XUV and Soft X-Ray Laser Radiation from Ni-Like Au

doi:10.4236/opj.2011.13019

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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

E-mail: [email protected]

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].

jji ejiji

ijijc ij

ei ijiiji ij

ij ijij

NANC C

NNC NCNA



 



































 

(1)

where Nj is the the population of level j,

is the

spontaneous decay rate from level j to level i, e

C is the

W. S. ABDELAZIZ ET AL.111

electron collisional excitation rate coefficient, and d

is the electron collisional de-excitation rate coefficient,

which is related to electron collisional excitation rate

coefficient by [16,17].

exp

iij jie

CC EKT

 



 









(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

8.6287 10exp cmsec

ij ij

CKT









(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],

NNN

(4)

where

N is the quantity of ions which reach to ioniza-

tion stage I, is given by

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,











 (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

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

FNg g













(7)

where u

and l

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.

8π2π

ul u









 (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.

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

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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