Journal of Modern Physics, 2012, 3, 1670-1677
http://dx.doi.org/10.4236/jmp.2012.330204 Published Online October 2012 (http://www.SciRP.org/journal/jmp)
Detailed Theoretical Investigations on the L-Shell
Absorption of Open-M-Shell Germanium Plasmas:
Effect of Autoionization Resonance Broadening
Wenjun Xiang, Jiaolong Zeng, Yongsheng Fu, Cheng Gao
Department of Physics, College of Science, National University of Defense Technology, Changsha, China
Received August 23, 2012; revised September 25, 2012; accepted October 2, 2012
ABSTRACT
Radiative opacity of open-M-shell germanium plasmas in the L-shell photon energy region were investigated in detail
by using a fully relativistic detailed level accounting approach. Among other physical effects such as relativistic and the
interaction between fine-structure levels belonging to the same non-relativistic configuration and different configura-
tions, particular attention is paid on the effect of autoionization resonance broadening on the L-shell absorption. The
results show that for plasmas at present and past typical experimental conditions, line width due to autoionization reso-
nance broadening dominate among all the physical broadening mechanisms including electron impact and Doppler
broadenings. Such an effect is most pronounced for ions with just a few 2p-nd transition lines such as , while it is
not so pronounced for complex ions such as
14
Ge 
16
Ge

, where there are so many 2p-nd lines that line overlapping partly
conceal the effect of autoionization resonance broadening. After taking the effect of autoionization resonance broaden-
ing into account, detailed comparisons are made with available experimental spectra at different physical conditions of
different plasma temperatures and densities. The L-shell absorption is sensitive to the plasma temperature, especially in
the 2p-3d excitation energy region. The potential of utlizing the relative shape and intensity of the 2p-3d spin-orbit
splitting as temperature diagnostics is investigated.
Keywords: Autoionization Resonance Broadening; Germanium; Absorption; Radiative Opacity
1. Introduction
Germanium is one of the absorption and switching mate-
rial in indirectly driven inertial confinement fusion and
therefore its radiative property is of great interest both
experimentally and theoretically [1-9]. The radiative opa-
city of open-M-shell germanium plasmas are of particu-
lar experimental interest, especially in the region of 2p-
3d and 2p-4d transition arrays. Foster et al. [1] measured
the L-shell absorption spectrum of a germanium plasma,
which was generated by radiation heating using thermal
X radiation from a laser-produced gold plasma. Tracer
elements of Al and Mg were used to characterize the
temperature (76 eV) and density (0.05 g/cm3) of the
plasma. Perry et al. [2] experimentally measured the X-
ray absorption of germanium plasmas at a lower tempe-
rature of about 38 eV. Renaudin et al. [3] measured the
absorption spectra of germanium plasma in the 0.8 - 1.1
nm range. The germanium sample was radiatively heated
by a gold hohlraum. Recently, Loisel et al. [4] experi-
mentally measured the radiative opacity of medium Z
element plasmas including germanium in the X-ray re-
gion (0.8 - 1.8 nm) at temperatures between 15 and 25
eV and densities between 2 and 10 mg/cm3.
The experimental observations provide valuable data
to validate different approximations made in the opacity
calculations. In order to interpret these experiments, va-
rious theoretical methods were used to analyze the ob-
served spectra. Foster et al. [1] used a detailed configura-
tion accounting (DCA) model which includes an appro-
ximate treatment of term widths using the unresolved
transition array (UTA) approach. Perry et al. [2] em-
ployed a Super Transition Array (STA) approach [10] to
describe the state of plasmas, which can be thought as a
hybrid approach between an average atom description
and a full DCA scheme. In these statistical methods, the
line width caused by the statistical approach are gener-
ally dominant and therefore a Gaussian line shape is used.
Renaudin et al. [3] took into account of the term structure
using UTA statistical methods and a detailed line ac-
counting approach in pure jj coupling with orbital relaxa-
tion effect being considered. In their work, a Gaussian
shape is used, which assumed that Doppler broadening
C
opyright © 2012 SciRes. JMP

W. J. XIANG ET AL. 1671
dominates all other broadening mechanisms.
In a recent work, Blenski et al. [11] carried out theo-
retical interpretation of the X-ray photo-absorption ex-
periments measured at LULI2000 facility [4]. Their ana-
lysis was performed using the statistical superconfigura-
tion code SCO, two line-by-line opacity codes based on
the HULLAC and FAC packages and a hybrid statistical-
detailed code SCORCG. The authors pointed out that in
the detailed line-by-line treatment the autoionization (AI)
resonance broadening appeared to be the most important
in all broadening mechanisms. Yet no detailed investiga-
tions were found in the literature on this effect partly due
to the very challenging computations of the detailed line
spectrum with the complex open-M-shell Ge ions.
With the development of computational ability, com-
putation of plasma opacities is developing toward more
accurate direction including DLA, mixed DLA and UTA
and improvement of UTA [12-14]. In this work, we in-
vestigated the radiative opacity of Ge plasmas by using a
detailed level accounting (DLA) approach. In such a
DLA method, we do not need to introduce additional line
broadening caused by the statistical method, and there-
fore we include only true physical broadening mecha-
nisms such as Doppler, electron impact and AI resonance
broadenings. Among other physical effects on the opac-
ity, particular attention was paid on the effect of AI re-
sonance broadening of L-shell excitation region. To the
best of our knowledge, no detailed systematic investiga-
tions were found in the literature on this physical effect
on the L-shell absorption of open-M-shell germanium
plasmas, although many researches (for example, see
[15-21]) highlighted the importance of AI process to de-
termine the population balance and radiative properties in
non-local thermodynamic equilibrium (non-LTE) plas-
mas with a wide range of temperature and density.
2. Theoretical Method
The total radiative opacity for a plasma at a temperature
and mass density
T

is the sum of the bound-bound,
bound-free, free-free and scattering processes. The con-
tribution of bound-bound process for radiation of energy
h

can be obtained from the cross sections of bound-
bound lines:

il ll
l
Nh
bb il









Nl

h
(1)
where il is the population density of level of ioni-
zation stage and ll
i


l
 is the cross section for
photoexcitation from level to l of ionization state
and can be expressed in terms of the absorption oscil-
lator strength
i
ill
f


as

2
π
iill ll
he
hfSh
mc




hcm
(2)
where is the Planck constant, is the speed of light
in vacuum, e is the electron charge, e is the rest
mass of electron, and


Sh

is the line shape function.
In the DLA approach, the line shape function takes the
Voigt profile:
 
ln 2,
πd
ShHa (3)

 


,Ha

is the Voigt function: where
 
2
2
2
e
,d
π
x
a
ax
ax






H
ln 2ld a




0
ln 2d hh 


where d

nd l

are the Doppler and Lorentzian half
width at half maximum (HWHM), respectively. The
Doppler HWHM is related to the temperature of the
plasma and transition energy
T
0
h

[22]:
 
12
5
0
3.858 10
dkT Ah

  (4)

where
A
is atomic weight of the ion in gram and the
units of , 0
kT h

and d

are eV. The Lorentzian
HWHM (l

) is contributed by the electron impact
broadening (e

), AI resonance broadening (a

) and
natural life broadening. In general, line width due to
natural life are much smaller than the electron impact and
AI resonance broadening. Yet the line width caused by
AI resonance broadening is in many cases the dominant
broadening mechanism and therefore should be taken
into account. The accurate determination of the AI reso-
nance broadening is complicated because of the complex
atomic structure for open-M-shell Ge ions and thus is not
carefully considered in previous work. In this work, we
systematically investigated the effect of AI resonance
broadening on the L-shell absorption of open-M-shell Ge
plasmas. For the line width of electron impact broaden-
ing, we use a semiempirical method [23,24]

1/2
3
2
2
22
,
8π2π1.1
0.9
6π3
31
2
ee
jjjj
jif
m
NkT z
me
nnll
z

 
 
 
 
 




2
n2
(5)
where i (i l) and
f
n (
f
l
bf

) are the effective principal
(orbital angular momentum) quantum numbers of the
lower and upper energy levels of the transition, respec-
tively.
The contribution of bound-free opacity can be

W. J. XIANG ET AL. 1672
obtained from the photoionization cross sections per ion:

,
il il
il
Nh
bf

  

N

h
(6)
where il is the total population density of all possible
levels of ionization stage and i i


i is the photo- ionization cross section per ion and it can be calcu-
lated from the photoionization cross sections


il h


l
from level in ion i
 
/
il
EkT
iil
i
hh
e
il
l
g
Z



  (7)
where il
g
is the statistical weight for level of ion i,
il is the energy of level of ion above the ground
state and
l
Eli
i
Z
is the partition function for ion . i
N


ehL
 




L
5
Ge 
In the X-ray region, the bound-bound and bound-free
contributions to the opacity are generally dominant and
thus only simple approximations are used to describe the
free-free (Kramers cross section) and scattering (Thomp-
son scattering cross section) contribution to the opacity.
The population density of different charge states i
is determined by ionization equilibrium equation in LTE.
For a particular level of each charge state, the population
density obeys the Boltzmann distribution. The ionization
potential depression is considered by using the Debye-
Huckel model [25].
The fraction of radiation transmitted with respect to
some incident source of arbitrary intensity is given by
Fh (8)
where is the path length traversed by the light source
through the plasma. To compare directly with experiment,
one should include the effects of instrumental broaden-
ing.
3. Results and Discussion
For the experimental conditions [1-4], the charge states
which contribute to the L-shell absorption range from
(the ground configuration


269
33 3ds p
21
Ge Ne

) to
(the ground configuration

e3Ns
 
ππ
c
n
i
i
). For these
ionization stages of Ge, the upper levels of 2p-nd transi-
tions are autoionized ones, and therefore it is necessary
to include the effect of AI resonance broadening on the
L-shell absorption. These charge states have complex
atomic structure with an open-M-shell characteristics and
it is a challenging work to accurately determine the ato-
mic data including energy levels, oscillator strengths,
photoionization cross sections and line width due to au-
toionized levels.
J
aJ

 

n

a
In order to take into account of the configuration in-
teraction (CI), an atomic state is approximated by a linear
combination of configuration state functions (CSFs) with
same symmetry
(9)
where c is the number of CSFs and i

denotes
the representation of the atomic state in this basis. The
CSFs are anti-symmetrized products of a common set of
orthogonal orbitals which are optimized on the basis of
the relativistic Hamiltonian. Once the CI wavefunctions
have been obtained, the oscillator strengths can be calcu-
lated
2
2
3
iijij
E
gf  P (10)
where
j
i
EE E E, i and
j

E
i
are, respectively, the
energies of initial and final levels and
g
is the statisti-
cal weight of the lower state, i.e. . is 21
ii
gJP
1
N
dipole transition operator with
p
p
 Pr in the length
formalism and
1
2
P
N
p
p
E



in the velocity formalism,
where is the total number of bound electrons. The
AI rates are obtained in the relativistic distorted-wave
approximation, which reads in the first order perturbation
theory (in atomic units)
N
2
1
2,;
a
ijjT Ti
ijij
AJM
r

 

 (11)
where i

is the autoionizing state,
f

is the final
state which has one less electron than i

,

is the
relativistic angular quantum number of the free electron.
The total angular quantum number of the coupled final
state must be equal to that of i

, i.e., Ti
J
J

and
Ti
M
M

. The AI resonance width of level can be
obtained by summing all final levels
i
aa
iij
j

A
(12) 
where 2πh


5
Ge
. All atomic data required in the calcu-
lation of opacity were obtained out using the Flexible
Atomic Code (FAC) developed by Gu [26].
We first investigate the effect of AI resonance broad-
ening on the opacity of Ge plasma. Extensive calcula-
tions were carried out and the results show that the AI
resonance HWHM for the inner shell 2p excited levels
range from 0.05 eV to 0.4 eV for charge states from
20
Ge

to

. For Ge14

, the ground configuration


26
e3 3Nsp
52 6
2333dpsp
only has one fine-structure level. The 2p
excited configuration is split into 12
fine-structure levels, where

1
23dp
3232 1,

1
23dp
3252 1,
and


1
12
23dp
32 1 the total angular momentum is 1.


1
23dp
3232 1 means one hole in orbital 2p, one electron
in orbital 3d and full electron orbitals have been omitted.

W. J. XIANG ET AL. 1673
For the 2p-3d transition array, there are three dipole al-
lowed transitions: 32 32 23dp,32 52, and 23dp
12 32
3d2p
2 3dp14 Ge 
Ge
. The radiative transition probability of the
first transition is much smaller than the last two lines.
The effect of AI resonance width on the absorption in the
2p-3d region can clearly be seen from Figure 1, which
shows the absorption cross section for the transition array
of of . In order to
obtain the results, was assumed to be embedded
in an LTE plasma at a temperature of 60 eV and a den-
sity of 0.01 g/cm3. In Figure 1(b), the electron impact
broadening and Doppler broadening mechanisms are
considered, while the AI resonance broadening is not
included. In Figure 1(a), three broadening mechanisms
are all taken into account. One can see that when AI
resonance broadening is included, the peak absorption
cross section is one order of magnitude smaller, which is
a reflection of the effect of AI resonance broadening on
the absorption. In the above plasma condition, the
HWHM due to electron impact and Doppler broadening
is evaluated to be 0.003 eV and 0.041 eV, respectively.
The HWHM due to AI resonance broadening is calcu-
lated to be 0.247 eV and 0.263 eV for 2p excited levels
of
62 6
233psp52 6 33sp
14

1
3252 1 and 23pd

1
12

23dp
32 1, respectively. Among
the three broadening mechanisms, the AI resonance
broadening is the dominant broadening mechanism. The
AI resonance width is larger than the electron impact and
Doppler width by more than one order of magnitude.
The effect of AI resonance broadening on the absorp-
tion of is evident from the inspection of Figure 1.
As there are only two strong absorption lines and the
2p-3d spin-orbit splitting (~30 eV) is much larger than
14
Ge 
Figure 1. Absorption cross section for the transition array
2p63s23p6 − 2p53s23p63d of Ge14+: (a) including and (b) not
including the effect of AI resonance broadening.
the line width caused by all broadening mechanisms, two
2p-3d transition lines are separate each other with an
interval of ~30 eV. With the decrease of the number of
3p electrons, especially near the half full 3p orbital, the
number of 2p-3d lines becomes rapidly great and the
absorption approaches unresolved quasi-continuum bands.
Figure 2 shows the absorption cross section for the tran-
sition array of of
62 452 4
233 2333dpsp psp16 Ge

,
which was assumed to be embedded in an LTE plasma at
a temperature of 90 eV and a density of 0.015 g/cm3.
Similar to 14
Ge

, the AI resonance width is also larger
than the electron impact and Doppler width by more than
one order of magnitude. Yet the peak absorption cross
section without considering the AI resonance broadening
is just 2.43 times larger than that which includes this ef-
fect. This is due to many lines overlapped together re-
sulting in less pronounced for the effect of AI resonance
broadening than in 14
Ge

, where lines do not overlap.
The two strong absorption bands with an interval of
spin-orbit splitting of ~30 eV in Figure 2 originate from
32 52
23dp

and 12 32
23dp

transitions for the lower
and higher photon energy range, respectively. Such a
feature differ obviously from that of Ge . With the
further decrease of ionization stage, the 2p-3d absorption
shows a different feature from Ge and
14
1416
Ge

, as
illustrated in Figure 3, which shows the absorption cross
section for the transition array of
626 5526 6
2333d2333dpsp psp99 Ge of Ge .

was
assumed to be embedded in an LTE plasma at a tem-
perature of 38 eV and a density of 0.015 g/cm3. For
14
Ge

and Ge16

, 32 52 23dp

absorption is weaker
than 9 Ge

. Fur-
12 32
23dp, while this is reversed for

Figure 2. Absorption cross section for the transition array
2p63s23p4 − 2p53s23p43d of Ge16+: (a) including and (b) not
including the effect of AI resonance broadening.

W. J. XIANG ET AL. 1674
Figure 3. Absorption cross section for the transition array
2p63s23p63d5 − 2p53s23p63d6 of Ge9+: (a) including and (b)
not including the effect of AI resonance broadening.
thermore, the AI width for many upper levels of
32 52
23dp transitions is much smaller than those of
12 32
As an illustrative example, Figure 4 shows the effect
of AI resonance broadening on the radiative opacity of
Ge plasma at a temperature of 38 eV and a density of
0.015 g/cm3 with plot (a) including and (b) not including
such an effect. Due to many overlapped lines, it was
found that the effect of AI resonance broadening reduce
the peak value of opacity by only 25% for 2p-3d transi-
tion arrays. For 2p-4d and higher transition arrays, this
effect is small as line width caused by the electron im-
pact broadening is comparable or even larger than that of
AI resonance broadening.
23dp.
After investigating the effect of AI resonance broad-
ening on the opacity of Ge plasma, we turn to the com-
parison of our theoretical results with the experimental
data. Figure 5 shows the calculated transmission of Ge
plasma at temperatures of 58, 60 and 62 eV, while the
mass density is fixed to be 0.01 g/cm3 in solid lines. The
dashed lines show the experimental data measured by
Renaudin et al. [3]. Areal density used in the calculations
is equal to 0.11 mg/cm2. It can be seen that the transmis-
sion is sensitive to the temperature of the plasmas, in
particular in 2p-3d region. At the temperature of 58 eV,
there is a close agreement for absorption line position
between theory and experiment at the higher photon en-
ergy wing of the 2p-3d (1300 - 1340 eV), while such a
good agreement turned to the lower photon energy region
(1220 - 1260 eV) at the temperature of 62 eV. This shows
that there is small temperature or density gradient in the
experiment. In the whole shown photon energy range,
Figure 4. The effect of AI resonance broadening on the ra-
diative opacity of Ge plasma at a temperature of 38 eV and
a density of 0.015 g/cm3: (a) including and (b) not including
such an effect.
Figure 5. Transmission of Ge plasma at temperatures of (a)
58; (b) 60 and (c) 62 eV with the mass density being 0.01
g/cm3 in solid lines. The dashed lines refer to the experi-
mental data of Renaudin et al. [3].
there is a better agreement between theory and experi-
ment at the temperature of 60 eV, which is consistent
with the experimental determination of plasma tempera-
ture from element tracer of Mg and radiative-hydrody-
namic simulations [3]. At the temperature of 60 eV, a
more complete comparison between experiment and dif-

W. J. XIANG ET AL. 1675
ferent theoretical results is shown in Figure 6. Two addi-
tional theoretical results are compared in Figure 6 which
were obtained by average atom calculations including
UTA with and without orbital relaxation (OR) treatment
[3]. Renaudin et al. [3] also carried out DLA calculations,
yet it is difficult to extract the data from the original fig-
ure.
At the experimental condition of Renaudin et al. [3],
the 2p-3d absorption does not show an interval of spin-
orbit splitting. 32 52 and 23dp1232 are
smoothly merged together, expanding an extended pho-
ton energy region from 1220 to 1320 eV. Similar conclu-
sion applies for the experimental spectra of Foster et al.
[1]. To save space, we do not show detailed comparison
between theory and experiment under the physical condi-
tion of Foster et al. [1]. With the decrease of plasma
temperature, the separation of 2p-3d spin-orbit splitting
begins to appear evidently. Such a trend can easily be
seen from Figures 7 and 8, which shows the transmis-
sion at temperatures near 38 eV and 24 eV.
23dp
In Figure 7, the spectrally resolved transmission of Ge
plasma are shown in solid lines at temperatures of 36, 38
and 40 eV with the mass density being fixed to be 0.012
g/cm3. The dashed lines shows the experimental data
measured by Perry et al. [2] with the temperature being
determined to be 38 ± 2 eV and density 0.012 ± 0.003
g/cm3. In plot (b), the STA prediction is also given for
Ge plasma at the temperature of 38 eV. Areal density
used in the calculations is equal to 0.111 mg/cm2. In this
case, the 2p-3d spin-orbital splitting is very sensitive to
the temperature of the plasmas. With just 2 eV difference
in temperature from (a) to (c), the 2p-3d spin-orbital
Figure 6. Comparison of different theoretical (DLA and
UTA) and experimental spectra of transmission of Ge pla-
sma at a temperature of 60 eV and a density of 0.01.
Figure 7. Transmission of Ge plasma at temperatures of (a)
36; (b) 38 and (c) 40 eV with the mass density being 0.012
g/cm3 in solid lines. The dashed lines refer to the experi-
mental data of Perry et al. [2].
splitting is much more obvious at 36 eV than at 40 eV,
even the shape of absorption structures is much different
at the three temperatures. For example, look at the ab-
sorption feature near photon energy 1240 eV. The ab-
sorption structure for the spin-orbital splitting is sharper
at 36 eV than at 38 and 40 eV. For the wide and rela-
tively flat absorption bottom at 38 and 40 eV, the varia-
tion trend with photon energy is reversed. This is an in-
dication that the 2p-3d absorption has the potential of
temperature diagnosis, especially in temperature region
where absorption is very sensitive to the temperature. As
there are enormous numbers of absorption lines, the in-
dividual lines merged to become quasi-continuum ab-
sorption bands, DLA results tend to agree with UTA and
STA ones. Note, however, that at some particular tem-
perature, where there are not so many absorption lines to
merge together, DLA results will have distinct difference
from those of UTA and STA.
The 2p-3d spin-orbit splitting becomes more evident
with the further decrease of temperature. In Figure 8, the
spectrally resolved transmission of Ge plasma are shown
in solid lines at temperatures of 16, 18, 20, 22 and 24 eV
and the mass density being fixed to be 0.015 g/cm3. The
dashed lines shows the experimental data [4,11]. In plot
(e), the SCO and SCORCG predictions [11,27] are given
for Ge plasma at temperature of 24 eV. Areal density

W. J. XIANG ET AL. 1676
Figure 8. Transmission of Ge plasma at temperatures of (a)
16; (b) 18; (c) 20; (d) 22 and (e) 24 eV with the mass density
being 0.015 g/cm3 in solid lines. The dashed lines refer to the
experimental data [11,13]. In plot (f), the dotted and dot-
dashed lines refer to results of SCO and SCORCG codes,
respectively.
used in the calculations is equal to 0.08 mg/cm2. At these
temperatures, the shape and intensity of the 2p-3d spin-
orbital splitting is more sensitive to the temperature of
the plasmas than in physical conditions of Figures 5 and
7. With just 2 eV difference in the temperature, the shape
and relative intensity of the 2p-3d spin-orbital splitting is
noticeably different from case to case for plot (a)-(e), and
therefore the potential of temperature diagnosis at these
temperatures is better than in Figures 5 and 7. Reason-
able agreement is found between our work and those of
SCO and SCORCG predictions at 24 eV, although
stronger absorption is predicted by SCO and SCORCG
codes for the 1232 transition lines near the pho-
ton energy 1240 eV. Compared with the experiment, all
theoretical results deviate from experimental spectrum, in
particular in the 2p-3d region of 1190 - 1260 eV. Such a
deviation is due to the strong gradients of temperature
and density in the experimental plasma.
23dp
14
Ge
In conclusion, spectrally resolved L-shell absorption
spectra of open-M-shell germanium plasmas were inves-
tigated by using a detailed line-by-line method. In the
DLA approach, spectral line profile plays an important
role on the radiative opacity of plasmas. In this work, we
focus on the effect of AI resonance broadening on the
L-shell absorption of germanium plasmas. It was found
that for plasmas at typical present and past experimental
conditions, line width due to AI resonance broadening is
an order of magnitude larger than that due to electron
impact and Doppler broadenings. For germanium ion
with near closed atomic structure such as

, the
effect of AI resonance broadening is most pronounced
with the peak absorption cross section of one particular
2p-3d absorption line being an order of magnitude
smaller than that of not including this effect. For germa-
nium ion with near half filled 3d or 3p electron such as
9
Ge

and Ge16

, such an effect is not so pronounced
due to many 2p-nd transition lines merged together to
form quasi-continuum bands. Detailed comparisons are
carried out with available experimental spectra at differ-
ent physical conditions of different plasma temperatures
and densities. The results show that absorption spectra
are sensitive to the temperature of plasmas and show the
potential of temperature diagnostics by using the 2p-3d
transition arrays. The relative shape and intensity of the
2p-3d spin-orbit splitting is very sensitive to the tem-
perature and therefore should be an ideal tool of tem-
perature diagnostics.
4. Acknowledgements
This work was supported by the National Natural Sci-
ence Foundation of China under Grant Nos. 11274382,
11274383, and 11204376.
REFERENCES
[1] J. M. Foster, D. J. Hoarty, C. C. Smith, P. A. Rosen, S. J.
Davidson, S. J. Rose, T. S. Perry and F. J. D. Serduke,
“L-Shell Absorption Spectrum of an Open-M-Shell Ger-
manium Plasma: Comparison of Experimental Data with
a Detailed Configuration-Accounting Calculation,” Phy-
sical Review Letter, Vol. 67, No. 23, 1991, pp. 3255-3258.
doi:10.1103/PhysRevLett.67.3255
[2] T. S. Perry, K. S. Budil, R. Cauble, R. A. Ward, D. R.
Back, C. A. Iglesias, B. G. Wilson, J. K. Nash, C. C. Smi-
th, J. M. Foster, S. J. Davidson, F. J. D. Serduke, J. D.
Kilkenny and R. W. Lee, “Quantitative Measurement of
Mid-z Opacities,” Journal of Quantitative Spectroscopy
& Radiative Transfer, Vol. 54, No. 1-2, 1995, pp. 317-
324. doi:10.1016/0022-4073(95)00066-T
[3] P. Renaudin, C. Blancard, J. Bruneau, G. Faussurier, J.-E.
Fuchs and S. Gary, “Absorption Experiments on X-Ray-
Heated Magnesium and Germanium Constrained Sam-
ples,” Journal of Quantitative Spectroscopy & Radiative
Transfer, Vol. 99, No. 1-3, 2006, pp. 511-522.
doi:10.1016/j.jqsrt.2005.05.041
[4] G. Loisel, P. Arnault, S. Bastiani-Ceccotti, T. Blenski, T.

W. J. XIANG ET AL. 1677
Caillaud, J. Fariaut, W. Folsner, F. Gilleron, J.-C. Pain, M.
Poirier, C. Reverdin, V. Silvert, F. Thais, S. Turck-Chieze
and B. Villette, “Absorption Spectroscopy of Mid and
Neighboring Z Plasmas: Iron, Nickel, Copper and Germa-
nium,” High Energy Density Physics, Vol. 5, No. 3, 2009,
pp. 173-181. doi:10.1016/j.hedp.2009.05.015
[5] D. J. Hoarty, S. F. James, C. R. D. Brown, B. M. Williams,
H. K. Chung, J. W. O. Harris, L. M. Upcraft, B. J. B.
Crowley, C. C. Smith and R. W. Lee, “Measurements of
Emission Spectra from Hot, Dense Germanium Plasma in
Short Pulse Laser Experiments,” High Energy Density
Physics, Vol. 6, No. 1, 2010, pp. 105-108.
doi:10.1016/j.hedp.2009.05.019
[6] J. W. O. Harris, L. M. Upcraft, D. J. Hoarty, B. J. B. Cro-
wley, C. R. D. Brown and S. F. James, “A Comparison of
Theory and Experiment for High Density, High Tempera-
ture Germanium Spectra,” High Energy Density Physics,
Vol. 6, No. 1, 2010, pp. 95-98.
doi:10.1016/j.hedp.2009.06.001
[7] Y. L. Peng, D. Xia and J. M. Li, “A Generalized Quasi-
Sum Relations for Oscillator Strengths in Transition Ar-
rays: Theoretical Study of the Opacity of Ge Plasmas,”
Journal of Quantitative Spectroscopy & Radiative Trans-
fer, Vol. 87, No. 1, 2004, pp. 95-106.
doi:10.1016/j.jqsrt.2003.12.024
[8] V. J. L. White, J. M. Foster, J. C. V. Hansom and P. A.
Rosen, “Measurements of Radiation Heat Transport in
Germanium: Validationinebreak of an Opacity Model,”
Physical Review E, Vol. 49, No. 6, 1994, pp. R4803-
R4806. doi:10.1103/PhysRevE.49.R4803
[9] J. Yan and J. M. Li, “Theoretical Simulation of the Tran-
smission Spectra of Fe and Ge Plasmas,” Chinese Physi-
cal Letter, Vol. 17, No. 3, 2000, pp. 194-196.
doi:10.1088/0256-307X/17/3/014
[10] A. Bar-Shalom, J. Oreg and W. H. Goldstein, “Configu-
ration Interaction in LTE Spectra of Heavy Elements,”
Journal of Quantitative Spectroscopy & Radiative Trans-
fer, Vol. 51, No. 1-2, 1994, pp. 27-39.
doi:10.1016/0022-4073(94)90062-0
[11] T. Blenski, G. Loisel, M. Poirier, F. Thais, P. Arnault, T.
Caillaud, J. Fariaut, F. Gilleron, J.-C. Pain, Q. Porcherot,
C. Reverdin, V. Silvert, B. Villette, S. Bastiani-Ceccotti,
S. Turck-Chieze, W. Foelsner and F. de Gaufridy De Dor-
tan, “Theoretical Interpretation of X-Rays Photo-Absorp-
tion in Medium-Z Elements Plasmas Measured at LULI-
2000 Facility,” High Energy Density Physics, Vol. 7,
2011, pp. 320-326. doi:10.1016/j.hedp.2011.06.004
[12] Q. Porcherot, J. C. Pain, F. Gilleron and T. Blenski, “A
Consistent Approach for Mixed Detailed and Statistical
Calculation of Opacities in Hot Plasmas,” High Energy
Density Physics, Vol. 7, No. 4, 2011, pp. 234-239.
doi:10.1016/j.hedp.2011.05.001
[13] F. Gilleron, J. C. Pain, Q. Porcherot, J. Bauche and C.
Bauche-Arnoult, “Corrections to Statistical Modeling of
Spectra for Plasmas at Moderate or Low Temperatures,”
High Energy Density Physics, Vol. 7, No. 4, 2011, pp.
277-284. doi:10.1016/j.hedp.2011.05.005
[14] J. A. Gaffney and S. J. Rose, “The Effect of Unresolved
Transition Arrays on Plasma Opacity Calculations,” High
Energy Density Physics, Vol. 7, No. 4, 2011, pp. 240-246.
doi:10.1016/j.hedp.2011.05.003
[15] C. J. Fontes, J. Abdallah Jr., C. Bowen, R. W. Lee and Yu
Ralchenko, “Review of the NLTE-5 Kinetics Workshop,”
High Energy Density Physics, Vol. 5, No. 1-2, 2009, pp.
15-22. doi:10.1016/j.hedp.2009.02.004
[16] J. R. Albritton and B. G. Wilson, “Non-LTE Ionization
and Energy Balance in High-Z Laser Plasmas Including
Two-Electron Transitions,” Physical Review Letter, Vol.
83, No. 8, 1999, pp. 1594-1597.
doi:10.1103/PhysRevLett.83.1594
[17] Y. Hahn, “Electron-Ion Recombination Processes: An
Overview,” Reports on Progress in Physics, Vol. 60, No.
7, 1997, pp. 691-759. doi:10.1088/0034-4885/60/7/001
[18] V. L. Jacobs, “Autoionization Phenomena in Plasma Ra-
diation Processes,” Journal of Quantitative Spectroscopy
& Radiative Transfer, Vol. 54, No. 1-2, 1995, pp. 195-
205. doi:10.1016/0022-4073(95)00055-P
[19] J. Bauche, C. Bauche-Arnoult and O. Peyrusse, “Role of
Dielectronic Recombination and Autoionizing States in
the Dynamic Equilibrium of Non-LTE Plasmas,” High En-
ergy Density Physics, Vol. 5, No. 1-2, 2009, pp. 51-60.
doi:10.1016/j.hedp.2009.02.003
[20] V. L. Jacobs, “Kinetic and Spectral Descriptions for Ato-
mic Processes Involving Autoionizing Resonances in High-
Temperature Plasmas,” High Energy Density Physics, Vol.
5, No. 1-2, 2009, pp. 80-88.
doi:10.1016/j.hedp.2009.03.001
[21] C. Gao and J. L. Zeng, “Validity of Analytical Formulas
for Autoionization and Dielectronic Capture Rates Used
in Collisional-Radiative Models,” Physical Review A, Vol.
82, No. 6, 2010, pp. 1-8.
doi:10.1103/PhysRevA.82.062515
[22] R. D. Cowan, “The Theory of Atomic Structure and Spec-
tra,” University of California Press, Berkeley, 1981.
[23] M. S. Dimitrijevic and N. Konjevic, “Stark Widths of
Doubly- and Triply-Ionized Atom Lines,” Journal of
Quantitative Spectroscopy & Radiative Transfer, Vol. 24,
No. 6, 1980, pp. 451-459.
doi:10.1016/0022-4073(80)90014-X
[24] M. S. Dimitrijevic and N. Konjevic, “Simple Estimates
for Stark Broadening of Ion Lines in Stellar Plasmas,”
Astronomy & Astrophysics, Vol. 172, 1987, pp. 345-349.
[25] D. J. Heading, J. S. Wark, G. R. Bennett and R. W. Lee,
“Simulations of Spectra from Dense Aluminium Plas-
mas,” Journal of Quantitative Spectroscopy & Radiative
Transfer, Vol. 54, No. 1-2, 1995, pp. 167-180.
[26] M. F. Gu, “Indirect X-Ray Line-Formation Process in
Iron L-Shell Ions,” The Astrophysical Journal, Vol. 582,
No. 2, 2003, pp. 1241-1250. doi:10.1086/344745
[27] F. Gilleron, J. Bauche and C. Bauche-Arnoult, “A Statis-
tical Approach for Simulating Detailed-Line Spectra,” Jour-
nal of Physics B: Atomic, Molecular and Optical Physics,
Vol. 40, No. 15, 2007, pp. 3057-3074.
doi:10.1088/0953-4075/40/15/007