Energy structure of hollow atoms or ions in the bulk of metallic materials
X. M. Tong,
1,
* D. Kato,
1
T. Watanabe,
1
H. Shimizu,
1
C. Yamada,
1,2
and S. Ohtani
1,2
1
‘‘Cold Trapped Ions’’ Project, ICORP, JST, Axis 3F, 1-40-2 Fuda Chofu, Tokyo 182-0024, Japan
2
University of Electro-Communication, Chofu, Tokyo 182-0021, Japan
Received 17 October 2000; published 13 April 2001
The local-spin-density functional method, with an optimized effective potential and self-interaction correc-
tion, is used to study the energy structure of hollow atoms and ions in the bulk of metallic materials. The
energy structure of conduction electrons in the bulk of metallic material is treated by the jellium model. Based
on this method, we have studied the x-ray spectra and Auger spectra of N
q+
hollow atoms and ions in the bulk
of Al, as well as in the vacuum. The experimental Auger spectra in the collision of N
6+
with an insulating
surface and conducting surface can be well understood based on our studies. Our calculated x-ray and Auger
spectra of hollow atoms or ions in the vacuum and in the bulk of material suggest the need for further
systematic experimental investigation.
DOI: 10.1103/PhysRevA.63.052505 PACS numbers: 32.30.Rj, 71.15.Mb, 36.20.Kd
The interaction of highly charged ions HCI’s with a sur-
face is a subject of increasing interest 1–3. Basically, three
steps are involved in the interaction of HCI’s with surfaces:
1 formation of hollow atoms or ions above the surfaces, 2
decay of hollow atoms or ions at or below the surfaces, and
3 total neutralization of hollow atoms or ions in the bulk of
materials 1. The formation of hollow atoms or ions is
strongly related to the HCI’s impact velocity, incident angle,
and other dynamic parameters 4. In the final neutralization
process, hollow atoms or ions emit Auger electrons 5,6 or x
rays 7–9. The emitted x rays provide static information of
hollow atoms or ions in the bulk of materials from the energy
position, and dynamic information from the spectral inten-
sity. Usually, the Hartree-Fock method is used to study hol-
low atoms or ions in vacuum 10,11, but the method cannot
provide detailed information about the hollow atom or ion in
the bulk of materials. To investigate the detailed information
of the hollow atom or ion in the bulk of materials, we need to
take the conduction-electron screening effect into account.
The conduction-electron screening effect was first studied by
Zaremba et al. 12 using density-functional theory. Re-
cently, Arnau et al. 13 used the local-density-functional
method to study the energy structure of hollow atoms and
ions in the bulk of metallic materials. The advantage of this
method is that the total energy of the N-electron system is a
functional of the total electron density. Like traditional local-
density-functional theory 14, this method contains a spuri-
ous self-interaction energy, which should be removed in the
exact calculation. To remove the self-interaction energy, we
use the local-spin-density-functional method with an opti-
mized effective potential and a self-interaction correction
method 15,16. This method was successfully applied to
study the atomic energy structure both in nonrelativistic 16
and relativistic 17 cases. Different from atoms or ions in
the vacuum, hollow atoms or ions in the bulk of metallic
materials interact with free electrons in the conduction band.
Here we treat the conduction electron using the jellium
model. The advantages of our method are that 1 we use
local-spin-density approximation, which allows us to study
the spin polarized hollow atoms or ions in the bulk of me-
tallic materials; and 2 we use the optimized effective po-
tential with self-interaction correction for bound electrons,
which can completely remove the bound electron self-
interaction energy. In our calculations, the Auger and x-ray
spectra of N
q +
hollow atomic ions obtained in the vacuum
and near the surface show dramatic differences. Based on our
calculated results, the shift and broadening of KLL Auger
spectra from N
6 +
collisions on the insulating LiF surface, as
compared to those from collisions on the conducting Si sur-
face, can clearly be understood. Meanwhile, the x-ray spectra
of a hollow ion in the vacuum can be measured through a
microcapillary experiment 18. Therefore, our theoretical
studies will call for a systematic experimental study of the
x-ray and Auger spectra of hollow atoms or ions in the
vacuum as well as in the bulk of materials.
The energy structure of the conduction electrons in a me-
tallic material can be represented by a jellium model 19. In
the jellium model, the discrete ion cores are replaced by a
homogeneous positive background charge, with the charge
density equal to the conduction-electron density due to the
neutralization requirement. For a given electron density , an
effective radius r
s
=(3/(4 ))
1/3
is defined, and the conduc-
tion electrons are filled up to the Fermi energy
F
=(1/
2r
s
2
)(9 /4)
2/3
. Using density-functional theory with an opti-
mized effective potential and self-interaction correction 16,
the total energy E
of a hollow atom or ion in the bulk of
metallic materials can be expressed as atomic units with
=m =e =1 are used throughout unless explicitly stated oth-
erwise
E
=T
s
+E
xc
↑
,
↓
+V
ext
+J
A
+E
SIC
b
-T
s
o
-E
xc
o
↑
,
o
↓
-V
ext
o
, 1
with *Email address: tong@hci.jst.go.jp
PHYSICAL REVIEW A, VOLUME 63, 052505
1050-2947/2001/635/0525054/$20.00 ©2001 The American Physical Society 63 052505-1