collisions. The fragments produced after the colli-
sion were detected at angles in the range from 20° to 160°
with respect to the incident beam direction, using a single-
stage spectrometer which consists of an electrostatic parallel-
plate analyzer. The intrinsic energy resolution of the exit ana-
lyzer was 5% full width at half maximum. The fragment
acceptance angle was ⬃2°. The length ᐉ0of the ion beam, as
seen by the spectrometer at 90°, was ⬃4 mm. This length,
increasing according to ᐉf=ᐉ0/sin
␪
as the observation angle
␪
decreases, was taken into account in our determination of
the differential cross sections in energy and angle.
III. SPECTRA ANALYSIS AND DISCUSSION
A. Role of outer- and inner-shell electrons
in the capture process
Figure 1 shows fragment spectra for detection angles of
20°, 90°, and 160°. These spectra consist of several struc-
tures whose energies range from 3 to 100 eV. As explained in
the Introduction, the observed peaks are attributed to protons
following the Coulomb explosion of multiply charged HCl
after the electron-capture process. The occurrence of high
proton energies originates from multiple electron capture. In
order to separate the different charge-state contributions of
the target, each peak in the spectrum was fitted with Gauss-
ian curves 共only shown at 160° in Fig. 1兲and the experimen-
tal energies for each peak were compared 共Table I兲with the-
oretical energies derived from the simple Coulomb explosion
FIG. 1. Energy distribution of protons and chlorine ions 共open
circles兲at detection angles of 20°, 90°, and 160° following the
fragmentation of HCl ions after multiple capture in 98-keV N7+
+HCl collisions. The full curves are the results of a fit procedure of
the spectrum using Gaussian curves.
FRÉMONT et al. PHYSICAL REVIEW A 71, 042706 共2005兲
042706-2

model. This model assumes that the final total kinetic energy
E
¯
kin of the H+and Clq+fragments is equal to the initial Cou-
lomb repulsion energy q/R0, where qis the charge of the
Clq+fragments 共the charge of H+is 1兲, and R0is the inter-
nuclear distance between H and Cl at equilibrium 共R0
⬇2.41 a.u.兲. It is first seen from Table I that H+fragments
are associated with Clq+fragments whose charge can reach
values as large as 6. This is an indication that up to seven
target electrons may be active during the capture process.
For q=1, corresponding to energy release from HCl2+,
five structures are observed, suggesting that excited states of
HCl2+ are produced in the ionization process. To our knowl-
edge, while doubly excited states of HCl are reported in the
literature, detailed information on the resulting fragment en-
ergies is missing. Only a few energies are available 关18,19兴.
The origin of these peaks will be discussed in detail in Sec.
III C.
Two reaction pathways can lead to formation of H+with
identical kinetic energies, but we are able to use Auger spec-
tra to discriminate between the two possibilities. The reac-
tions that can lead to H+fragments are as follows.
共i兲After the capture of qelectrons 关Eq. 共1a兲兴, the ionized
molecular target may first deexcite by autoionization 关Eq.
共1b兲兴 共molecular autoionization兲, and then dissociate 关Eq.
共1c兲兴:
N7+ + HCl →N共7−q兲++ HClq+*,共1a兲
HClq+* →HCl共q+1兲++e−,共1b兲
HCl共q+1兲+→H++Cl
q++E
¯
kin.共1c兲
共ii兲The projectile may also capture 共q+1兲target elec-
trons 关Eq. 共2a兲兴, the target dissociates 关Eq. 共2b兲兴:
N7+ + HCl →N共6−q兲++ HCl共q+1兲+,共2a兲
HCl共q+1兲+→H++Cl
q++E
¯
kin.共2b兲
For both of the pathways above 共i兲and 共ii兲, the Clq+ion
关Eq. 共1c兲and 共2b兲兴 may remain in an excited state. Thus the
chlorine fragments may autoionize 共atomic autoionization兲:
Clq+* →Cl共q+1兲++e−.共3兲
Both 共i兲and 共ii兲pathways lead to the same kinetic energy
releases E
¯
kin. Therefore, in principle, a given proton energy
共reported in Table I兲may be associated with the capture of
either qor 共q+1兲target electrons. However, the atomic auto-
ionization process does not depend on the fragmentation dy-
namics. Therefore, atomic autoionization gives rise to well-
defined structures in Auger electron energy distributions 关20兴
while in contrast, molecular autoionization produces a con-
tinuous background.
Thus, we used the Auger spectrum 共measured at an obser-
vation angle of 90°兲to reveal possible autoionization process
of the excited target 共Fig. 2兲. As shown in Fig. 2, two distinct
groups of peaks are clearly separated. In the range 0 to 100
eV 共left side of Fig. 2兲, double electron capture populates
configurations of quasiequivalent electrons 3ᐉnᐉ⬘and 4ᐉnᐉ⬘
共n艌4兲of the projectile, while the lines in the range from
300 to 600 eV are essentially due to the capture of more than
two electrons, which gives rise to KAuger electrons 关21,22兴.
As shown by Wills et al. 关23兴, the ejection of an inner-shell
4
␴
target electron gives rise to an Auger electron with an
energy less than 3 eV. In our spectrum 共Fig. 2兲, no peak
appears at low energy 共⬍10 eV兲and the background is
found to be negligible. This result indicates that the target or
chlorine autoionization is unlikely to occur. Consequently,
the reaction pathway 共ii兲is favored; the projectile captures
TABLE I. Experimental and calculated energies of H+frag-
ments following the dissociation of HCl in 98-keV N7++HCl colli-
sions, as a function of the charge qof Clq+. The letters 共a兲—共h兲
refer to the peaks in Fig. 1.The energy EH+共column 2兲is deter-
mined by fitting each peak with Gaussian curves. The uncertainties
given in column 2 take into account the standard deviation in the fit
procedure. The calculated mean energies are derived from the
simple Coulomb explosion model 共see text兲.
qE
H+共eV兲E
¯
H+共eV兲共calc.兲
1a3.0±0.1
b4.5±0.1
c5.8±0.1 11.3
d7.7±0.1
e11.1±0.1
2f15.8±0.5
g19±0.5 22.6
h21±0.5
3 29.1±1.0 33.9
4 40.6±1.5 45.2
5 53±4 56.5
6 63±5 67.7
FIG. 2. Spectrum of Auger electrons produced in 98-keV N7+
+HCl collisions at an observation angle of 90°. The lines in the
range 5–100 eV correspond to the decay of projectile states associ-
ated with 3ᐉnᐉ⬘and 4ᐉnᐉ⬘共n艌4兲. The lines in the range 300–600
eV are essentially due to multiple electron capture.
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共q+1兲target electrons giving rise to the HCl共q+1兲+→H+
+Clq++E
¯
kin pathway.
To theoretically investigate the role of outer-shell valence
electrons in the electron capture process, we applied the mul-
tichannel Landau-Zener model 关24兴for single 共SC兲and
double electron capture. Very briefly, the transition probabil-
ity pif between initial 共i兲and final 共f兲states is given, at a
curve crossing with projectile-target distance RC,by
pif =1−exp
冉
−2
␲
兩Hif兩2
vr共b兲⌬F共RC兲
冊
.共4兲
In this expression, bis the impact parameter, vr共b兲is the
radial velocity, and ⌬F共RC兲is a measure of the relative in-
clination of the potential curves at crossing RC. For SC and
DC, ⌬F共RC兲=共q−1兲/Rc
2and ⌬F共RC兲=共q−3兲/Rc
2, respec-
tively. The matrix element Hif, which describes the interac-
tion at RC, was calculated by using the formula derived by
Olson and Salop 关25兴.
To evaluate the crossing radii RC, diagrams for approxi-
mate potential curves of the N7++HCl system were used
共Fig. 3兲. It is recalled that the electronic ground state of HCl
is 共1
␴
22
␴
23
␴
21
␲
44
␴
25
␴
22
␲
4兲1⌺+. The capture of outer-
shell 2
␲
共or 5
␴
兲and inner-shell 4
␴
electrons is described on
the left and right sides of Fig. 3, respectively. The entrance
channel N7++HCl共2
␲
兲crosses the N6+共nᐉ兲+HCl+共with n
=3, 4, and 5兲channels 共circles兲at internuclear distances of
⬃2.7, 5.7, and 12 a.u., respectively, where resonance condi-
tions for a single transition are created for the first transition.
At ⬃2.6 and 8.2 a.u., further crossings 共circles兲allow a sec-
ond transition from N6+共4ᐉ兲+HCl+to N5+共3ᐉ4ᐉ⬘兲+HCl2+
and from N6+共5ᐉ兲+HCl+to N5+共4ᐉ5ᐉ⬘兲+HCl2+. It is recalled
that both 3ᐉ4ᐉ⬘and 4ᐉ5ᐉ⬘configurations are dominantly
populated, as shown in the Auger spectrum of Fig. 2. Figure
3 also shows that the 3ᐉ4ᐉ⬘and 4ᐉ5ᐉ⬘configurations can
also be created via dielectronic transitions 共squares in Fig. 3兲,
at internuclear distances of ⬃2 and 3.8 a.u., respectively. The
determination of the dielectronic matrix element Hif which
describes the dielectronic transitions is by no means straight-
forward. Nevertheless, according to previous evaluations
关26兴, a reasonable value of 0.05 a.u. for Hif was retained in
our calculations.
The situation is quite different in the case of a capture of
an inner-shell 4
␴
electron 共right side of Fig. 3兲. First, no
crossing appears between the entrance channel and the final
channels N6+共5ᐉ兲+HCl+and N5+共4ᐉ5ᐉ⬘兲+HCl2+. Conse-
quently, the capture of 4
␴
electrons into 5ᐉand 4ᐉ5ᐉ⬘con-
figurations is unlikely to occur. The capture of 4
␴
electrons
into 4ᐉand 3ᐉ4ᐉ⬘configurations are also expected to give
rise to negligible cross sections, because the transitions occur
at large internuclear distances 共⬎20 a.u. for 4ᐉ兲. Conse-
quently, the major contribution would be due to a capture
into 3ᐉand 2ᐉ3ᐉ⬘configurations, since the corresponding
transitions occur at projectile-target distances ranging from
⬃2 to 4 a.u.
In Fig. 4, the calculated differential cross sections
d
␴
/db=2
␲
bP共b兲db, where P共b兲=pif共1−pif兲is the capture
probability, are shown as a function of the impact parameter
b, in the case of capture of a 2
␲
electron 共left side兲and a 4
␴
electron 共right side兲. The capture of one outer-shell electron
gives rise mainly to a 5ᐉorbital of the projectile, while the
3ᐉorbital is mainly populated when an inner-shell electron is
involved. As mentioned above, the configurations 3ᐉ4ᐉ⬘and
4ᐉ5ᐉ⬘共2ᐉ3ᐉ⬘兲are dominantly populated when two outer-
shell 共inner-shell兲electrons are active during the double cap-
ture process.
The cross sections
␴
2
␲
and
␴
4
␴
for the capture of outer-
and inner-shell electrons, respectively, were determined by
integration of d
␴
/db over the impact parameter b共Table II兲.
In addition, the ratio
␴
4
␴
/共
␴
2
␲
+
␴
4
␴
兲is reported. For a single
electron capture, the role of a 4
␴
electron is not negligible,
since the corresponding cross section represents ⬃23% of
the total single-capture cross section. Nevertheless, this ratio
decreases to ⬃9% for a double electron capture. This finding
is consistent with our experiment where no target autoioniz-
ation is found 共Fig. 2兲. Hence, it is reasonable to neglect in
the following the role of 4
␴
electrons in the multiple electron
capture process.
FIG. 3. Diagrams of approximate potential
curves of the N7++HCl system. On the left side
共right side兲, capture of an outer-shell 2
␲
共inner-
shell 4
␴
兲electron is supposed. Dashed lines and
solid lines correspond to single and double cap-
ture, respectively.
FRÉMONT et al. PHYSICAL REVIEW A 71, 042706 共2005兲
042706-4

B. Energy position of the fragments
When varying the observation angle
␪
d, a detailed analy-
sis of the spectra reveals a small shift 共Ⰶ0.5 eV兲for frag-
ments that follow a DC process. This result contrasts with
that found for the O5++H2system at a projectile energy of
105 keV 关27兴. For this system, it was found that the mean
energy of H+following the fragmentation of H2
2+ increases
when increasing
␪
d共from ⬃8.9 eV at 20° up to 10 eV at
160°兲. The shift of ⬃1 eV was interpreted using a two-step
model, based on two successive two-body interactions 关4兴.In
the first step, after the capture process, the residual target
recoils with a velocity v
ជ
r. Then, in the second step, the ion
dissociates with a velocity v
ជ
f
c.m. in the frame of the molecular
center of mass. Thus, the detected proton, whose velocity is
defined by v
ជ
f
L=v
ជ
f
c.m.+v
ជ
r, can have energy in the range
共Emin,Emax兲with
Emin =1
2mH共vf−vr兲2,共5a兲
Emax =1
2mH共vf+vr兲2,共5b兲
where mHis the proton mass.
To determine Emin and Emax for N7++HCl collisions, it is
necessary to estimate the residual target recoil velocity vr.
The mean energy of the recoiling residual target is evalu-
ated using the momentum and energy conservation laws,
which result in the following expressions for the longitudinal
p
储
and transverse p⬜momenta of the recoiling target given in
the laboratory frame,
p
储
⬇−Q
vproj −ncvproj
2,共6a兲
p⬜⬇
␪
P0.共6b兲
In these expressions Qis the inelastic energy transfer, ncis
the number of captured electrons,
␪
is the scattering angle of
the projectile, and P0is the initial projectile momentum.
To simplify, we only treat the case of a DC process. The
angle
␪
is then given by
␪
⬇1
2EpRDC
冋
2共qp−2兲+共qp−1兲冑1−
冉
RDC
RSC
冊
2
册
,共7兲
where Epand qpare the projectile energy and charge, respec-
tively, and RSC and RDC refer to the projectile-target dis-
tances at which a SC and a DC occur. Then the average
momentum pr=共p
储
2+p⬜
2兲1/2 of the recoiling target and the
corresponding recoil velocity vrwere deduced 共Table III兲.
The results for Emin and Emax are given, assuming capture
into the 3ᐉ4ᐉ⬘and 4ᐉ5ᐉ⬘configurations and a typical mean
H+energy of 5 eV 共Table III兲. For comparison, the results for
the collision system O5++H2关4兴are also reported. It is seen
that, due to the difference between the target masses, the
recoil velocity of the HCl target is significantly smaller than
that of the H2target. In addition, the fragment velocity vfis
much larger than the recoil velocity vrfor N7++HCl colli-
FIG. 4. Differential cross sections d
␴
/db
=2
␲
bP共b兲db as a function of the impact param-
eter b, for 98-keV N7++HCl collisions, in the
case of capture of 2
␲
共left side兲and 4
␴
共right
side兲electrons.
TABLE II. Cross sections
␴
2
␲
and
␴
4
␴
for the single and double
capture of outer- and inner-shell electrons, respectively, in 98-keV
N7++HCl collisions, calculated by means of the multichannel
Landau-Zener model 关24兴. In the last column, the ratio
␴
4
␴
/共
␴
2
␲
+
␴
4
␴
兲is given.
Configurations
␴
4
␲
共cm2兲
␴
4
␴
共cm2兲
␴
4
␴
/共
␴
2
␲
+
␴
4
␴
兲
3ᐉ1.3⫻10−23 3.9⫻10−16
4ᐉ6.1⫻10−17 2⫻10−23
5ᐉ1.2⫻10−15
Total 1.26⫻10−15 3.9⫻10−16 0.23
2ᐉ3ᐉ⬘6.7⫻10−18
3ᐉ4ᐉ⬘3.6⫻10−17 1.7⫻10−22
4ᐉ5ᐉ⬘3⫻10−17
Total 6.6⫻10−17 6.7⫻10−18 0.09
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sions 共Table III兲. Thus, while a shift of ⬃1.1 eV is observed
in H+energy distributions for O5++H2collisions, the differ-
ence between Emin and Emax is found to be smaller than 0.4
eV in the present work. This result is in agreement with the
shift observed in the experiment.
C. Experimental kinetic-energy releases and comparisons
to results from model calculations
It is not the purpose of the present work to perform an
exhaustive analysis of the kinetic-energy spectra. Rather, in
order to show what is involved in a full calculation, we now
consider in detail the kinetic-energy releases that arise from
the Coulomb explosion of HCl2+ 共peaks a–eof Fig. 1兲and
reserve for future work the calculations relating to the more
highly charged molecular species. To assign the measured
kinetic-energy releases we calculated potential-energy curves
for the ground state of HCl, and for the electronic states of
HCl2+ shown in Table IV. The states correspond to those
shown in Fig. 1 of Ref. 关28兴. We included states with Cl2+
+H dissociation channels because we did not wish to assume
that the fragmentation process was adiabatic. All possible
nonadiabatic energy release channels were considered in our
assignment.
The potential-energy curves were calculated using the
MOLPRO program package 关29兴using similar methodology to
that of Ref. 关30兴. Multireference configuration-interaction
wave functions 关31,32兴based on state-averaged multicon-
figuration self-consistent-field 共MCSCF兲关33,34兴molecular
orbitals were calculated for each electronic state considered.
The basis set used was Dunning’s cc-pV5Z generally con-
tracted Gaussian basis 关35兴, which in previous work 关36兴
gave excellent agreement with vibrationally resolved experi-
mental data for the X3⌺−and a1⌬states.
To calculate the dissociation asymptotes we calculated
one potential-energy point at d=50 Å for each potential. By
50 Å the potentials are purely Coulombic and dissociation
asymptotes for each potential were therefore calculated as
V共⬁兲=V共d兲−e2
4
␲
␧0
1
d=V共d兲− 0.29 eV.
We assigned the kinetic-energy release spectra as follows.
We assumed that the ionization process was Franck-Condon
in nature and calculated Franck-Condon factors for excita-
tions from the ground state of HCl into the bound states and
continua of HCl2+ using Le Roy’s programs LEVEL 关37兴and
BCONT 关38兴, as described in 关36兴. In this work final energies
for each state were calculated relative to the dissociation as-
ymptote of the state itself 共adiabatic fragmentation兲,ora
lower-lying state 共nonadiabatic fragmentation兲. The resulting
theoretical energy spectra were each independently convo-
luted with an instrument function and then fitted with a
Gaussian to find the energy releases reported in Table V. We
found that states corresponding to the uppermost three dis-
sociation limits do not contribute to the observed structure.
Our final assignments are given in Table V. Calculations
and experiment are in agreement between 0.1 and 0.5 eV,
except for one nonadiabatic channel. Two cases of nonadia-
batic dissociation are found, and correspond to spin-orbit-
mediated coupling between the a1⌬and the 1 3⌸, and be-
tween the b1⌺+and 1 3⌸states. These couplings are strong
TABLE III. Energies Emin and Emax that can reach a proton after the dissociation of HCl following a DC process. The scattering angle
␪
is determined from relation 共7兲. The longitudinal and transverse components of the recoil-ion momentum are then deduced from relations
共6a兲and 共6b兲. The quantities Q,RSC, and RDC are evaluated from the potential-energy curves of Fig. 3. For comparison, the results for the
collision system O5++H2关4兴are also reported.
N7++HCl RSC 共a.u兲RDC 共a.u兲Q共a.u兲
␪
共rad兲p⬜共a.u兲p
储
共a.u兲pr共a.u兲vr共a.u兲vf共a.u兲Emin 共eV兲Emax 共eV兲
N5+共4ᐉ5ᐉ⬘兲11.8 8.3 0.98 3.4⫻10−4 4.7 −2.4 5.3 7.8⫻10−5 0.014 4.945 5.055
N5+共3ᐉ4ᐉ⬘兲5.7 2.5 2.61 1.2⫻10−3 16.9 −5.6 17.8 2.6⫻10−4 0.014 4.82 5.19
O5++H24.9 6.1 1.03 1.2⫻10−3 1.6 −2.1 2.6 7.2⫻10−4 0.0195 8.8 10.2
TABLE IV. Calculated electronic states and asymptotic energies
V共⬁兲after the dissociation of the HCl2+ molecular ion.
Dissociation limit Electronic states V共⬁兲共eV兲
Cl+共3Pg兲+H+X3⌺−,13⌸−459.2215
Cl+共1Dg兲+H+a1⌬,b1⌺+,11⌸−459.1691
Cl+共1Sg兲+H+21⌺+−459.0956
Cl2+共4Su兲+H c5⌺−,23⌺−−458.8643
Cl2+共2Dg兲+H 23⌸,21⌸,11⌺−,21⌬,33⌺−,1 3⌬−458.7801
TABLE V. Measured Eexpt and calculated Ecalc kinetic-energy
releases 共in eV兲and assignments. In the third column, the difference
⌬Ebetween Ecalc and Eexpt is given. The assignments given in pa-
rentheses are the only possible nonadiabatic energy releases 共see
text兲.
Peak Eexpt 共eV兲Ecalc 共eV兲⌬E共eV兲Assignment
Excitation Dissociation
a3.5
b4.6 4.63 0.03 X3⌺−X3⌺−
b4.6 4.71 0.11 a1⌬a1⌬共weak兲
c5.8 5.92 0.12 b1⌺+b1⌺+共weak兲
c5.8 共6.14 0.34 a1⌬13⌸兲共strong兲
c5.8 共7.35 1.55 b1⌺+13⌸兲共strong兲
d8.0 共7.35 −0.65 b1⌺+13⌸兲共strong兲
d8.0 8.47 0.47 1 1⌸11⌸
d8.0 8.51 0.51 1 3⌸13⌸
e11.4 11.49 0.09 2 1⌺+21⌺+
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because of curve crossings. The majority of the intensity in
the peaks comes from quasibound levels trapped behind the
barriers 关39兴. The quasibound levels predissociate predomi-
nantly by spin-orbit interaction 共a nonadiabatic process兲,
with lifetimes calculated to be at least two orders of magni-
tude shorter than adiabatic predissociation by tunneling 关30兴.
Therefore, in both cases dissociation through the nonadia-
batic channel should be far stronger than adiabatic dissocia-
tion.
The worst agreement between experiment and theory is
for the nonadiabatic channel b1⌺+→13⌸, and it is not clear
whether this channel should be assigned to peak cor d共both
assignments are given in Table V兲. The energy of the adia-
batic dissociation channel b1⌺+→b1⌺+does agree well
with the measured energy of peak c, but unless the lifetime
calculations of Ref. 关30兴were in error by two orders of mag-
nitude, this must be a minor dissociation channel. In previous
work by others 关18兴, the nonadiabatic channels do not appear
to have been considered, but the propensity to follow the
nonadiabatic dissociation channel for both the a1⌬and
b1⌺+states is high.
D. Experimental cross sections and comparison
with model calculation
The measured fragment emission spectra were used to
evaluate single-differential cross section d
␴
qt/d⍀for H+
emission associated with a given charge qt共qt=q+1兲of the
residual target. Thus, the corresponding fragment energy dis-
tributions 共Fig. 1兲were integrated with respect to the frag-
ment energy. The results are given in Table VI and Fig. 5.
The relative statistical uncertainties are of the order of 15%
for small qtand increase to ⬃50% for qt=7. Cross sections
are found to be isotropic, within the error bars. From this
result, we can conclude that the influence of the projectile
Coulomb field on the H+fragments is negligible for the in-
vestigated impact energy.
The cross sections
␴
qtfor the capture of qttarget electrons
were determined by integration of d
␴
qt/d⍀over the obser-
vation angle. Our experimental cross sections were compared
共Fig. 6兲with model calculations derived from the over-
barrier model 关10兴and from the semiempirical scaling law
by Selberg et al. 关16兴, which is devoted to multiple capture in
slow ion-atom collisions. The experimental double-capture
cross section was normalized to that obtained with the OB
model. The results are presented in Fig. 6.
Neither the OB model nor the scaling law is satisfactory
to fully reproduce the experimental cross sections. The dis-
TABLE VI. Relative single-differential cross sections d
␴
qt/d⍀共in arbitrary units兲for fragment emission
associated with a given charge qtof the residual molecular target, as a function of the observation angle
␪
d.
d
␴
q/d⍀
␪
d2 34567
20° 1123±62 598 ±53 873±85 157±87 120±51 20±10
30° 991±27 723±156 502±69 292±140 102±50 27 ±12
40° 852±33 591± 28 599±90 154±90 102± 55 20± 10
50° 873±49 496± 28 539±42 204±48 80±40 30 ±15
60° 814±116 529 ±36 485±90 248±50 61±30 19 ±10
70° 786±47 643± 28 414±43 214±49 114± 48 36± 20
80° 948±47 549± 37 526±53 242±142 84±40 34± 15
90° 1275±75 757 ±40 781±70 400±70 137±60 30±15
160° 1175±54 790±55 621 ±49 346±62 114±60 8 ± 5
FIG. 5. Relative single-differential cross sections d
␴
qt/d⍀共in
arbitrary units兲for fragment emission associated with a given
charge qtof the residual molecular target, as a function of the ob-
servation angle
␪
d. The averaged cross sections 共dashed horizontal
lines兲are used as a guide for the eyes.
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agreement is much more pronounced for the OB model,
which gives negligible cross sections for the capture of seven
electrons. In contrast, the scaling law shows a similar behav-
ior to the experiment, since the cross sections do not differ
by more than a factor of 2, except for the capture of seven
electrons. This qualitative agreement indicates that, at such
projectile energies, the HCl target can be viewed by the pro-
jectile as an atom.
IV. CONCLUSION
The collision system 98-keV N7++HCl has been studied
by means of ion and electron spectroscopy. Fragments with
energy as high as 100 eV are observed. We first showed
using the Landau-Zener model 关24兴that the projectile mainly
captures outer-shell electrons. Consequently, the Auger deex-
citation of the target is negligible. Thus, our spectra indicate
that the proton energy is directly connected to the number of
captured electrons 共up to seven兲.
In contrast with previous studies involving H2targets
关4,6,12,27兴, the energy shift due to the recoil of the residual
ionized target is found to be negligible. This is due to the fact
that the HCl mass is much larger than that for H2. Moreover,
for the DC contribution, several peaks are observed, indicat-
ing that excited states of the HCl2+ molecular ion are popu-
lated during the collision. The kinetic energy of the H+frag-
ments following the production of these excited states could
be calculated. Calculations and experiment are found to be in
good agreement.
Finally, the experimental cross sections were determined,
as a function of the target charge, and compared with the
over-barrier model 关10兴and a semiempirical scaling law for
collisions between highly charged ions and multielectronic
targets 关16兴. While large discrepancies are observed for the
OB model, a reasonable agreement is seen for the scaling
law.
This study shows that the detection of fragments is an
efficient tool to obtain information on the primary process
共i.e., capture兲. In the future, we plan a more systematic study
of the electron capture process in N7++HCl collisions at
lower projectile energies 共down to a few eV兲. The goal of
this work would be first to see the influence of the projectile
velocity on the charged fragments, in order to obtain the
impact-parameter distributions, since the capture process
strongly depends on the impact parameter. Second, the de-
pendence of the number of captured electrons, as well as
their nature 共outer shell, inner shell, and core electrons兲,on
the projectile velocity will be analyzed.
关1兴H. O. Folkerts, R. Hoekstra, and R. Morgenstern, Phys. Rev.
Lett. 77, 3339 共1996兲.
关2兴B. R. Beck, J. Steiger, G. Weinberg, D. A. Church, J. Mc-
Donald, and D. Schneider, Phys. Rev. Lett. 77, 1735 共1996兲.
关3兴M. Tarisien, L. Adoui, F. Frémont, and A. Cassimi, Phys. Scr.,
T80, 182 共1999兲.
关4兴P. Sobocinski, J. Rangama, J-Y. Chesnel, M. Tarisien, L.
Adoui, A. Cassimi, X. Husson, and F. Frémont, in Application
of Accelerators in Research and Industry, edited by J. L. Dug-
gan and I. L. Morgan, AIP Conf. Proc. No. 576 共AIP, Melville,
NY, 2001兲,p.114.
关5兴D. M. Kearns, R. W. McCullough, and H. B. Gilbody, J. Phys.
B35, 4335 共2002兲.
关6兴P. Sobocinski, J. Rangama, G. Laurent, L. Adoui, A. Cassimi,
J-Y. Chesnel, A. Dubois, D. Hennecart, X. Husson, and F.
Frémont, J. Phys. B 35, 1353 共2002兲.
关7兴C. J. Wood and R. E. Olson, Phys. Rev. A 59, 1317 共1999兲.
关8兴C. R. Feeler, R. E. Olson, R. D. DuBois, T. Schlathölter, O.
Hadjar, R. Hoekstra, and R. Morgenstern, Phys. Rev. A 60,
2112 共1999兲.
关9兴R. E. Olson and C. R. Feeler, J. Phys. B 34, 1163 共2001兲.
关10兴A. Niehaus, J. Phys. B 19, 2925 共1986兲.
关11兴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 33,L11共2000兲.
关12兴P. Sobocinski, J. Rangama, J-Y. Chesnel, M. Tarisien, L.
Adoui, A. Cassimi, X. Husson, and F. Frémont, J. Phys. B 34,
L367 共2001兲.
FIG. 6. Cross sections
␴
qtfor the capture of qttarget electrons
determined by integration of d
␴
qt/d⍀over the observation angle, in
98-keV N7++HCl collisions. The full squares are the results of ex-
periment. The dashed curve is derived from the semiempirical scal-
ing law by Selberg et al. 关16兴, and the full curve is the result of the
over-barrier model 关10兴.
FRÉMONT et al. PHYSICAL REVIEW A 71, 042706 共2005兲
042706-8

关13兴B. Siegmann, U. Werner, R. Mann, Z. Kaliman, N. M. Ka-
bachnik, and H. O. Lutz, Phys. Rev. A 65, 010704共R兲共2001兲.
关14兴T. Kaneyasu, T. Azuma, M. Ehrich, M. Yashino, and K.
Okuno, Nucl. Instrum. Methods Phys. Res. B 205, 624 共2003兲.
关15兴Z. D. Pesic, J-Y. Chesnel, R. Hellhamer, B. Sulik, and N.
Stolterfoht, J. Phys. B 37, 1405 共2004兲.
关16兴N. Selberg, C. Biedermann, and H. Cederquist, Phys. Rev. A
54, 4127 共1996兲.
关17兴F. Frémont, K. Sommer, D. Lecler, S. Hicham, P. Boduch, X.
Husson, and N. Stolterfoht, Phys. Rev. A 46, 222 共1992兲.
关18兴S. Harper, P. Calandra, and S. D. Price, Phys. Chem. Chem.
Phys. 3, 741 共2001兲.
关19兴R. Abusen, F. R. Bennett, I. R. McNab, D. N. Sharp, R. C.
Shiell, and C. A. Woodward, J. Chem. Phys. 108, 1761
共1998兲.
关20兴P. Sobocinski, J. Rangama, J-Y. Chesnel, M. Tarisien, L.
Adoui, A. Cassimi, X. Husson, and F. Frémont, J. Phys. B 34,
L367 共2001兲.
关21兴P. Benoit-Catin, A. Bordenave-Montesquieu, M. Boudjema, A.
Gleizes, S. Dousson, and D. Hitz, J. Phys. B 21, 3387 共1988兲.
关22兴F. Frémont, C. Bedouet, J-Y. Chesnel, H. Merabet, X. Husson,
M. Grether, A. Spieler, and N. Stolterfoht, Phys. Rev. A 54,
R4609 共1996兲.
关23兴A. A. Wills, D. Cubric, M. Ukai, F. Currell, B. J. Goodwin, T.
Reddish, and J. Comer, J. Phys. B 26, 2601 共1993兲.
关24兴L. D. Landau, Phys. Z. Sowjetunion 2,46共1932兲; C. Zener,
Proc. R. Soc. London, Ser. A 137, 696 共1932兲.
关25兴R. E. Olson and A. Salop, Phys. Rev. A 14, 579 共1976兲.
关26兴C. Bedouet, F. Frémont, J-Y. Chesnel, X. Husson, H. Merabet,
N. Vaeck, N. Zitane, B. Sulik, M. Grether, A. Spieler, and N.
Stolterfoht, Phys. Rev. A 59, 4399 共1999兲.
关27兴F. Frémont, C. Bedouet, M. Tarisien, L. Adoui, A. Cassimi, A.
Dubois, J-Y. Chesnel, and N. Stolterfoht, J. Phys. B 33, L249
共2000兲.
关28兴A. Banichevich, S. D. Peyerimhoff, M. C. Van Hemert, and P.
G. Fournier, Chem. Phys. 121, 351 共1988兲.
关29兴H-J. Werner and P. J. Knowles with contributions from J. Alm-
löf, R. D. Amos, S. T. Elbert, W. Meyer, E-A. Reinsch, R. M.
Pitzer, A. J. Stone, and P. R. Taylor, Computer code MOLPRO.
关30兴F. R. Bennett and I. R. McNab, Chem. Phys. Lett. 251, 405
共1996兲.
关31兴P. J. Knowles and H-J. Werner, Chem. Phys. Lett. 145, 514
共1988兲.
关32兴H-J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803
共1988兲.
关33兴P. J. Knowles and H-J. Werner, Chem. Phys. Lett. 115, 259
共1985兲.
关34兴H-J. Werner and P. J. Knowles, J. Chem. Phys. 82, 5053
共1985兲.
关35兴T. H. Dunning, J. Chem. Phys. 90, 1007 共1989兲.
关36兴F. R. Bennett, A. D. J. Critchley, G. C. King, R. J. LeRoy, and
I. R. McNab, Mol. Phys. 97,35共1999兲.
关37兴R. J. Le Roy, University of Waterloo Chemical Physics Re-
search Report No. CP-329R3, 1993 共unpublished兲, available at
http://leroy.uwaterloo.ca
关38兴R. J. Le Roy, University of Waterloo Chemical Physics Re-
search Report No. CP-555R, 1996 共unpublished兲, available at
http://leroy.uwaterloo.ca
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