Photoionization of doubly-charged scandium ions
A. M. Sossah, H.-L. Zhou, and S. T. Manson
*
Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA
Received 23 September 2008; published 11 November 2008
Photoionization cross-section calculations are performed for the ground Ne3s
2
3p
6
3d
2
D
3/2
e
and the first
two excited states Ne3s
2
3p
6
3d
2
D
5/2
e
, Ne3s
2
3p
6
4s
2
S
1/2
e
of doubly-charged scandium Sc
2+
for photon
energies from threshold to 68.0 eV. The discrete Sc
3+
orbitals are generated using the computer program
AUTOSTRUCTURE; 24 configurations are included in the configuration-interaction calculation for Sc
3+
. In addi-
tion to the nonrelativistic LS-coupling R-matrix, we have used the relativistic Breit-Pauli R-matrix method
to carry out the calculations to focus on relativistic effects. Relativistic and nonrelativistic results are compared
to demonstrate the influence of relativistic effects. The prominent 3p →3d giant resonances are analyzed and
identified, and our calculated positions and widths are compared with experimental results. Total oscillator
strength calculations suggest that the experimental cross section is too small and should be multiplied by a
factor of 1.63; with this factor, rather good agreement between theoretical and experimental cross section is
found.
DOI: 10.1103/PhysRevA.78.053405 PACS numbers: 32.80.Fb, 32.80.Zb
I. INTRODUCTION
Open-shell atoms represent more than 70% of the total
number of elements in the atomic periodic table, but atomic
data involving the dynamics of open-shell atoms and their
ions are far fewer than their proportion in the periodic table.
This lack of data is mainly due to the serious challenge that
both theorists and experimentalist have faced while working
on open-shell atoms. Considering the whole group of open-
shells atoms, open d- and f -subshell atoms and ions have
drawn much less attention so far compared to open s- and
p-subshell atoms. However, during the last few decades, the
advent of third generation synchrotron radiation sources 1
and the extremely rapid development of computational
power have produced significant advances in the investiga-
tion of dynamical atomic processes, and open d- and
f -subshell atoms and ions have been subject to increasing
interest both theoretically and experimentally. Among the dy-
namical process of interest is the response of these atoms and
ions to ionizing radiation, the photoionization process, which
is of interest as a fundamental process of nature, along with
applications to a number of areas of science and technology,
most notably the modeling of plasmas, astrophysical and oth-
erwise.
In this work we report on the first stage of a study of the
photoionization of the 3d transition metal atoms and ions.
These atoms and ions hold particular interest owing to the
open 3d subshell which allows the possibility of giant dipole
resonances 2 resulting from 3p → 3d n = 0 transitions. Our
study begins with scandium, motivated by its position in the
group of open 3d-subshell elements in the periodic table. The
ground state of scandium, in fact, has a single electron in the
3d subshell outside closed shells, Ar3d4s
2
, and is the first
and simplest transition metal atom. Thus an understanding of
the photoionization of scandium, with a single electron in the
open 3d subshell, can serve as a springboard to the under-
standing of the photoionization of all of the 3d transition
metal atoms and ions generally.
However, the photoionization is quite complicated, owing
to the proximity of the 3d and 4s levels, so that there is
significant mixing in the initial state among 3d4s
2
,3d
2
4s,
and 3d
3
configurations which, in turn, leads to a plethora of
final state configurations, thereby complicating the giant di-
pole resonances. Calculations in this energy region have
been performed using various theoretical methodologies
3–5, none of which give satisfactory agreement with ex-
periment 2,6–8. Thus we turn to an even simpler system,
the Sc
2+
ion for the initial investigation. The Sc
2+
system, the
simplest atomic system with an open d shell, has a ground
state structure given by Ar3d, isoelectronic to potassium,
but with a valence 3d electron rather than a 4s. Another
reason for the choice of doubly-ionized scandium is the ex-
istence of experimental work 9,10 to benchmark the theo-
retical results. Note that theoretical work using both nonrel-
ativistic and relativistic R-matrix methods to study Sc
2+
has
been reported 11,12, but poor agreement with experiment
was found. Clearly, further theoretical study is required to
bring the calculated and measured cross sections into agree-
ment. This work is to be considered as part of a broader
effort to produce accurate data in order to understand atomic
processes involving open d-subshell atoms.
The photoionization of doubly-charged scandium, Sc
2+
also designated Sc III in spectroscopic notation is given
schematically as
Sc
2+
+ h → Sc
3+
+ e , 1
which is the direct photoionization pathway. In addition,
however, the photoionization can proceed through an inter-
mediate resonance; this pathway is represented as
Sc
2+
+ h → Sc
2+
*
→ Sc
3+
+ e . 2
While we are primarily interested in photoionization of the
ground state, in this work, the initial states of Sc III consid-
ered in the nonrelativistic calculations are both the ground
*
smanson@gsu.edu
PHYSICAL REVIEW A 78, 053405 2008
1050-2947/2008/785/05340510 ©2008 The American Physical Society 053405-1