Optics and Photonics Journal, 2011, 1, 110-115
doi:10.4236/opj.2011.13019 Published Online September 2011 (http://www.SciRP.org/journal/opj)
XUV and Soft X-Ray Laser Radiation from Ni-Like Au
Wessameldin S. Abdelaziz1, Hamed Mahmoud Hamed Ibrahim2
1Laser Metrology Department, National Institute of Laser Enhanced Sciences (NILES),
Cairo University, Giza, Egypt
2Laser Sciences and Interactions Department, National Institute of Laser Enhanced Sciences (NILES),
Cairo University, Giza, Egypt
Received May 27, 2011; revised July 2, 2011; accepted July 11, 2011
Abstract
Atomic structure data and effective collision strengths from literature for 1s2 2s2 2p6 3s2 3p63d10 and 34 fine-
structure levels contained in the configurations 1s2 2s2 2p6 3s2 3p63d9 4l (l = s, p, d) for the nickel-like Au ion
are used in the determination of the reduced population for these levels over a wide range of electron densi-
ties and at various electron plasma temperatures. The gain coefficient for those transitions with positive
population inversion factor are determined and plotted against the electron density.
Keywords: Atomic Structure Data, Effective Collision Strengths, Reduced Population, Ni-Like Au
1. Introduction
Experimentally there exist in the literature some studies
trying to develop high-efficiency X-ray laser with sig-
nificant gain. For example Vinogradov et al. and Norton
et al. [1,2] proposed the original mechanism for demon-
strating X-ray lasing by resonant photopumping. Several
authors during the past three decades [3-8] have studied
this lasing mechanism experimentally and theoretically,
in the hope of developing high-efficiency X-ray laser.
In another study by N. Qi and M. Krishnan [9], the
shortest wavelength at which the significant gain has
been measured using the resonant photopumping was in
the beryllium-like carbon at 2163 Å, which is far from
the X-ray spectral region.
Nickel-like ions are of considerable interest in la-
ser-plasma interaction because of the large gain in the
EUV and X-ray regions. Their ground state (1s2 2s2 2p6
3s2 3p6 3d10 1S0) is analogous to the (1s2 2s2 2p6 1S0)
ground state of neon-like ions, which have already
shown significant amplification in a number of elements
such as selenium, germanium, and titanium. Similar laser
gain has been predicted and observed by Goldstein et al.
[10] in a number of nickel-like ions, including tin, neo-
dymium, samarium, gadolinium, europium, tantalum,
and tungsten.
Theoretical calculations are needed to approve these
observations. Recently, Zeng et al. [11] calculated the
energy levels, the spontaneous radiative decay rates, and
the electron impact collisional strengths for Ni-like Gold
ion. But no much work has been done to predict the laser
gain of Ni-like Au theoretically. In this paper, we present
the gain predicted for the Ni-like Au ion by a steady-
state model of Ni-like ions, our model treats the kinetic
of the Ni-like charge state in isolation from other ioniza-
tion stages. The present gain calculations included the
ground state 1s2 2s2 2p6 3s2 3p63d10 and 34 fine-structure
levels contained in the configurations 1s2 2s2 2p6 3s2
3p63d9 4l (l = s, p, d) for the nickel-like Au ion. The
model includes all radiative transitions as well as elec-
tron-impact transitions between all levels.
2. Computation of Gain Coefficient
The possibility of laser emission from plasma of Au51+
ion via electron collisional pumping, in the XUV and
soft X-ray spectral regions is investigated at different
plasma temperatures and plasma electron densities.
The reduced population densities are calculated by
solving the coupled rate equations [12-15].
de
jji ejiji
ijijc ij
ed
ei ijiiji ij
ij ijij
NANC C
NNC NCNA

 





 










 
(1)
where Nj is the the population of level j,
j
i
A
is the
spontaneous decay rate from level j to level i, e
j
i
C is the

W. S. ABDELAZIZ ET AL.111
electron collisional excitation rate coefficient, and d
j
i
C
is the electron collisional de-excitation rate coefficient,
which is related to electron collisional excitation rate
coefficient by [16,17].
exp
de i
j
iij jie
j
g
CC EKT
g
 

 




(2)
where gi and gj are the statistical weights of lower and
upper levels, respectively.
The electron impact excitation rates usually are ex-
pressed via the effective collision strengths γij as
6
3
12
8.6287 10exp cmsec
ij
e
ij ij
e ie
E
CKT
gT


1



(3)
where the values of γij and Aji are obtained by [11].
The actual population density NJ of the j th level is ob-
tained from the following identity [10],
J
j
NNN
I
(4)
where
I
N is the quantity of ions which reach to ioniza-
tion stage I, is given by
I
Ie avg
NfNZ (5)
where fI is the fractional abundance of the Ni-like ioniza-
tion stages calculated by Goldstein et al. [10], Ne is the
electron density, and Zavg is the average degree of ioniza-
tion
Since the populations calculated from Equation (1) are
normalized such that,
35
11
J
J
I
N
N





 (6)
where 35 is the number of all the levels of the ion under
consideration, the quantity actually obtained from Equa-
tion (1) is the fractional population
j
I
NN.
After the calculation of levels population, the quanti-
ties Nu /guand Nl /gl can be calculated.
By application of electron collisional pumping, the
collision in the lasant ion plasma will transfer the
pumped quanta to other levels, and will result in popula-
tion inversions between the upper and lower levels. Once
a population inversion has been ensured a positive gain
through F > 0 [18] is obtained.
uu l
uul
g
NN
FNg g






(7)
where u
u
N
g
and l
l
N
g
are the reduced populations of the
upper level and lower level respectively. Equation (7)
has been used to calculate the gain coefficient (α) for
Doppler broadening of the various transitions in the
Au51+ ion.
12
3
8π2π
lu
ul u
i
M
A
NF
KT




 (8)
where M is the ion mass, u

 is the transition wave-
length in cm, i is the ion temperature in K and u, l rep-
resent the upper and lower transition levels respectively.
T
As seen from Equation (8), the gain coefficient is ex-
pressed in terms of the upper state density (Nu). This
quantity, Nu depends on how the upper state is populated,
as well as on the density of the initial source state. The
source state is often the ground state for the particular
ion.
3. Result and Discussions
3.1. Level Population
The reduced population densities are calculated for 35
fine structure levels arising from 1s2 2s2 2p6 3s2 3p63d10
and 34 fine-structure levels contained in the configura-
tions 1s2 2s2 2p6 3s2 3p63d9 4l (l = s, p, d) configurations
that emit radiation in the XUV and soft X-ray spectral
regions. The calculations were performed by solving the
coupled rate Equation (1) simultaneously using MAT-
LAB version 7.8.0 (2009a) computer program.
The present calculations for the reduced populations as
a function of electron densities are plotted in Figures 1-3
at three different plasma temperatures (0.5, 1, 1.5 KeV)
for Au51+ ion.
In the calculation we took into account spontaneous
radiative decay rate and electron collisional processes
between all levels under study.
The atomic structure data and effective collision
strength data needed were taken from Reference [11].
The behavior of level populations can be explained as
follows: in general at low electron densities the reduced
population density is proportional to the electron density,
where excitation to an excited state is followed immedi-
ately by radiative decay, and collisional mixing of ex-
cited levels can be ignored.
This result is in agreement with that of Feldman et al.
[14,15,19]. See also the data for nickel-like Sm , W, and
Eu [20-22].At high electron densities (), the
radiative decay to all the levels will be negligible com-
pared to collisional depopulations and all the level popu-
lations become independent of the electron density (see
Figures 1-3). The (3d3/2 4d3/2)0 level has higher popula-
tion density from electron density 1021 to 1022 cm−3 than
the other levels at electron temperature 0.5 KeV, from
electron density 1021 to 2 × 1022 cm−3 at electron tem-
perature 1 KeV, and from electron density 1021 to 4 ×
1022 cm−3 at electron temperature 1.5 KeV which mean
23
10
e
N

W. S. ABDELAZIZ ET AL. 112
Figure 1. Reduced population of Au51+ levels after electron collisional pumping as a function of the electron
density at temperature 0.5 KeV.
Figure 2. Reduced population of Au51+ levels after electron collisional pumping as a function of the electron
density at temperature 1.0 KeV.
Figure 3. Reduced population of Au51+ levels after electron collisional pumping as a function of the electron
density at temperature 1.5 KeV.

W. S. ABDELAZIZ ET AL. 113
that the population inversion occur in these ranges. The
population inversion is largest where the electron colli-
sional deexcitation rate for the upper level is comparable
to the radiative decay rate for this level [14,19]. The dif-
ference between this work and our previous work on
Gd-like nickel [23] we took into account the n = 4 shell,
however in the case of Au-like nickel we took n = 3 shell
only to decrease the time and complexity of calculations
because we did not find any significant laser transitions
come from 3d9 4f - 3d9 4d transitions and all laser transi-
tions mainly from 3d9 4d - 3d9 4p. The population inver-
sion in case of Au-like nickel is at higher electron den-
sity than the in the case of Gd-like nickel.
3.2. Gain Coefficient
As a result of population inversion there will be positive
gain in laser medium. Equation (8) has been used to cal-
culate gain coefficient for the Doppler broadening of
various transitions in the Au51+ ion. Our results for the
maximum gain coefficient in cm−1 for those transitions
having a positive inversion factor F > 0 in the case of
Au51+, in Figures 4-6.
The figures show that the population inversions occur
for several transitions in the Au51+ ion, however, the
largest gain occurs in (3d3/2 4d3/2)0 → (3d5/2 4p3/2)1
(35→12) transition at wavelength 41.4 Å at an electron
Figure 4. Gain coefficient of possible laser transitions against electron density at temperature 0.5 KeV in Au51+.
Figure 5. Gain coefficient of possible laser transitions against electron density at temperature 1.0 KeV in Au51+.

W. S. ABDELAZIZ ET AL. 114
Figure 6. Gain coefficient of possible laser transitions against electron density at temperature 1.5 KeV in Au51+.
Table 1. Parameters of the most intense laser transitions.
Transition Atomic data Au XXXXXII
Wavelength λ (Å) 35.1
Maximum gain α (cm−1) 572
Electron density Ne (cm−3) 6.00E+22
(3d3/24d3/2)0→ (3d3/24p1/2)1
Electron temperature Te (KeV
) 1.5
Wavelength λ (Å) 41.4
Maximum gain α (cm−1) 442
Electron density Ne (cm−3) 1.00E+23
(3d3/24d3/2)0→ (3d5/24p3/2)1
Electron temperature Te (KeV) 1.5
Wavelength λ (Å) 51
Maximum gain α (cm−1) 166
Electron density Ne (cm−3) 8.00E+22
(3d3/24d3/2)0→ (3d3/24p3/2)1
Electron temperature Te (KeV) 1.5
temperature 0.5 KeV, and in (3d3/2 4d3/2)0 → (3d3/2 4p1/2)1
(35→9) transition at wavelength 35.1 Å at an electron
temperatures 1.0, and 1.5 KeV
For Ni-like Au, the population inversion is due to
strong monopole excitation from the 3d10 ground state to
the 3d9 4d configuration and also the radiative decay of
the 3d9 4d level to the ground level is forbidden, while
the 3d9 4p level decays very rapidly to the ground level.
This short wavelength laser transitions was produced
using plasmas created by optical lasers as the lasing me-
dium.
For electron densities and electron temperatures that
are typical of laboratory high-density plasma sources,
such as laser produced plasmas, it is possible to create a
quasi-stationary population inversion between the 3d94d
and 3d94p in Au51+ ion. Our calculations have shown that
under favorable conditions large laser gain for these
transitions in the XUV and soft X-ray regions of the
spectrum can be achieved in the nickel like Au51+ ion. It
is obvious that the gain increases with the temperature.
4. Conclusions
The analysis that have been presented in this work shows
that electron collisional pumping (ECP) is suitable for
attaining population inversion and offering the potential

115
for laser emission in the spectral region between 30 and
100 Å from Au51+ ion. This class of lasers can be
achieved under suitable conditions of pumping power as
well as electron density. If the positive gain obtained
previously for some transitions in the ion under studies
(Au51+ ion) together with the calculated parameters could
be achieved experimentally, then successful low-cost
electron collisional pumping XUV and soft X-ray lasers
can be developed for various applications. The parame-
ters of most intense laser transitions in Ni-like Au ion are
summarized in Table 1.
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