Resonant (RTE) and Non Resonant (NTE) Transfer
Excitation in 4 MeV B4 collisions with H2, He and Ar
studied by zero-degree Auger projectile electron spectroscopy
T.J.M. Zouros , E.P. Benis† , A.D. González† , T.G. Lee† , P. Richard† and T.W.
Gorczyca †
Department of Physics, University of Crete and IESL-FORTH, P.O. Box 2208, 71003 Heraklion, Crete, Greece
James R. Macdonald
Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506-2604
Department of Physics, Western Michigan University, Kalamazoo, MI 49008
Abstract. It is well known that for very asymmetric collisions between a highly charged ion and H2 near the RTE resonance,
NTE is practically negligible. However, even though the interplay between RTE and NTE and their possible interference
has been addressed formally and more recently by concrete calculations, experimentally very little work has been done
on fast collision systems of increasing symmetry. We report on recent Auger electron RTE/NTE double differential cross
section measurements of H-like B4 ions in 4 MeV collisions with H2 , He and Ar gas targets. Calculations using an atomic
orbital close coupling (AOCC) method indicate NTE to be negligible for B4 collisions with H2 , but possibly substantial
(depending on screening considerations) for He and Ar targets. R-matrix calculations are also presented for elastic (resonant
and non-resonant) electron scattering from B4 . Within the electron scattering model (ESM), the active target electron can
be considered to scatter as a free particle with a momentum distribution governed by its Compton profile. Thus, a single
R-matrix calculation combined with the individual momentum distribution of each target should be sufficient to describe the
RTE process. While this is found to be the case for H2 and He, results for Ar are not in such good agreement, even allowing
for the possibility of destructive RTE-NTE interference.
INTRODUCTION
the projectile, (as viewed from the projectile frame), the
“quasi-free” target electron can be considered to scatter
from the projectile ion as a free particle with a momentum distribution (due to its orbital motion around the target) given by its Compton profile.
The quasi-free target electron may also scatter elastically without forming bound resonant states. This process is just a particular case of target ionization in ionatom collisions giving rise to the well-known Binary Encounter electron (BEe) peak. Its free electron analogue is
the process of non-resonant elastic scattering. The production of BEe has been extensively studied over the past
ten years, investigating the dynamics of small impact parameter collisions (for recent reviews, see Refs. [12, 13]).
Simple scattering models have been found to be adequate
for an accurate prediction of the BEe peak shape, magnitude and position [14, 15, 16, 17, 18].
Recently, a coherent RTEA (RTE followed by Auger
decay)-BEe treatment [19] has been made possible by
combining R-matrix calculations with the ESM [19, 20].
Combined resonant and non-resonant elastic scattering
R-matrix calculations have been shown to be successful
in treating scattering of quasi-free electrons of H2 from
H-like ions (Z=5-9) [20, 11] and from He-like B3 ions
Transfer-excitation (TE) in energetic ion-atom collisions
is a two-electron process involving the transfer of a target
electron to the projectile with the simultaneous excitation
of a projectile electron (in the same collision), giving
rise to doubly-excited states. If the excitation is due
to the Coulomb interaction between the transferred and
projectile electrons, TE is a correlated process known
as RTE [1, 2, 3, 4]. TE can also occur by uncorrelated
one-electron excitation and transfer events mediated by
electron-nucleus interactions, in which case it is referred
to as NTE [1, 2, 3, 4, 5, 6, 7]. The study of TE, and
in particular of RTE, has received considerable attention
in the last fifteen years [3, 4] since it can provide direct
information on electron correlation phenomena of great
and continuing interest in atomic physics.
Theoretically, RTE has been successfully described
by the impulse approximation (IA) [8, 1, 9] within the
framework of the ESM [10, 11]. To the extent that the
active target electron can be considered free, RTE can
be seen as the analogue of the time-reversed Auger effect [1]. Thus, in collisions where the velocity, vt , of the
target electron is much smaller than the velocity, Vp , of
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
36
R
[11]. The H2 target is well-known to have negligible contributions from NTE [21, 22] in very asymmetric collisions. However, as shown in recent calculations [21], as
the target atomic number Z increases, e.g. with He and Ar
targets, NTE is expected to play an increasingly important role and may even destructively interfere with RTE
[9, 21]. NTEA (NTE followed by Auger decay) contributions are expected to only affect the production of
the bound doubly-excited states, but not the BEe part of
the electron spectrum. Contributions from processes described by quasi-free scattering (RTEA and BEe) should
be proportional to the R-matrix elastic scattering singledifferential cross-section (SDCS). Processes due to the
influence of the target nucleus, lying outside the ESM
frame work, however, will not be proportional to this
SDCS. Thus, by comparing the measured double differential cross sections (DDCS) to the R-matrix calculations, any observed differences should be attributable
to other processes outside the ESM, such as NTE.
In this study, we report on high resolution RTEA
measurements of the B3 2l2l doubly excited states,
formed in collisions of 3.92 MeV B4 with H2 , He
and Ar targets performed by zero-degree Auger projectile electron spectroscopy (ZAPS) [16]. Absolute DDCS
were obtained by normalizing to Rutherford scattering
BEe measurements for 13 MeV B5 + H2 . R-matrix calculations are also provided to describe 180 elastic (resonant and non-resonant) electron scattering from the B4 ions [11]. Finally, NTE calculations within a standard
semi-classical impact parameter atomic orbital closecoupling method (AOCC) are also presented to assess the
strength of the NTEA process.
œ ž]Ÿ
˜™š ›
• –—
1 2
1 2
V vzVp v EI
i
2 p
2 z
N
with
f ree
f ree
J vzi vzi ∑ Vpi i
vzi ǻ 2 E EI Vp
(3)
obtained by solving Eq. 1 for vz . The Compton profile,
Ji vzi , gives the probability of finding the target electron
in the i-th subshell with a velocity component vzi . The
index i in Eq. 2 runs over all target electron subshells
satisfying the basic IA assumption, i.e. Vp ¬­¬ vti , which
at Vp 3 8 a.u. (3.92 MeV) includes only the Ar 3s
and 3p electrons [15]. Calculated Hartree-Fock Compton
profiles are available in the literature [23], while for H2
and He targets, analytic expressions have been fitted to
high energy electron scattering measurements [24, 20].
In Fig. 1 we compare the Compton profiles of H2 , He
and Ar 3s 3p . H2 is seen to have the narrowest profile,
while He and Ar 3s 3p are comparable in width.
The theoretical elastic electron scattering SDCS,
d σ E ® θ i¯ dΩ, was obtained using an R-matrix method.
First, a basis set of orbitals nl ±° 1s ® 2s ® 2p ® 3s ® 3p ® 3d ²
was determined from Hartree-Fock calculations [25]
for the 1snl configurations for B4 . Then all nln l (n ® nl 2 ® 3) configurations were used to describe the 11
lowest states of B3 . A basis of 40 additional orbitals
was coupled to these configurations to represent the resonance or continuum wavefunctions. With this atomic
structure, the R-matrix suite of codes [26, 27] was utilized to compute scattering transition matrices Ti³ f E .
For the present investigation, a new code, based closely
on the work of Griffin and Pindzola [28], was developed
to compute the differential cross section at each energy
E from Eq. 4 in Ref. [28]. Since that expression involves
cross-terms between lower and higher partial wave symmetries L, we found it necessary to include more partial
(1)
i
"! #$ %"& ')( *,+ -/. 021 3/4 576)8 9;:)< =?>)@ A;B/C DFEHG IKJHL M
¡s¢¤£ ¥W¦ §q¨ ©
i
components of v perpendicular to V p Vp ẑ, which are
assumed to be much smaller than Vp , are neglected [14].
The free electron-ion scattering SDCS is then related to
the quasi-free electron-ion scattering DDCS by
d σ E θ dΩ SUTWVYXZ []\_^a` bdc e f gih
jlknm oqpsrqtvuxw
yaz|{ }~W€ i‚iƒ
„†…ˆ‡ ‰sŠW‹ Œd
FIGURE 1. Compton profiles Ji vz for H2 , He and Ar normalized at the Ar Compton profile maximum for comparison.
In the case of Ar only contributions of 3s 3p electrons are
included. The normalization factors are shown in parenthesis.
EI is the i-th target subshell ionization potential. The
d 2 σ E θ dΩ dE quasi O
Ž 
In the ESM, the bound target electron, as seen from
the rest frame of the ion, is considered to interact as
a free electron, with its velocity distribution given by
its Compton profile J vz [1]. Thus, the velocity of the
impinging quasi-free electron V , is related to the ion
velocity V p by the frame transformation, V V p v.
The
velocity v of the electron due to its bound motion around
the target atom and E, its kinetic energy in the ion rest
frame, are related (in a.u.) by [14]
1
V p v 2 EI
i 2
P
’ “”‘
ESM AND R-MATRIX CALCULATION
E
Q
(2)
37
ç
öø÷
ÿ
NTE CALCULATIONS
The SDCS for NTEA at zero-degree observation can be
calculated from the expression [7]:
ih
2L 1 4π
σNT E E p ® ML 0 ξ
0
mexc
2π ¶ Pcmc b E p Pexc
b E p δ mc ab
´
>
Z[
XY
=
mexc · 0 bdb
(5)
š<›
¿ÁÀ‰Â‰ÃJÄ
Å
ÆÈÇÉÁÊÌËJÍ
– —
”<•
“
ýþ
ûü
¦§
¤¥
¢¡ £
žŸ
ÿ
!"#$%&'( )*,+-.0/124365798:<;
˜™
’
¨ª© «­¬¯®±°³²µ´·¶¹¸»º0¼¾½
ÎpÏÐ Ñ
ÒÈÓ ÔÖÕ× Ø Ù ÚÜÛ ÝÞ ß à á â
ãÈä åÖæç è é êÜë ìí î
ïÈð ñÖòó ô õ öÜ÷ øù ú
œ
‘


jk6lmnporqs6tu v6wrx yz{ |}~ 6€r ‚ƒ9„6…6†4‡‰ˆŠŒ‹‰Ž
!#"%$'&)(+*,.-
FIGURE 2. Zero-degree electron spectra for collisions of
3.92 MeV B4 with H2 , He and Ar targets in the range of 184204 eV in the ion rest-frame. Also shown are the theoretical
DDCS which were computed using the R-matrix SDCS calculation and the Compton profiles Ji as given by Eq. 2.
Z2 Z3 r µ e ¹ Z4 r
r
was used to represent the B4 ion
and the He and Ar targets. Two separate calculations are
performed for the capture and excitation processes. The
parameters Zi for capture are fitted so that the binding
energies of the quasi one electron are close to the experimental values. However, for the Ar/He-B4 excitation
process, we fitted the potential parameters Zi for Ar and
He to the static potential, using the electron densities calculated from analytic Hatree-Fock-Slater wave functions
made up of normalized one-electron orbitals [30]. The
purpose of this is to ensure that, in the separated atom
limit, the excited ion B4 only sees a neutral Ar or He
atom. Therefore capture and excitation were represented
by different sets of parameters ° Zi ² . Calculated NTEA
SDCS (Eqs. 4-5) are shown in Fig. 3. For 4 MeV collisions of B4 with H2 and He (screened),NTEA is negligible contributing with less than 1 º 10 » 20 cm2 ¯ sr. Howr ?
\]
VW
BDC6E F
GDHJILK6MONQP R
SUT
@
_` ^
mexc ®
where Pcmc b ® E p and Pexc
b E p are the capture and excitation probabilities, respectively, with magnetic quantum numbers mc mexc ML 0. For Vp ¬­¬ 1 0 a.u.,
it is legitimate to employ the one electron model in our
calculation. Briefly, in this model, the time-dependent
wave function of the active electron is expanded in terms
of traveling atomic orbitals placed at both centers. The
transition amplitudes to particular nlm states were obtained by solving the time-dependent coupled differential equations for each impact parameter and energy. A
quasi one-electron pseudo-potential of the form V r ¸
Z1
¼/½d¾À¿/Ái«Ã/ÄdÅÀÆ/ÇiÈ«É/ÊdËÍÌ)ÎdÏÀÐ/ÑiÒ«Ó/ÔiÕ×ÖqØiÙÛÚqÜdÝ×Þqßsà
A
c de
where L and ML are the total angular momentum and
magnetic quantum number, respectively, of the intermediate doubly-excited state (e.g. L 2 for the 2p2 1D state)
and ξ is the Auger yield for the particular decay channel. The factor ´ 2L4π 1 µ σNT E E p ® ML 0 accounts for
the electron emission at zero-degrees. The state-selective
NTE cross section, σNT E E p ® ML 0 , can be calculated
from a standard semi-classical impact parameter atomic
orbital close-coupling method (AOCC) [29]
σNT E E p ML
áâ
fg
(4)
ìlíïî_ðvñnòôó õ
åæ
ãä
ûüý þ
ùú
d σ E p ® 0 ]
dΩ
èlévê ë
waves than are needed to converge the total cross section
(which does not involve cross-terms); partial waves up to
L 9 were used. A final convolution with the analyzer’s
response function to account for the 0.5 eV resolution
enabled a direct comparison to the data using Eq. 2 as
seen in Fig. 2.
ever, for He (unscreened) and Ar targets, NTEA is / 10
times stronger and could be important.
In Fig. 2 we present our zero-degree electron spectra
for 3.92 MeV B4 collisions with H2 , He and Ar targets
in the range of 184-204 eV in the ion rest-frame. The
ZAPS [16] apparatus has been already described [31] and
is not presented here. Single collision conditions were
verified for the pressures used, i.e. 20 mTorr for H2 /He
and 5 mTorr for Ar, respectively. The strong line around
193.5 eV is due to the 2p2 1D resonance, which cannot
be resolved from the lower intensity 2s2p 1P line at 194.2
eV. Other observed lines are the 2s2 1S at 186.2 eV and
2s2p 3P at 187.5 eV. In the case of He and Ar these lines
are stronger due to NTEA.
38
~
z { |}y
C+DFE
@BA
m nop
fgh
3.
0
1
4.
JLK
PRQTSVUXWY[Z \^]
_'`
acb
de
;=< >
576 8:9
2.
MON
σ
kl
ij
ž[ŸV ¡ ¢£
¤'¥Ž¦¨§V©[ª=«:¬ ­V®”¯:°V±V²
³c´¶µ¨·¹¸[º=»[¼ ½¹¾”¿[ÀVÁ¹Â
ÃcĶŠÆ=Ç:È ÉVʔË:ÌVÍVÎ
ÏÐRÑ Ò=Ó[Ô ÕVÖ×[ØVÙ¹Ú
?
Ω
uvxt w
qrs
I€‚„ƒ†…7‡‰ˆ†Š„‹TŒŽ[
5.
6.
GIH
2
!‘:’”“ •V–.—˜š™V›œ
3
4
7.
8.
FIGURE 3. Lines: NTEA SDCS model AOCC calculations
for the production of zero-degree electrons from the 2s2p 1P
and 2p2 1D states in B4 collisions with H2 ( Û 2H), He and Ar
(3s+3p electrons only). NTEA with the excitation due to either
a screened or an unscreened He nucleus are compared. Data:
measured SDCS from Fig. 2.
9.
10.
11.
12.
13.
It is important to realize that the same single R-matrix
SDCS is multiplied in each case by the appropriate
Compton profile as indicated in Eq. 2. Only R-matrix
results are included in Fig. 2 and thus any deviations
in the agreement of the R-matrix results with experiment should be attributable to NTE. In Fig. 2, we note
that for all three targets, the non-resonant (BEe continuum) part of the spectrum is very well reproduced. In the
case of H2 and He, the resonant part is also in excellent
agreement with the calculation, indicating practically no
NTEA. However, in the case of Ar 3s and 3p contributions, the resonant ESM result is seen to be larger than
experiment even though the non-resonant part is well reproduced. This discrepancy is even more puzzling in as
much as any NTEA contribution incoherently added to
the R-matrix results, would make the discrepancy for Ar
even larger. Destructive RTEA-NTEA interference, although in principle possible [9, 21, 32], has never been
experimentally proven. Clearly, more work has to be performed both in the collisional energy dependence and in
the target dependence using other less complicated targets such as Li. We are in the process of such further
investigations.
Work partially supported by the Division of Chemical
Sciences, Geosciences and Biosciences, Office of Basic
Energy Sciences, US Department of Energy. TWG was
supported in part by NASA Space Astrophysics Research
and Analysis Program Grant NAG5-10445.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
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