Production of the 2s2p2 2De triply excited state in collisions of
quasi-free electrons with He-like B3 , C4 , N5 , O6 , and F7
ions
E.P. Benis , M. Zamkov , P. Richard , T.J.M. Zouros† and K.R. Karim‡
James R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506-2604
†
Dept. of Physics, University of Crete, P.O. Box 2208, 71003 Heraklion, Crete, Greece
Institute of Electronic Structure and Laser, P.O Box 1527, 71110, Heraklion, Crete, Greece
‡
Department of Physics, Illinois State University, Normal, Illinois 61790-4560
Abstract. We report on a study of the isoelectronic sequence of the 2s2p2 2De triply excited state formed in collisions of
He-like B3 , C4 , N5 , O6 and F7 ions with H2 gas targets. The ions were prepared in a mixture of 1s2 1S ground state
plus 1s2s 3 S metastable state that allowed for the formation of the 2s2p2 2De state via the process of resonant transfer and
excitation (RTE). The electron yield from the decay of this state to the 1s2s 3S and 1s2p 3P states was recorded at zero degrees
with respect to the beam direction. Absolute singly differential cross section measurements were obtained after determining
the 1s2s 3S fraction for each ion beam experimentally. Fairly good agreement between the measured and calculated single
differential cross sections was observed.
state ion beams in thin (5 µ g/cm2) carbon foils. The Helike ion beams were then magnetically selected and focused in a 5 cm long differentially pumped gas cell to
be collided with H2 gas targets. The electron emission
spectra were obtained at zero-degrees with respect to the
beam axis with a single-stage high-efficiency hemispherical spectrograph utilizing a focusing/decelerating lens
system and a large (40 mm active diameter) position sensitive detector [4]. A FWHM resolution of 0 3% in the
projectile rest frame was attained after decelerating the
electrons by a factor of F 4. All spectra shown here
were recorded in one shot by tuning the spectrograph
at the appropriate tuning energy and deceleration factor
(F 4). The beam current was collected in a shielded
Faraday Cup (FC) using electron suppression located at
the exit aperture of the spectrograph, and was used for
the data acquisition charge normalization. Single collision conditions were ensured by using an H2 target pressure of 20 mTorr.
INTRODUCTION
Li-like triply excited states represent a fundamental case
of a four-body Coulomb system dominated by electronelectron interaction. These states, also referred to as hollow states, have received increased attention over the last
decade, studied primarily with the method of photoexcitation by synchrotron radiation (see for example Ref. [1]
and Refs. therein). However, to date, only Li excited
states have been studied with the above method, while
only a few data from the use of the beam-foil technique
are available for other elements [2].
In this paper we report first time systematic experimental results on the Z-dependence of the formation of
the 2s2p2 2De triply excited state in collisions of He-like
B3 , C4 , N5 , O6 , and F7 ions with H2 gas targets.
The initial ion beams were prepared in a mixed 1s2 1S
ground state and 1s2s 3 S metastable state of well known
fractions. The state was populated via the process of RTE
[3] from the 1s2s 3 S metastable part of the beams.
DATA ANALYSIS AND CALCULATIONS
EXPERIMENT
The spectra were energy calibrated with the use of a typical oscilloscope tube electron-gun. The ion beams’ kinetic energies were determined after aligning the measured 1s2p2 2D Auger line with the theoretically calculated values [2]. The experimental Double Differential
The experiments were performed in the J.R. Macdonald
Laboratory at Kansas State University, using the 7 MV
EN tandem Van de Graaff accelerator. The ion beams
were produced by post-stripping the appropriate charge-
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
168
Cross Section (DDCS) was obtained according to the formula:
d 2 σi
dΩd εi
DDCSi Nei DTC
NI L n ∆Ω ∆Ei T ηi
is the Compton profile, which gives the probability to
find the target electron with a z-momentum component
pz . ΩRES is the resonant excitation strength given by: [10]
(1)
ΩRES where i refers to the i-th channel, Ne is the number
of electron counts, DTC is the data acquisition dead
time correction, NI is the number of ions collected at
the FC, L is the length of the gas cell, n is the target
number density, ∆Ω is the solid angle subtended by
the lens entrance aperture, ∆E is the energy step of the
spectrum per channel, T is the transmission of the two
grids used in the spectrograph and η is the detector’s
efficiency. The average efficiency value was determined
by normalizing the 4.0 MeV B3 + H2 Binary Encounter
electron (BEe) spectra to the Electron Scattering Model
(ESM) calculations [5] (see below). An overall efficiency
determination of 20% was established in this way. The
absolute uncertainty was estimated to be about 20%.
A very crucial factor in obtaining absolute cross section data is the determination of the beam’s 1s2s 3S
metastable fraction. Recently, we published a series of
studies on the determination, production mechanism, energy dependence and control of the metastable part of
He-like ion beams for Z=5-9 [6, 7, 8]. The metastable
fraction assignments adopted in this paper are based on
these publications. The absolute uncertainty for the fractions was estimated to be about 30% resulting in an overall absolute uncertainty of 35%.
A comparison of the theoretical predictions to the
measurements was made possible by the use of the ESM
calculations also known as the Impulse Approximation
(IA) [9, 3]. According to the IA, in fast ion-atom collisions the atom-target electron is considered as “quasifree”, localized only by the target nucleus, which plays a
role of spectator in the collision process. Under the ESM,
the zero-degree (θ 0 at the lab frame corresponds
to θ 180 to the ion’s rest frame) Single Differential
Cross Section (SDCS) for the process of RTE followed
by Auger decay (RTEA) is described by the following
formula [3] (atomic units throughout):
where
RESULTS AND DISCUSSION
In Fig. 1 the normalized electron yields obtained in
collisions of B3 , C4 , N5 , O6 , and F7 mixed
(1s2 1S 1s2s 3S) state beams with H2 targets are shown.
The spectra
were transformed to the ion’s rest frame,
while the non-resonant BEe continuum was subtracted
after being fit with a polynomial. The shaded peaks are
the ones identified as the triply excited states formed by
RTE from the 1s2s 3S metastable part of the ion beams.
Recent R-matrix electron
elastic scattering calculations
involving pure B3 1s2 1S ground state beams in collisions with H2 atoms [13] were used as a benchmark
to identify the Li-like doubly-excited states. Then, theoretical calculations on energies and Auger rates for the
Li-like triply-excited states from Ref. [11] were utilized
to identify the triply-excited states. In this way, the intermediate 2s2p2 2De state, which Auger decays to the
1s2s 3S or the 1s2p 3P states, became evident in the spectra. Recently, the formation of the 2s2p2 2De state from
the initial 1s2s 3S state was verified in an experiment that
involved pure ground state and mixed state B3 beams
[14]. Also, in a recent paper [12], it was shown that RTE
is the main process contributing to the formation of the
2s2p2 2De state from the initial 1s2s 3S metastable state.
Therefore, the Auger decay to the 1s2s 3S state corresponds to the elastic scattering channel, while the decay
to the 1s2p 3P state corresponds to the inelastic scattering
channel.
The rest of the peaks shown in the spectra correspond
to the formation of the Li-like doubly excited states from
the 1s2 1S ground state part of the beam. An exception
is the case of B3 , where the He-like doubly excited
2s2p 3P state, formed mainly by 1s 2p excitation from
the 1s2s 3S metastable part of the beam, is also present.
From the spectra in Fig. 1 it is evident that the doubly
and triply excited states have different Z-scaling for their
transition energies. Thus, in the case of B3 the triply excited states are located almost after the series limit of the
doubly excited states, while for the case of O6 they are
located right before the threshold of the doubly excited
states. For the cases of C4 and N5 , their energy spans
(2)
pz 2 ε EI Vp
(3)
is the z-momentum component of the electron, z being
the beam direction. Vp is the ion beam velocity, ε is the
electron kinetic energy in the ion’s rest frame, and EI is
the ionization potential of the target electron.
J pz d px d py ψ p 2
(5)
Here, Li Ld and Si Sd are the angular momentum and
spin quantum
numbers
of the initial i and intermediate
d states, respectively, ER is the RTE resonance energy,
Aαd i is the Auger transition rate and ξ is the Auger yield.
2L
1 J pz d σRT EA θ 180 ΩRES d dΩ
4 π V p pz π 2h̄3 2Ld 1 2Sd 1 Adα i
ξ
2
2Li 1 2Si 1 ER
(4)
169
qr
â ã
œ ž Ÿ¡
¢£¥¤ ¦ § ¨¥© ª
«¬ ­®&¯&° ±² ³&´¥µ ¶
·¥¸ ¹º&» ¼½ ¾#¿ À ÁÃÂÄ
op
s/tvuxw yz {
mn
ÿ
kl
þ
Œ Ž
€
j
i
úûýü
ù
™š ›
~
|}
“”
†‡
g
ß
ð
í îï
ëì
èéê
ç
äåKæ
âã
ß àá
ñò
l
íî
Ý
üý
ëì
|}
‰Š
z{
xy
i
À Á ÂÄà ŠÆÈÇ É ÊÈË Ì ÍÏÎ Ð ÑÈÒ Ó ÔÄÕ Ö ×ÄØ Ù Ú
a6b c
^ _`
[ \]
X YZ
U VW
R ST
O PQ
L MN
I JK
F GH
C DE
ýþ ÿû ü
j
úû
‡ˆ
…†
h
!#" $%& ')(+*-, .0/ 1+243 567 89+:;=< >@? A4BDCFE
€
~
Ž
‹Œ
g
ìsí‰î¦ï ðñ ò
k
øù
Ü
 ‘
‚ƒ „
ïð
‚ƒ
p#q#rts uFv w
m
Û
é-ê ë
æ-ç è
ã-ä å
à-á â
Ý-Þ ß
Ú ÛÜ
× ØÙ
Ô-Õ Ö
Ñ-Ò Ó
’+“” •-–—˜™›šFœ  ž Ÿ¡ ¢+£D¤ ¥§¦-¨© ª@« ¬+­® ¯4°²± ³-´-µ¶¸· ¹Fº »4¼¾½0¿
n
þÿ
Þ
9 : ;=< > ?A@ B CAD EGFAH IKJ7L M NPO Q RPS T U7V W XPY Z []\ ^ _P`a bPcd e
ñò ó
óô
„…
f
ôõ
o
äåæ4ç èé ê
õö ÷
Š‹
ˆ‰
‘’

h
ö ÷ø
—˜
•–
!#" $&%' (*) +,&-/.10 23 4*5768
à á
÷ øùõ úö
óô
§ ¨ ©«ª ¬ ­«® ¯ °²± ³ ´¶µ · ¸¶¹ º »¶¼ ½ ¾¶¿ À6Á«Â Ã Ä«Å Æ Ç«È6É Ê«Ë-Ì Í«Î Ï Ð
G H IKJ L MON P QKR S TOU V)WOX Y)ZK[ \ ]O^ _ `Ka b cOd e f
qsrut vxwzy|{~}€~ ‚ ƒ „u… †~‡‰ˆ ŠŒ‹xŽ ’‘ “x”–• —~˜–™ šx›Œœs’ž Ÿ’ ¡s¢¤£¦¥
no pl m
h ijf kg
de
! " #%$ & '%( ) *%+-, .!/-0 132 465!7 8 93: ; <3= > ?3@ A B
ÅÇÆ È=ÉËÊÍÌ#ÎÐÏÒÑÇÓPÔÐÕÖA×ÙØÛÚAÜÞÝ
FIGURE 1. Normalized electron yields obtained in collisions of B3 , C4 , N5 , O6 , and F7 mixed state (1s2 1S 1s2s 3S)
beams with H2 targets. Shaded peaks are the ones identified as the triply excited states formed by RTE from the 1s2s 3S metastable
part of the ion beams. Both peaks correspond to the same intermediate 2s2p2 2De state but different final states. The Auger decay
to the 1s2s 3S state corresponds to the elastic scattering channel while the decay to the 1s2p 3P state corresponds to the inelastic
scattering channel. The rest of the peaks correspond to the formation of the Li-like doubly excited states from the 1s2 1S ground
state part of the beam, with the exception of the B3 case where the He-like doubly excited 2s2p 3P state is also present. In the case
of C4 the inelastic branch is not indicated as it is embedded in the spectrum of doubly excited states. Solid lines are Gaussian fits
to the data.
overlap, however the transition 2s2p2 2De 1s2s 3S is
well resolved from the neighboring 1s2l2l | 1s2 1S transitions. In the case of C4 the inelastic part is not indicated as it is embedded in the spectrum of doubly excited
states.
It is very interesting to see that in the case of F 7 the
inelastic peak is not evident in the spectrum. The fact is
not well understood as calculated Auger decay rates vary
slightly with the atomic number Z [11].
The Auger rates in Ref. [11] were used, after statistically averaging the 2Dej 3 2 and 2Dej 5 2 substates, within
Eq. (5) to obtain the theoretical ΩRES in each case. Then,
applying the IA by using Eq. (2), the SDCSs were calculated. The Auger yield was estimated from the ratio
of the state’s partial Auger rate to the total Auger obtained from Ref. [11]. The radiative decay channel was
not considered since it is negligible for all Z=5–9. Also,
the COWAN code was utilized to calculate the transition
energies and Auger rates for the case of boron.
Absolute experimental SDCSs were obtained after fitting the normalized electron yields with Gaussians having the same FWHM as the spectrograph’s resolution and
dividing the obtained integrated electron yields with the
metastable fraction of the beam in each case. The experimental ΩRES were obtained from the experimental SDCSs with the use of Eq. (2).
The theoretical and experimental results are presented
in Table 1, where it is evident that the calculations, both
from Ref. [11] and COWAN code are in fairly good
agreement with the measurements.
CONCLUSIONS
The iso-electronic sequence study of the formation of
the 2s2p2 2De triply excited state in collisions of Helike B3 , C4 , N5 , O6 , and F7 mixed (1s2 1S 1s2s 3S)
state beams with H2 targets was reported. The state
was
3
populated via RTE from the 1s2s S metastable part of
the beams and two decay channels, the elastic scattering
(decay back to the 1s2s 3S state) and the inelastic scattering (decay to the 1s2p 3P state) were identified. Absolute zero-degree SDCSs were obtained for the elastic
scattering channel after determining the 1s2s 3S fraction
for each ion beam experimentally. Fairly good agreement
between the measured and calculated SDCSs was found.
170
REFERENCES
21 8
8 3
10 4
4 1.4
SDCSexp
16 6
1.
SDCSth
2.
4.1 0.8
3.2 1.1
0.03
0.08
0.05
0.08
4.
5.
1.6
0.6
1.1
0.5
2.1
1.9
1.6
1.0
0.10
0.25
0.15
0.25
Y
Ωexp
RES
6.
4.4
1.8
3.0
1.5
7.
3 84
6 31
4.50
3.37
2.62
2.09
Ωth
RES
3.
0.4
0.4
0.3
0.2
f [12]
0.25 0.08
19 4
32 0
21.4
14.1
9.4
5.7
ξ
8.
0.56‡
0.56‡
0.56‡
0.56‡
0.56‡
9.
10.
Aα
17 03
28‡
28‡
28‡
28‡
28‡
206 6
205 12†
287.71†
384.25†
494.47†
618.42†
N5
O6
F7
C4
12.
13.
14.
‡
11.
This work
From Ref. [11]
Read from Figs. 7 and 8 in Ref. [11]
†
B3
Z state
287.2
384.1
493.4
618.1
0.5
0.5
0.5
0.5
205.4 0.5
Eexp
R
Eth
R
TABLE 1. Calculated and experimental resonance parameters for the production of 2s2p2 2De intermediate state. ER is the Auger
decay energy in units of eV, Aα the Auger decay rate in units of 1013 s 1 , ξ the Auger yield, ΩRES the resonant excitation strength
in units of 10 18 cm2 eV, Y the normalized electron yield in units of 10 21 cm2 /sr, f the 1s2s 3S metastable fraction and SDCS the
single differential cross section in units of 10 21 cm2 /sr.
ACKNOWLEDGMENTS
This work was supported by the Division of Chemical
Sciences, Geosciences and Biosciences, Office of Basic
Energy Sciences, Office of Science, U.S. Department of
Energy.
171
Madsen, J. N., Schlagheck, P., and Lambropoulos, P.,
Phys. Rev. Lett., 85, 42–45 (2000).
Rødbro, M., Bruch, R., and Bisgaard, P., J. Phys. B, 12,
2413 (1979).
Zouros, T. J. M., “Resonant Transfer and Excitation
Associated with Auger Electron Emission,” in
Recombination of Atomic Ions, edited by W. G. Graham,
W. Fritsch, Y. Hahn, and J. Tanis, NATO Advanced
Study Institute Series B: Physics, Plenum Publishing
Corporation, New York, 1992, vol. 296, pp. 271–300.
Benis, E. P., Zouros, T. J. M., Aliabadi, H., and Richard,
P., Physica Scripta, T80B, 529–31 (1999).
Richard, P., “Two-center effects in Electron Spectra from
Ion-Atom Collisions,” in Two-Center Effects In Ion-Atom
Collisions, edited by T. J. Gay and A. F. Starace, American
Institute of Physics Conference Series, New York, 1996,
vol. 362, p. 69.
Zamkov, M., Aliabadi, H., Benis, E. P., Richard, P.,
Tawara, H., and Zouros, T. J. M., Phys. Rev. A, 64, 052702
(2001).
Zamkov, M., Benis, E. P., Zouros, T. J. M., and Richard,
P., Phys. Rev. A, 65, 062706 (2002).
Benis, E. P., Zamkov, M., Zouros, T. J. M., and Richard,
P., Phys. Rev. A, 65, 064701 (2002).
Brandt, D., Phys. Rev. A, 27, 1314 (1983).
Kilgus, G., Berger, J., Blatt, P., Grieser, M., Habs, D.,
Hochadel, B., Jaeschke, E., Krämer, D., Neumann, R.,
Neureither, G., Ott, W., Schwalm, D., Steck, M., Stokstad,
R., Szmola, E., and Wolf, A., Phys. Rev. Lett., 64, 737–40
(1990).
Safronova, U. I., and Bruch, R., Physica Scripta, 57, 519
(1998).
Zamkov, M., Benis, E. P., Zouros, T. J. M., and Richard,
P., Phys. Rev. A, 65, 032705 (2002).
Zouros, T. J. M., Benis, E. P., and Gorczyca, T. W.,
submitted to PRL, (2003).
Benis, E. P., Závodszky, P. A., Zouros, T. J. M., Aliabadi,
H., and Richard, P., “Production of triply excited states
in Li-like boron,” in XXI ICPEAC, Sendai, Japan,
edited by Y. Itikawa, K. Okuno, H. T. A. Yagishita, and
M. Matsuzawa, AIP, New York, 1999, p. 505.