J. Plasma Fusion Res. SERIES, Vol.7 (2006) 199-202

Electron Capture Processes in Low Energy Collisionsof C4+ Ions with Excited H Atoms
SHIMAKURA Noriyuki, HONMA Mayumi1 and KUBO Hirotaka2
Faculty of Science, Niigata University, Niigata 950-2181, Japan
1 Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
2 Japan Atomic Energy Research Institute, Naka 311-0193, Japan（Received : 5 October 2004 / Accepted : 9 February 2006）

Abstract
Cross sections for electron capture in collisions of C4+ ions with H*(n = 2) atoms have been calculatedusing a molecular-basis close-coupling method in the collision energy range from 60 eV/amu to 6 keV/amu.
The calculated results show that electrons are dominantly captured in the n = 6 states of the C 3+ ions and themaximum of the total cross sections is about 900 × 10−16 cm2 and 600 × 10−16 cm2 in the C4+ (1s2 ) + H∗ (2s)and C4+ (1s2 ) + H∗ (2p) collisions, respectively.
Keywords:
electron capture, C V ion, excited H atom, Tokamak divertor, ion temperature, low energy collisionin collisions of C4+ ions with H∗ (n = 2) atoms havebeen calculated using a molecular-basis closecoupling method [7] in the collision energy range from
60 eV/amu to 6 keV/amu.

1．Introduction
It has recently been recognized that in tokamak divertors, emission from n = 6 and 7 states of C3+ ions
is sometimes quite strong and hence the measurementof spectral lines from C3+ (n = 5, 6, 7) ions is appropriate for study of carbon impurity behavior [1,2]. It is
anticipated that the C3+ (n = 5, 6, 7) ions are mainly
produced by electron capture by C4+ ions from excitedH∗ (n = 2) atoms. Therefore, the cross sections for electron capture are needed for analysis of the spectroscopicmeasurements. The cross sections for electron capture
in collisions of C4+ ions with ground H atoms have beenobtained by Bliek et al. [3] experimentally and by Tsengand Lin [4] and Errea et al. [5] theoretically. However,no estimation has been performed for the case of excitedH∗ (n = 2) atoms except for classical trajectory Monte
Carlo (CTMC) calculations by Zaniol et al. [1] at a collision energy of 1 eV/amu. On the other hand, Macekand Ovchinnikov [6] developed a simple model for electron capture from high n states of H atoms by multiplycharged ions and predicted that the cross sections depend upon n as n5 . They have insisted that this highn dependence explains why a small fraction (less than0.1 %) of hydrogen in high n states contributes 30 % of
the capture yield at 50 eV/amu in O5+ + H collisions.
Combining this model with the cross sections for theground H atoms, we can anticipate that the cross sections for the excited H atoms have maximum value ofabout 1000 × 10−16 cm2 .
In this paper, cross sections for electron capture

2．Calculation method
Since the details of the theoretical treatment in thispaper have already been described [7], only the specificinformation used for the present calculation is given below.
2.1 Electronic states and couplings

The electronic structures were calculated using
a generalized valence-bond configuration-interaction(CI) method with l-dependent Gaussian-type pseudopotential representing the C4+ (1s2 ) ion. Hence onlyone active electron was treated explicitly. The pseudopotential parameters were taken from the paper by
Kimura and Olson [8]. In the CI calculations, Slatertype orbitals (STOs) were used to construct basis sets.
The orbital exponents of the STOs were obtained by optimizing the energies of the respective electronic states.
The accuracy of the present electronic state calculations
with respect to the spectroscopic values [9] is better than
0.05 eV except for the C3+ (2s) and C3+ (3s) states, these
two states contributing only little to the electron capture.
We calculated the radial and rotational couplings
C 2006 by The Japan Society of Plasma

Science and Nuclear Fusion Research
Corresponding author’s e-mail: shima@shimakura.gs.niigata-u.ac.jp

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Electron Capture Processes in Low Energy Collisions of C4+ Ions with Excited H Atoms–16
2
4+Table 1 Partial n-shell cross sections (in 10 cm ) in C + H*(n = 2) collisions calculated with basis set A.

E (keV/amu)
C3+ (n = 2)
C3+ (n = 3)
C3+ (n = 4)
C3+ (n = 5)
C3+ (n = 6)
C3+ (n = 7)
C3+ (n = 8)0.248
0.018
0.630
4.504
32.22
182.3
112.6
8.955

0.558
0.022
1.490
5.031
33.53
189.2
125.7
18.25

0.992
0.079
2.646
6.894
36.68
180.6
125.0
24.15

with atomic-type electron translation factors (ETFs) tosolve the close-coupling equations. The ETFs were included to the first order in velocity.

1.550
0.231
5.443
7.582
26.79
184.0
113.4
16.36

3.038
0.417
5.076
9.478
41.32
170.3
133.9
11.96

5.022
0.820
4.276
8.458
40.19
141.3
131.5
14.62

6.200
0.952
5.263
7.711
40.66137.2
126.2
14.12

to the first dominant ones. The results by CTMC calculations has also shown that the most dominant states
were the n = 6 states, but the second dominant ones was
the n = 5 states at the collision energy of 1 eV/amu [1].
Both our calculated results and CTMC results show thatthe contributions of the C3+ (1s2 nl; n = 2, 3, 4) + H+
states to the electron capture are less than 3 % of thetotal cross sections.

2.2 Collision dynamics

A semi-classical molecular-state close-coupling
method was employed at collision energies from
60 eV/amu to 6 keV/amu. The coupled equations weresolved numerically under the assumption of straightline trajectories for the heavy-particle motion. Bysquaring the resulting amplitude, the transition probability was obtained as a function of collision energy
and impact parameter. The cross sections were given
by an integration of impact-parameter-weighted transition probability over the impact parameter.

3.2 Cross sections with basis set B

As described in the above paragraph, theC3+ (1s2 nl ; n = 2, 3, 4) + H+ states scarcely contribute to the electron capture under the condition
calculated in this paper. So, we next performed theclose-coupling calculations with the basis set B, inwhich not only the Σ states but also Π, ∆, and Φstates were included instead of the above-mentioned
non-eﬀective Σ states. The obtained results are shownin Figs. 1 and 2 for the C4+ (1s2 ) + H∗ (2s) andC4+ (1s2 ) + H∗ (2p) collisions, respectively. In order toconfirm the convergence of the cross sections to thesize of basis set, we also performed the calculations
removing nine Φ states from the basis set B for theC4+ (1s2 ) + H∗ (2s) collisions. The solid and broken
curves in Fig. 1 show the cross sections calculated withand without the Φ states, respectively. Both results

3．Results and discussion
The close-coupling calculations were performed using two kinds of basis sets. One basis set (basisset A) includes 31 channels of only Σ states fromC3+ (1s2 nl; nl = 2s, 2p, 3s – 3d, 4s – 4f, 5s – 5g, 6s– 6h, 7s – 7i, 8s) + H+ and C4+ (1s2 ) + H (1s, 2s, 2p)
states and the other (basis set B) includes 58 channelsof Σ, Π, ∆, and Φ states from C3+ (1s2 nl; nl = 5s – 5g,6s – 6h, 7s – 7i, 8s) + H+ and C4+ (1s2 ) + H (1s, 2s, 2p)
states.
3.1 Cross sections with basis set A

Calculations for the C4+ (1s2 ) + H (2s) and C4+ (1s2 ) +H (2p) collisions were performed separately. Table 1shows the partial n-shell cross sections obtained bysumming the calculated cross sections for the C4+ (1s2 )+H (2s) and C4+ (1s2 ) + H (2p) collisions with statisticalweights. This table shows that the most dominant states
for the electron capture processes are the n = 6 states
and the second dominant ones are the n = 7 states. The
sum of the contributions from the two states amounts
to about 90 % of the total cross sections over the collision energies treated in this paper. At higher collisionenergies, the contributions of the n = 6 states decrease
slowly with the collision energy and the contributions of
the second dominant n = 7 states become comparable

Fig. 1 Cross sections for the electron capture in the C4+ +H* (2s) collisions.

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Electron Capture Processes in Low Energy Collisions of C4+ Ions with Excited H Atoms

Fig. 3 Total cross sections for the electron capture in theC4+ + H (1s) and C4+ + H* (2l ) collisions.

Fig. 2 Cross sections for the electron capture in the C4+ +H* (2p) collisions.

so large compared with the value of 1000 × 10−16 cm2
which is anticipated by the Macek-Ovchinnikov modelusing the maximum value for the C4+ + H (1s) collisions. On the other hand, as described in the above
paragraph, our molecular-basis close-coupling calculations show that the total cross sections reach maximum
values of about 900×10−16 cm2 and 600×10−16 cm2 for
the C4+ (1s2 ) + H∗ (2s) and C4+ (1s2 ) + H∗ (2p) collisions,
respectively. The classical method like CTMC does notseem to be good at low collision energy of 1 eV/amu,
but in order to obtain more definite results about thispoint, we are performing full quantum calculations atlow collision energies. We can explain the reason why
the cross sections for the C4+ (1s2 ) + H∗ (2l) collisions isso large, as follows. The electrons in the H∗ (2l) states
distribute more widely than that in the H (1s) state, so
the C4+ ions can capture the electrons in the H∗ (2l)states even at larger distances compared with the caseof the H (1s) states. For the C4+ + H (1s) collisions, theelectrons are mainly captured into the C3+ (3l) states andthe region of the eﬀective avoided crossing for the electron capture is 6.5 ≤ RC (au) ≤ 8.0. On the other hand,for the C4+ (1s2 ) + H∗ (2l) collisions, the electrons aremainly captured into the C3+ (6l) states and the region of
the eﬀective avoided crossing is 20.0 ≤ RC (au) ≤ 30.0.
At lower collision energies, the transitions are localized
in the neighborhood of the avoided crossing points, so
only the C3+ (6l) + H+ states contribute mainly to theelectron capture. However, with increasing the collision energy, the electron capture occurs also at a wide
region of internuclear distances away from the avoided
crossing points, so the cross section for electron capture
into the C3+ (7l) states gradually becomes large.

are similar each other, so we can conclude that onlythe Σ, Π, and ∆ states contribute to the electron capture
processes. In Fig. 2, the partial n-shell and total
cross sections are shown for the C4+ (1s2 ) + H∗ (2p)collisions. The general trend of the cross sections
for the C4+ (1s2 ) + H∗ (2p) collisions is similar withthat for the C4+ (1s2 ) + H∗ (2s) collisions, but the crosssections for the former are a little smaller than thosefor the latter. As the case of basis set A, the mostdominant states are the n = 6 states over the collisionenergies treated in this paper and the second dominantstates are the n = 7 states at higher collision energies.
However, at lower collision energies the n = 7 stateschange oﬀ with the n = 5 states. Our results also showthat the captures into lower angular momentum states
dominate at low collision energies (E < 10 keV/amu),
but at higher collision energies the contributions of theeach angular momentum states become close to thestatistical weight.
3.3 The comparison of the cross sections calculated
for the C4+ + H∗ (2l) collisions with the cross sections for the C4+ + H (1s) collisions

In Fig. 3, all the available total cross sections for theelectron capture in the C4+ + H (1s) and C4+ + H∗ (2l)collisions are compared except for one calculation by
CTMC method at very low collision energy. Threegroups have reported the cross sections for the electron capture in the C4+ + H (1s) collisions [3 – 5]. Thereis about 30 % discrepancy among them, but roughly
speaking all the total cross sections give maximum values of about 30 × 10−16 cm2 at collision energy of about
250 eV/amu. On the other hand, the total cross section
obtained by CTMC method for the C4+ (1s2 )+H∗ (n = 2)
collisions is about 380 × 10−16 cm2 at a collision energy of 1 eV/amu. This value is pretty large, but is not

Acknowledgements
The authors would like to express their thanks to Dr.
T. Shirai and Dr. T. Ozeki of JAERI for their support
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Electron Capture Processes in Low Energy Collisions of C4+ Ions with Excited H Atomsand encouragement. This work was supported in partby Japan Atomic Energy Research Institute and by
a grant-in-aid for scientific research (No. 15540382)
and a grant-in-aid for scientific research on priority areas, “Control of Molecules in Intense Laser Fields”(Area No. 419) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

[4]
[5]

[6]
[7]

[1]
[2]

[3]

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