Fine structure energy levels, wavelengths, log gf and allowed transition probabilities (E1) have been calculated for Lithium-like Ar XVI. The optimized electrostatic parameters by a least square approach, have been used in the calculation to include the configuration interaction and relativistic effects. A total number of 69 Ar XVI levels having total angular momenta, 1/2 ≤
J ≤ 9/2 of even and odd parities, orbital angular momenta 2 ≤
l ≤ 4, with 546 E1 transitions for 6 ≤
n ≤ 10 are considered using the relativistic effect in the Breit-Pauli method, where n is the principal quantum number. A comparison is made with the available results in literature.
Atomic Data Transition Probabilities Ar XVI1. Introduction
Identification of X-rays and EUV fine structure lines of Lithium-like Argon is needed in laboratory and in astrophysical plasma. The X-rays emitted from highly ionized atoms are proved to be important in determining the various plasma parameters [1] [2] .
Experimental data [3] - [5] have been obtained in order to be compared with the theoretical predictions. Theoretical calculations of the energy levels, radiative rates and electron impact excitation rates for transitions in Li-like ions with 12 ≤ Z ≤ 20 and 2 ≤ n ≤ 5 were performed [6] . Electron self-energy screening approximations have been used in multi-electron atoms [7] . Relativistic configuration-interaction calculation of the energy levels of the core-excited states of lithium-like ions was presented [8] . The energies, transition probabilities and oscillator strengths for the electric dipole transitions between the levels of the ground and the low-lying excited states have been calculated using the multi-configuration Dirac-Hartree-Fock method [9] . Theoretical calculations were performed for the Kβ satellite X-rays in the active space approximation using multiconfiguration Dirac- Fock wave functions with the inclusion of the finite nuclear size effect, the Breit interaction and the quantum electrodynamic corrections [10] . The Breit-Pauli R-matrix method has been used to compute the transitions from the upper configurations (n = 4, 5) [11] . The dipole-length, dipole-velocity and dipole-acceleration absorption oscillator strengths were calculated using the energies and the multiconfiguration interaction wave functions obtained from a full core plus the correlation method, in which relativistic and mass-polarization effects on the energy, as a first-order perturbation corrections, are included [12] .
The relativistic energies, fine structures, hyperfine structures, Auger rates and widths of the core-excited states for the Li isoelectronic sequence were studied using the saddle-point variational method and the saddle-point com- plex-rotation method [13] . Electron-impact excitation for Li-like isoelectronic sequence has been obtained using the radiation and Auger damped intermediate-coupling frame transformation R-matrix approach [14] .
In the present work, fine structure energy levels, wavelengths, log gf and radiative allowed transition probabilities are presented for Ar XVI. The calculations have been performed using the Breit-Pauli (BP) approximation, for describing the relativistic interaction between electrons. That is to say, the calculations include both the relativistic Hartree-Fock (RHF) in LS coupling and relativistic correction. The interpretation of the configuration level structures are made by least-squares fit of the observed levels. The least-squares fitting procedure is used to regularize the energy levels. These adjusted fine structure energy levels are used to calculate the transition probabilities. The total number of considered Ar XVI levels is found to be 69, with 546 allowed transition rates. The configuration 1s22s of Li-like ions is taken as the ground state. The energy of the other electronic configurations nili is obtained by adjusting the scaling parameters Eav and ζi(ri) and is listed in Table 1. The calculated fine structure energy levels have been tabulated and compared with the experimental and theoretical data [4] [11] . The allowed electric dipole transition probabilities have been also compared with Ref. [11] using Breit- Pauli R-matrix (BPRM) method and no corresponding experimental data have been found in the literature.
2. Calculation Method2.1. Atomic Structure Theory
In nonrelativistic LS coupling calculations, the normal starting point is Schrödinger’s equation where the Hamiltonian for a multi-electron system, in atomic units is given as [15]
A stationary state of N-electrons is described by a wave function, where repre- sents the space and spin coordinates of the electron i.
The wave function is assumed continuous with respect to the space variables and is the solution of the wave equation.
In the multiconfiguration approximation, the wave functions for a state labeled aJMJ are expanded in terms of the configuration state functions
where a representing the configuration and also the set of quantum numbers both required to specify the state.
2.2. The Relativistic Effects
Breit-Pauli approximation, for describing the relativistic interaction between electrons in an approximate form is [16]
HNR is the non-relativistic multi-electron system hamiltonian. The fine-structure operator HFS is
where HSO is the nuclear spin-orbit term, HSOO is the spin-other-orbit term and HSS is the spin-spin term.
The relativistic shift operator HRS commutes with L and S and can be written
Radial function parameters for Ar XVI ion in units of 1000 cm<sup>−1</sup>
Configuration
Parameter
Configuration
Parameter
1s22s
Eav
0
1s22p
Eav
275.186
1s23s
Eav
4181.68
ζ
17.034
1s24s
Eav
5612.472
1s23p
Eav
4258.086
1s25s
Eav
6267.466
ζ
5.036
1s26s
Eav
6620.889
1s24p
Eav
5643.965
1s27s
Eav
6833.028
ζ
2.12
1s28s
Eav
6970.261
1s25p
Eav
6283.403
1s29s
Eav
7064.112
ζ
1.084
1s210s
Eav
7131.113
1s26p
Eav
6630.048
1s23d
Eav
4288.028
ζ
0.626
ζ
0.949
1s27p
Eav
6838.769
1s24d
Eav
5656.564
ζ
0.394
ζ
0.4
1s28p
Eav
6974.095
1s25d
Eav
6289.829
ζ
0.264
ζ
0.205
1s29p
Eav
7066.799
1s26d
Eav
6633.758
ζ
0.185
ζ
0.118
1s210p
Eav
7133.067
1s27d
Eav
6841.101
ζ
0.135
ζ
0.075
1s24f
Eav
5658.302
1s28d
Eav
6975.655
ζ
0.143
ζ
0.05
1s25f
Eav
6290.68
1s29d
Eav
7067.894
ζ
0.073
ζ
0.035
1s26f
Eav
6634.243
1s210d
Eav
7133.865
ζ
0.043
ζ
0.025
1s27f
Eav
6841.404
1s25g
Eav
6291.053
ζ
0.027
ζ
0.034
1s28f
Eav
6975.858
1s26g
Eav
6634.46
ζ
0.018
ζ
0.02
1s29f
Eav
7068.036
1s27g
Eav
6841.541
ζ
0.013
ζ
0.013
1s210f
Eav
7133.969
1s28g
Eav
6975.949
ζ
0.009
ζ
0.008
1s29g
Eav
7068.1
ζ
0.006
1s210g
Eav
7134.016
ζ
0.004
where is the mass correction term, and are the one and two body Darwin terms, is the orbit?orbit term and is the spin-spin contact term.
The radial wave functions have been generated using the Relativistic Hartree-Fock (RHF) method introduced, using the computer codes (Cowan ATOMIC STRUCTURE PACKAGE) [17] . The relativistic corrections included in the differential equations are derived from the Pauli-approximation to the Dirac-Hartree?Fock equations. The mass-velocity and the Darwin operators are included in the calculations. The radial parameters have been fitted in the least square optimizing program fitting the eigen-values of the hamiltonian to the available experimental energy levels. These optimized integrals have been used to compute both the wavelengths and the transition rates.
2.3. Electric Dipole Decay Rates
The strength of a line is defined as the square of the reduced dipole matrix element [18]
where ψ and ψ' are the wave functions composed of many basis states, the sum runs over all N electrons of the atom (or ion) and ri is the radial position of the ith electron.
The transition probability is related to S according to
where u and l represents the upper and lower levels, respectively, gu is the statistical weight of the upper level of the transition, ao is the Bohr radius and ∆E is the wave number of the spectral line in cm−1.
The weighted oscillator strength for the transition between ψ and ψ' is defined as
3. Results and Discussion
The diagonalization of the energy matrices with RHF values for the energy parameters leads to the theoretical predictions for the energy levels of the configurations. The computer code [17] is used to calculate energy levels, wavelengths, log gf and electric dipole transition probabilities. For even parity, the configurations 1s2ns, nd and ng (n = 6 - 10) have been considered while 1s2np and nf (n = 6 - 10) are considered for the odd parity configurations. They correspond to total angular momenta 1/2 ≤ J ≤ 9/2 of even and odd parities with n = 6 - 10 while orbital angular momenta 0 ≤ L ≤ 4 and spin multiplicity (2S + 1) = 2.
The mentioned configurations for the experimental energy levels taken from Ref. [4] are used in the fitting procedure for Ar XVI. For 1s2ns there is only one parameter (Eav) which is determined from the observed term 2S1/2, for 1s2nd there are two parameters (Eav, ζ2) which are determined from the observed terms 2D3/2 and 2D5/2, for 1s2ng there are two parameters (Eav, ζ2) which are determined from the observed terms 2G7/2 and 2G9/2, for 1s2np there are two parameters (Eav, ζ1) which are determined from the observed terms 2P1/2 and 2P3/2 and for 1s2nf there are two parameters (Eav, ζ2) which are determined from the observed terms 2F5/2, 2F7/2.
The energy of the other electronic configurations are obtained by adjusting the scaling parameters Eav and ζi(ri) are listed in Table 1.
A total of 69 fine structure energy levels for Ar XVI are listed in Table 2, as well as the values compiled by Ref. [4] and those calculated in Ref. [11] .
The calculated fine structure energy levels of the Ar XVI ion agree with the observed and calculated values within the range of 0.15% for most levels. However, ab initio calculations including relativistic effects in the Breit-Pauli R-matrix (BPRM) method by Nahar [11] show a good agreement with the present calculations of fine structure energy levels.
The wavelengths λ (in units of Ǻ), log gf and radiative transition probabilities for spontaneous emission (in units of 108 s−1) for 546 electric dipole allowed transitions E1 are obtained from BP calculations. Table 3 shows
The calculated energy levels in cm<sup>−1</sup> for Ar XVI in comparison with literatures
Configuration
Ecal
E [4]
E [11]
Configuration
Ecal
E [4]
E [11]
1s22s 2S1/2
0
0
0
1s27p 2P1/2
3,897,153
3,897,133
3,896,838
1s22p 2P1/2
1,920,620
1,920,590
1,920,622
1s27p 2P3/2
3,897,351
3,897,321
3,897,068
1s22p 2P3/2
2,002,380
2,002,060
2,002,377
1s27d 2D3/2
3,899,149
3,899,119
3,898,747
1s23s 2S1/2
2,388,872
2,388,872
2,388,861
1s27d 2D5/2
3,899,158
3,899,178
3,898,813
1s23p 2P1/2
2,441,940
2,441,532
2,441,941
1s27f 2F5/2
3,904,946
3,898,946
3,898,901
1s23p 2P3/2
2,444,335
2,443,937
2,444,322
1s27f 2F7/2
3,904,975
3,898,975
3,898,934
1s23d 2D3/2
2,463,791
2,463,771
2,463,789
1s27g 2G7/2
3,905,027
3,898,934
3,898,934
1s23d 2D5/2
2,464,481
2,464,521
2,464,470
1s27g 2G9/2
3,905,045
3,898,952
3,898,956
1s24s 2S1/2
3,202,101
3,202,101
3,202,025
1s28s 2S1/2
3,969,857
3,969,857
3,969,857
1s24p 2P1/2
3,223,450
3,223,425
3,223,446
1s28d 2D3/2
3,974,870
3,974,842
3,974,400
1s24p 2P3/2
3,224,555
3,224,438
3,224,543
1s28d 2D5/2
3,974,870
3,974,881
3,974,444
1s24d 2D3/2
3,232,733
3,232,673
3,232,642
1s28p 2P1/2
3,979,347
3,973,160
3,973,127
1s24d 2D5/2
3,233,089
3,232,989
3,232,861
1s28p 2P3/2
3,979,473
3,973,286
3,973,281
1s24f 2F5/2
3,239,433
3,233,483
3,233,662
1s28f 2F5/2
3,980,573
3,974,543
3,974,510
1s24f 2F7/2
3,239,591
3,233,641
3,233,827
1s28f 2F7/2
3,980,593
3,974,562
3,974,532
1s25s 2S1/2
3,573,450
3,573,451
3,573,442
1s28g 2G7/2
3,980,627
3,974,530
3,974,532
1s25p 2P3/2
3,584,656
3,584,616
3,584,646
1s28g 2G9/2
3,980,639
3,974,542
3,974,543
1s25d 2D3/2
3,588,906
3,588,878
3,588,849
1s29s 2S1/2
4,023,079
4,023,079
4,023,080
1s25d 2D5/2
3,589,068
3,589,004
3,589,036
1s29d 2D5/2
4,026,707
4,026,737
4,026,295
1s25p 2P1/2
3,590,099
3,584,099
3,584,141
1s29d 2D3/2
4,026,709
4,026,709
4,026,262
1s25f 2F5/2
3,595,165
3,589,275
3,589,255
1s29p 2P1/2
4,031,561
4,025,371
4,025,373
1s25f 2F7/2
3,595,247
3,589,357
3,589,354
1s29p 2P3/2
4,031,649
4,025,459
4,025,483
1s25g 2G7/2
3,595,383
3,589,318
3,589,343
1s29f 2F5/2
4,032,421
4,026,341
4,026,339
1s25g 2G9/2
3,595,432
3,589,367
3,589,409
1s29f 2F7/2
4,032,435
4,026,355
4,026,361
1s26s 2S1/2
3,771,342
3,771,342
3,771,342
1s29g 2G7/2
4,032,459
4,026,361
4,026,361
1s26p 2P1/2
3,779,502
3,779,471
3,779,145
1s29g 2G9/2
4,032,467
4,026,369
4,026,372
1s26p 2P3/2
3,779,801
3,779,770
3,779,507
1s210s 2S1/2
4,061,048
4,061,048
4,061,049
1s26d 2D3/2
3,782,704
3,782,726
3,782,173
1s210d 2D3/2
4,063,337
4,063,363
4,063,364
1s26d 2D5/2
3,782,750
3,782,820
3,782,283
1s210d 2D5/2
4,063,339
4,063,383
4,063,386
1s26f 2F5/2
3,788,420
3,794,320
3,782,426
1s210p 2P1/2
4,068,879
4,062,709
4,062,717
1s26f 2F7/2
3,788,467
3,794,367
3,782,481
1s210p 2P3/2
4,068,944
4,062,774
4,062,794
1s26g 2G7/2
3,788,549
3,782,481
3,782,481
1s210f 2F5/2
4,069,505
4,063,445
4,063,419
1s26g 2G9/2
3,788,577
3,782,509
3,782,513
1s210f 2F7/2
4,069,516
4,063,455
4,063,430
1s27s 2S1/2
3,891,943
3,891,943
3,891,943
1s210g 2G7/2
4,069,533
4,063,450
4,063,430
1s210g 2G9/2
4,069,539
4,063,456
4,063,441
Wavelengths (in Å) and the transition rates (in sec<sup>−1</sup>) is compared with Ref. [<xref ref-type="bibr" rid="scirp.59791-ref11">11</xref>]
λ (Å)
Transition
Log gf
Aij (Sec−1)
Aij [11]
14.019
1s22s 2S1/2 - 1s210p 2P1/2
−2.61
4.161E+10
4.000E+10
14.019
1s22s 2S1/2 - 1s210p 2P3/2
−2.309
4.163E+10
3.972E+10
14.15
1s22s 2S1/2 - 1s29p 2P3/2
−2.164
5.713E+10
5.442E+10
14.151
1s22s 2S1/2 - 1s29p 2P1/2
−2.465
5.710E+10
5.483E+10
14.339
1s22s 2S1/2 - 1s28p 2P1/2
−2.3
8.130E+10
7.795E+10
14.339
1s22s 2S1/2 - 1s28p 2P3/2
−1.999
8.133E+10
7.733E+10
14.544
1s22p 2P1/2 - 1s210d 2D3/2
−2.119
5.995E+10
5.942E+10
14.55
1s22p 2P1/2 - 1s210s 2S1/2
−3.539
4.559E+09
4.468E+09
14.598
1s22p 2P3/2 - 1s210d 2D3/2
−2.82
1.186E+10
1.167E+10
14.598
1s22p 2P3/2 - 1s210d 2D5/2
−1.865
7.113E+10
7.037E+10
14.604
1s22p 2P3/2 - 1s210s 2S1/2
−3.239
9.015E+09
9.165E+09
14.622
1s22s 2S1/2 - 1s27p 2P3/2
−1.808
1.213E+11
1.150E+11
14.623
1s22s 2S1/2 - 1s27p 2P1/2
−2.109
1.213E+11
1.160E+11
14.685
1s22p 2P1/2 - 1s29d 2D3/2
−1.969
8.305E+10
8.230E+10
14.693
1s22p 2P1/2 - 1s29s 2S1/2
−3.389
6.300E+09
6.171E+09
14.74
1s22p 2P3/2 - 1s29d 2D3/2
−2.67
1.643E+10
1.616E+10
14.74
1s22p 2P3/2 - 1s29d 2D5/2
−1.715
9.855E+10
9.748E+10
14.748
1s22p 2P3/2 - 1s29s 2S1/2
−3.09
1.246E+10
1.266E+10
14.887
1s22p 2P1/2 - 1s28d 2D3/2
−1.797
1.200E+11
1.188E+11
14.898
1s22p 2P1/2 - 1s28s 2S1/2
−3.221
9.030E+09
8.879E+09
14.943
1s22p 2P3/2 - 1s28d 2D3/2
−2.498
2.373E+10
2.334E+10
14.943
1s22p 2P3/2 - 1s28d 2D5/2
−1.544
1.424E+11
1.407E+11
14.955
1s22p 2P3/2 - 1s28s 2S1/2
−2.922
1.786E+10
1.822E+10
15.082
1s22s 2S1/2 - 1s26p 2P3/2
−1.58
1.926E+11
1.815E+11
15.084
1s22s 2S1/2 - 1s26p 2P1/2
−1.882
1.925E+11
1.832E+11
15.191
1s22p 2P1/2 - 1s27d 2D3/2
−1.597
1.829E+11
1.809E+11
15.209
1s22p 2P1/2 - 1s27s 2S1/2
−3.025
1.361E+10
1.347E+10
15.25
1s22p 2P3/2 - 1s27d 2D3/2
−2.297
3.615E+10
3.555E+10
15.25
1s22p 2P3/2 - 1s27d 2D5/2
−1.343
2.168E+11
2.143E+11
15.269
1s22p 2P3/2 - 1s27s 2S1/2
−2.726
2.690E+10
2.760E+10
15.685
1s22p 2P1/2 - 1s26d 2D3/2
−1.354
3.000E+11
2.965E+11
15.717
1s22p 2P1/2 - 1s26s 2S1/2
−2.79
2.190E+10
2.188E+10
15.748
1s22p 2P3/2 - 1s26d 2D3/2
−2.055
5.930E+10
5.830E+10
15.748
1s22p 2P3/2 - 1s26d 2D5/2
−1.1
3.558E+11
3.512E+11
15.78
1s22p 2P3/2 - 1s26s 2S1/2
−2.491
4.328E+10
4.483E+10
33.882
1s23s 2S1/2 - 1s210p 2P3/2
−2.038
1.329E+10
1.294E+10
33.884
1s23s 2S1/2 - 1s210p 2P1/2
−2.34
1.329E+10
1.309E+10
34.66
1s23s 2S1/2 - 1s29p 2P3/2
−1.882
1.821E+10
1.772E+10
34.663
1s23s 2S1/2 - 1s29p 2P1/2
−2.183
1.821E+10
1.793E+10
34.713
1s23p 2P1/2 - 1s210d 2D3/2
−1.81
2.141E+10
2.134E+10
34.746
1s23p 2P1/2 - 1s210s 2S1/2
−2.973
2.943E+09
2.720E+09
34.803
1s23p 2P3/2 - 1s210d 2D5/2
−1.556
2.550E+10
2.545E+10
34.804
1s23p 2P3/2 - 1s210d 2D3/2
−2.511
4.248E+09
4.235E+09
34.837
1s23p 2P3/2 - 1s210s 2S1/2
−2.673
5.840E+09
5.560E+09
35.12
1s23d 2D3/2 - 1s210f 2F5/2
−1.613
2.198E+10
2.196E+10
35.13
1s23d 2D3/2 - 1s210p 2P3/2
−4.08
1.123E+08
1.090E+08
35.133
1s23d 2D3/2 - 1s210p 2P1/2
−3.381
1.123E+09
1.137E+09
35.149
1s23d 2D5/2 - 1s210f 2F7/2
−1.458
2.349E+10
2.343E+10
35.15
1s23d 2D5/2 - 1s210f 2F5/2
−2.759
1.566E+09
1.556E+09
35.16
1s23d 2D5/2 - 1s210p 2P3/2
−3.127
1.008E+09
9.924E+08
35.527
1s23p 2P1/2 - 1s29d 2D3/2
−1.649
2.963E+10
2.951E+10
35.574
1s23p 2P1/2 - 1s29s 2S1/2
−2.811
4.074E+09
3.775E+09
35.621
1s23p 2P3/2 - 1s29d 2D5/2
−1.395
3.525E+10
3.520E+10
35.622
1s23p 2P3/2 - 1s29d 2D3/2
−2.35
5.875E+09
5.858E+09
35.67
1s23p 2P3/2 - 1s29s 2S1/2
−2.511
8.085E+09
7.719E+09
35.81
1s23s 2S1/2 - 1s28p 2P3/2
−1.701
2.588E+10
2.516E+10
35.815
1s23s 2S1/2 - 1s28p 2P1/2
−2.002
2.587E+10
2.546E+10
35.953
1s23d 2D3/2 - 1s29f 2F5/2
−1.441
3.117E+10
3.113E+10
35.968
1s23d 2D3/2 - 1s29p 2P3/2
−3.914
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1s23d 2D3/2 - 1s29p 2P1/2
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1s23d 2D5/2 - 1s29f 2F7/2
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35.984
1s23d 2D5/2 - 1s29f 2F5/2
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1s23d 2D5/2 - 1s29p 2P3/2
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1s23p 2P1/2 - 1s28d 2D3/2
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1s23p 2P3/2 - 1s28d 2D5/2
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1s23p 2P3/2 - 1s28d 2D3/2
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1s23p 2P3/2 - 1s28s 2S1/2
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1s23d 2D3/2 - 1s28p 2P3/2
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1s23d 2D3/2 - 1s28p 2P1/2
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1s23d 2D5/2 - 1s28f 2F5/2
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37.218
1s23d 2D5/2 - 1s28f 2F7/2
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1s23d 2D5/2 - 1s28p 2P3/2
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1s23s 2S1/2 - 1s27p 2P3/2
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1s23s 2S1/2 - 1s27p 2P1/2
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1s23p 2P1/2 - 1s27d 2D3/2
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1s23p 2P3/2 - 1s27d 2D5/2
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1s23p 2P3/2 - 1s27d 2D3/2
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1s23p 2P3/2 - 1s27s 2S1/2
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1s23d 2D3/2 - 1s27f 2F5/2
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1s23d 2D5/2 - 1s27f 2F7/2
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39.179
1s23d 2D5/2 - 1s27f 2F5/2
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1s23d 2D3/2 - 1s27p 2P1/2
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1s23d 2D5/2 - 1s27p 2P3/2
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1s23s 2S1/2 - 1s26p 2P1/2
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1s23p 2P1/2 - 1s26d 2D3/2
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1s23p 2P3/2 - 1s26d 2D5/2
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1s23p 2P3/2 - 1s26d 2D3/2
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1s23p 2P3/2 - 1s26s 2S1/2
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1s23d 2D5/2 - 1s26f 2F7/2
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1s23d 2D5/2 - 1s26f 2F5/2
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1s23d 2D3/2 - 1s26p 2P1/2
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1s23d 2D5/2 - 1s26p 2P3/2
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1s24s 2S1/2 - 1s210p 2P1/2
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1s24p 2P1/2 - 1s210d 2D3/2
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1s24p 2P1/2 - 1s210s 2S1/2
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1s24p 2P3/2 - 1s210d 2D5/2
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1s24p 2P3/2 - 1s210d 2D3/2
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1s24p 2P3/2 - 1s210s 2S1/2
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1s24d 2D3/2 - 1s210f 2F5/2
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1s24d 2D5/2 - 1s210f 2F7/2
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1s24p 2P1/2 - 1s29d 2D3/2
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1s24f 2F7/2 - 1s29d 2D5/2
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1s24s 2S1/2 - 1s28p 2P3/2
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1s24s 2S1/2 - 1s28p 2P1/2
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1s24f 2F7/2 - 1s28g 2G7/2
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1s24s 2S1/2 - 1s27p 2P1/2
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1s24d 2D3/2 - 1s27f 2F5/2
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1s24d 2D5/2 - 1s27f 2F7/2
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1s24d 2D5/2 - 1s27p 2P3/2
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1s24s 2S1/2 - 1s26p 2P3/2
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1s24s 2S1/2 - 1s26p 2P1/2
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1s24d 2D5/2 - 1s26f 2F7/2
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2.852E+09
436.752
1s27p 2P3/2 - 1s29d 2D5/2
−0.224
3.478E+09
3.445E+09
436.919
1s27p 2P3/2 - 1s29d 2D3/2
−1.179
5.790E+08
5.767E+08
440.487
1s27d 2D3/2 - 1s29f 2F5/2
−0.077
4.800E+09
4.789E+09
440.764
1s27d 2D5/2 - 1s29f 2F7/2
0.078
5.133E+09
5.132E+09
440.849
1s27d 2D5/2 - 1s29f 2F5/2
−1.223
3.420E+08
3.425E+08
441.044
1s27f 2F5/2 - 1s29g 2G7/2
0.182
6.521E+09
6.513E+09
441.175
1s27f 2F7/2 - 1s29g 2G9/2
0.295
6.757E+09
6.752E+09
441.227
1s27f 2F7/2 - 1s29g 2G7/2
−1.249
2.413E+08
2.412E+08
441.349
1s27f 2F5/2 - 1s29d 2D5/2
−2.287
2.943E+07
2.906E+07
441.413
1s27g 2G7/2 - 1s29f 2F7/2
−2.721
8.130E+06
8.033E+06
441.499
1s27g 2G7/2 - 1s29f 2F5/2
−1.29
2.925E+08
2.912E+08
441.519
1s27f 2F5/2 - 1s29d 2D3/2
−1.141
6.175E+08
6.175E+08
441.524
1s27g 2G9/2 - 1s29f 2F7/2
−1.177
2.844E+08
2.823E+08
441.532
1s27f 2F7/2 - 1s29d 2D5/2
−0.987
5.880E+08
5.844E+08
442.669
1s27d 2D3/2 - 1s29p 2P3/2
−1.807
1.327E+08
1.349E+08
442.993
1s27p 2P1/2 - 1s29s 2S1/2
−1.152
1.198E+09
1.258E+09
443.035
1s27d 2D5/2 - 1s29p 2P3/2
−0.853
1.191E+09
1.224E+09
443.214
1s27d 2D3/2 - 1s29p 2P1/2
−1.109
1.322E+09
1.389E+09
444.156
1s27p 2P3/2 - 1s29s 2S1/2
−0.852
2.377E+09
2.563E+09
458.554
1s26s 2S1/2 - 1s27p 2P3/2
−0.154
5.558E+09
5.114E+09
459.8
1s26s 2S1/2 - 1s27p 2P1/2
−0.457
5.510E+09
5.256E+09
472.662
1s26p 2P1/2- 1s27d 2D3/2
0.081
8.993E+09
8.711E+09
474.351
1s26p 2P3/2 - 1s27d 2D5/2
0.335
1.068E+10
1.055E+10
474.771
1s26p 2P3/2 - 1s27d 2D3/2
−0.62
1.775E+09
1.768E+09
481.299
1s26d 2D3/2 - 1s27f 2F5/2
0.52
1.588E+10
1.582E+10
481.769
1s26d 2D5/2 - 1s27f 2F7/2
0.674
2.262E+10
1.696E+10
481.987
1s26d 2D5/2 - 1s27f 2F5/2
−0.627
1.129E+09
1.133E+09
482.272
1s26f 2F5/2 - 1s27g 2G7/2
0.822
2.381E+10
2.378E+10
482.486
1s26f 2F7/2 - 1s27g 2G9/2
0.935
2.467E+10
2.466E+10
482.618
1s26f 2F7/2 - 1s27g 2G7/2
-0.609
8.803E+08
8.812E+08
483.011
1s26g 2G7/2 - 1s27f 2F7/2
−2.242
2.049E+07
2.022E+07
483.049
1s26f 2F5/2 - 1s27d 2D5/2
−1.771
8.065E+07
7.938E+07
483.221
1s26g 2G9/2 - 1s27f 2F7/2
−0.698
7.160E+08
7.105E+08
483.23
1s26g 2G7/2 - 1s27f 2F5/2
−0.811
7.363E+08
7.332E+08
483.397
1s26f 2F7/2 - 1s27d 2D5/2
−0.471
1.610E+09
1.597E+09
483.485
1s26f 2F5/2 - 1s27d 2D3/2
−0.626
1.689E+09
1.689E+09
486.887
1s26d 2D3/2 - 1s27p 2P3/2
−1.267
3.803E+08
3.861E+08
487.591
1s26d 2D5/2 - 1s27p 2P3/2
−0.313
3.408E+09
3.508E+09
488.293
1s26d 2D3/2 - 1s27p 2P1/2
−0.569
3.771E+09
3.992E+09
491.144
1s26p 2P1/2 - 1s27s 2S1/2
−0.588
3.572E+09
3.789E+09
493.421
1s26p 2P3/2 - 1s27s 2S1/2
−0.289
7.045E+09
7.743E+09
613.972
1s28s 2S1/2 - 1s210p 2P3/2
−0.645
1.003E+09
9.395E+08
614.735
1s28s 2S1/2 - 1s210p 2P1/2
−0.946
9.990E+08
9.616E+08
625.015
1s28p 2P1/2 - 1s210d 2D3/2
−0.457
1.490E+09
1.454E+09
626.314
1s28p 2P3/2 - 1s210d 2D5/2
−0.203
1.777E+09
1.759E+09
626.565
1s28p 2P3/2 - 1s210d 2D3/2
−1.157
2.958E+08
2.945E+08
631.432
1s28d 2D3/2 - 1s210f 2F5/2
−0.063
2.410E+09
2.405E+09
631.802
1s28d 2D5/2 - 1s210f 2F7/2
0.091
2.576E+09
2.579E+09
631.93
1s28d 2D5/2 - 1s210f 2F5/2
−1.21
1.717E+08
1.721E+08
632.178
1s28f 2F5/2 - 1s210g 2G7/2
0.193
3.251E+09
3.249E+09
632.351
1s28f 2F7/2 - 1s210g 2G9/2
0.305
3.368E+09
3.369E+09
632.428
1s28f 2F7/2 - 1s210g 2G7/2
−1.239
1.203E+08
1.204E+08
632.635
1s28f 2F5/2 - 1s210d 2D5/2
−2.145
1.990E+07
1.969E+07
632.694
1s28g 2G7/2 - 1s210f 2F7/2
−2.522
6.260E+06
6.201E+06
632.822
1s28g 2G7/2 - 1s210f 2F5/2
−1.091
2.252E+08
2.247E+08
632.846
1s28g 2G9/2 - 1s210f 2F7/2
−0.978
2.190E+08
2.178E+08
632.886
1s28f 2F7/2 - 1s210d 2D5/2
−0.844
3.977E+08
3.959E+08
632.89
1s28f 2F5/2 - 1s210d 2D3/2
−0.999
4.175E+08
4.181E+08
634.701
1s28d 2D3/2 - 1s210p 2P3/2
−1.704
8.183E+07
8.317E+07
635.204
1s28d 2D5/2 - 1s210p 2P3/2
−0.75
7.345E+08
7.546E+08
635.518
1s28d 2D3/2 - 1s210p 2P1/2
−1.006
8.150E+08
8.557E+08
635.802
1s28p 2P1/2 - 1s210s 2S1/2
−1.077
6.905E+08
7.230E+08
637.406
1s28p 2P3/2 - 1s210s 2S1/2
−0.777
1.371E+09
1.473E+09
708.221
1s27s 2S1/2 - 1s28p 2P3/2
−0.115
2.550E+09
2.345E+09
710.211
1s27s 2S1/2 - 1s28p 2P1/2
−0.418
2.528E+09
2.411E+09
728.835
1s27p 2P1/2 - 1s28d 2D3/2
0.1
3.955E+09
3.823E+09
731.321
1s27p 2P3/2 - 1s28d 2D5/2
0.354
4.698E+09
4.636E+09
731.988
1s27p 2P3/2 - 1s28d 2D3/2
−0.6
7.808E+08
7.772E+08
741.661
1s27d 2D3/2 - 1s28f 2F5/2
0.522
6.730E+09
6.711E+09
742.343
1s27d 2D5/2 - 1s28f 2F7/2
0.677
7.191E+09
7.198E+09
742.688
1s27d 2D5/2 - 1s28f 2F5/2
−0.624
4.787E+08
4.809E+08
743.066
1s27f 2F5/2 - 1s28g 2G7/2
0.808
9.715E+09
9.706E+09
743.376
1s27f 2F7/2 - 1s28g 2G9/2
0.921
1.006E+10
1.007E+10
743.585
1s27f 2F7/2 - 1s28g 2G7/2
−0.623
3.590E+08
3.598E+08
744.187
1s27g 2G7/2 - 1s28f 2F7/2
−1.984
1.561E+07
1.543E+07
744.3
1s27f 2F5/2 - 1s28d 2D5/2
−1.596
5.082E+07
5.013E+07
744.501
1s27g 2G9/2 - 1s28f 2F7/2
−0.44
5.455E+08
5.421E+08
744.534
1s27g 2G7/2 - 1s28f 2F5/2
−0.553
5.610E+08
5.592E+08
744.82
1s27f 2F7/2 - 1s28d 2D5/2
−0.296
1.014E+09
1.008E+09
744.992
1s27f 2F5/2 - 1s28d 2D3/2
−0.451
1.064E+09
1.066E+09
750.54
1s27d 2D3/2 - 1s28p 2P3/2
−1.143
2.128E+08
2.160E+08
751.592
1s27d 2D5/2 - 1s28p 2P3/2
−0.19
1.907E+09
1.962E+09
752.776
1s27d 2D3/2 - 1s28p 2P1/2
−0.446
2.109E+09
2.230E+09
758.232
1s27p 2P1/2 - 1s28s 2S1/2
−0.499
1.838E+09
1.940E+09
761.646
1s27p 2P3/2 - 1s28s 2S1/2
−0.2
3.627E+09
3.963E+09
1034.869
1s28s 2S1/2 - 1s29p 2P3/2
−0.079
1.298E+09
1.194E+09
1037.853
1s28s 2S1/2 - 1s29p 2P1/2
−0.381
1.287E+09
1.228E+09
1063.712
1s28p 2P1/2 - 1s29d 2D3/2
0.122
1.950E+09
1.881E+09
1067.211
1s28p 2P3/2 - 1s29d 2D5/2
0.375
2.317E+09
2.283E+09
1068.208
1s28p 2P3/2 - 1s29d 2D3/2
−0.579
3.850E+08
3.829E+08
1081.898
1s28d 2D3/2 - 1s29f 2F5/2
0.531
3.223E+09
3.215E+09
1082.843
1s28d 2D5/2 - 1s29f 2F7/2
0.685
3.444E+09
3.449E+09
1083.36
1s28d 2D5/2 - 1s29f 2F5/2
−0.616
2.293E+08
2.305E+08
1083.849
1s28f 2F5/2 - 1s29g 2G7/2
0.803
4.514E+09
4.512E+09
1084.274
1s28f 2F7/2 - 1s29g 2G9/2
0.916
4.675E+09
4.680E+09
1084.586
1s28f 2F7/2 - 1s29g 2G7/2
−0.628
1.669E+08
1.673E+08
1085.465
1s28g 2G7/2 - 1s29f 2F7/2
−1.802
1.116E+07
1.105E+07
1085.693
1s28f 2F5/2 - 1s29d 2D5/2
−1.463
3.250E+07
3.210E+07
1085.911
1s28g 2G9/2 - 1s29f 2F7/2
−0.258
3.901E+08
3.882E+08
1085.985
1s28g 2G7/2 - 1s29f 2F5/2
−0.371
4.012E+08
4.004E+08
1086.432
1s28f 2F7/2 - 1s29d 2D5/2
−0.162
6.487E+08
6.455E+08
1086.725
1s28f 2F5/2 - 1s29d 2D3/2
−0.317
6.808E+08
6.820E+08
1095.158
1s28d 2D3/2 - 1s29p 2P3/2
−1.044
1.256E+08
1.275E+08
1096.656
1s28d 2D5/2 - 1s29p 2P3/2
−0.09
1.126E+09
1.158E+09
1098.5
1s28d 2D3/2 - 1s29p 2P1/2
−0.346
1.245E+09
1.315E+09
1107.647
1s28p 2P1/2 - 1s29s 2S1/2
−0.425
1.022E+09
1.074E+09
1112.523
1s28p 2P3/2 - 1s29s 2S1/2
−0.126
2.017E+09
2.194E+09
1448.806
1s29s 2S1/2 - 1s210p 2P3/2
−0.045
7.163E+08
6.582E+08
1453.066
1s29s 2S1/2 - 1s210p 2P1/2
−0.347
7.100E+08
6.775E+08
1487.797
1s29p 2P1/2 - 1s210d 2D3/2
0.143
1.048E+09
1.009E+09
1492.551
1s29p 2P3/2 - 1s210d 2D5/2
0.397
1.245E+09
1.226E+09
1493.972
1s29p 2P3/2 - 1s210d 2D3/2
−0.557
2.070E+08
2.057E+08
1512.646
1s29d 2D3/2 - 1s210f 2F5/2
0.542
1.692E+09
1.688E+09
1513.921
1s29d 2D5/2 - 1s210f 2F7/2
0.696
1.809E+09
1.811E+09
1514.651
1s29d 2D5/2 - 1s210f 2F5/2
−0.605
1.204E+08
1.210E+08
1515.277
1s29f 2F5/2 - 1s210g 2G7/2
0.804
2.313E+09
2.312E+09
1515.845
1s29f 2F7/2 - 1s210g 2G9/2
0.917
2.396E+09
2.398E+09
1516.29
1s29f 2F7/2 - 1s210g 2G7/2
−0.628
8.549E+07
8.575E+07
1517.52
1s29g 2G7/2 - 1s210f 2F7/2
−1.662
7.881E+06
7.807E+06
1517.904
1s29f 2F5/2 - 1s210d 2D5/2
−1.355
2.130E+07
2.105E+07
1518.131
1s29g 2G9/2 - 1s210f 2F7/2
−0.118
2.755E+08
2.742E+08
1518.254
1s29g 2G7/2 - 1s210f 2F5/2
−0.231
2.833E+08
2.828E+08
1518.921
1s29f 2F7/2 - 1s210d 2D5/2
−0.054
4.252E+08
4.232E+08
1519.375
1s29f 2F5/2 - 1s210d 2D3/2
−0.209
4.460E+08
4.470E+08
1531.547
1s29d 2D3/2 - 1s210p 2P3/2
−0.961
7.773E+07
7.884E+07
1533.602
1s29d 2D5/2 - 1s210p 2P3/2
−0.008
6.965E+08
7.156E+08
1536.308
1s29d 2D3/2 - 1s210p 2P1/2
−0.264
7.700E+08
8.122E+08
1550.414
1s29p 2P1/2 - 1s210s 2S1/2
−0.361
6.040E+08
6.332E+08
1557.121
1s29p 2P3/2 - 1s210s 2S1/2
−0.062
1.192E+09
1.293E+09
10557.487
1s26s 2S1/2 - 1s26p 2P3/2
−0.379
6.250E+06
1.713E+07
11720.307
1s26s 2S1/2 - 1s26p 2P1/2
−0.725
4.569E+06
1.313E+07
16839.408
1s27s 2S1/2 - 1s27p 2P3/2
−0.31
2.880E+06
7.532E+06
18701.027
1s27s 2S1/2 - 1s27p 2P1/2
−0.656
2.104E+06
5.746E+06
24047.416
1s26p 2P1/2- 1s26d 2D3/2
−0.768
4.920E+05
1.143E+06
25215.587
1s28s 2S1/2 - 1s28p 2P3/2
−0.25
1.473E+06
3.738E+06
28010.42
1s28s 2S1/2 - 1s28p 2P1/2
−0.597
1.075E+06
2.841E+06
28449.899
1s26p 2P3/2 - 1s26d 2D5/2
−0.586
3.565E+05
8.673E+05
31068.444
1s26p 2P3/2 - 1s26d 2D3/2
−1.578
4.563E+04
1.156E+05
35984.154
1s29s 2S1/2 - 1s29p 2P3/2
−0.198
8.155E+05
2.025E+06
38252.606
1s27p 2P1/2 - 1s27d 2D3/2
−0.688
2.339E+05
5.559E+05
39980.809
1s29s 2S1/2 - 1s29p 2P1/2
−0.545
5.945E+05
1.536E+06
45258.064
1s27p 2P3/2 - 1s27d 2D5/2
−0.506
1.695E+05
4.232E+05
49449.846
1s210s 2S1/2 - 1s210p 2P3/2
−0.152
4.805E+05
1.175E+06
54948.074
1s210s 2S1/2 - 1s210p 2P1/2
−0.499
3.503E+05
8.903E+05
57160.79
1s28p 2P1/2 - 1s28d 2D3/2
−0.621
1.221E+05
2.919E+05
67636.072
1s28p 2P3/2 - 1s28d 2D5/2
−0.439
8.840E+04
2.220E+05
81453.058
1s29p 2P1/2 - 1s29d 2D3/2
−0.565
6.850E+04
1.644E+05
96394.741
1s29p 2P3/2 - 1s29d 2D5/2
−0.382
4.960E+04
1.252E+05
111775.431
1s210p 2P1/2 - 1s210d 2D3/2
−0.515
4.080E+04
9.796E+04
132266.211
1s210p 2P3/2 - 1s210d 2D5/2
−0.333
2.955E+04
7.471E+04
the comparison of the present calculations with calculated in the literature [11] . The calculated transition probabilities in the soft X-ray region in the range 14.019 - 98.333Ǻ is within the range 0.017% - 10% accuracy those calculated in Ref. [11] using the Breit-Pauli R-matrix method. The transition probabilities in the EUV region 100.833 - 761.646 Ǻ show a very good agreement within 0.0065% - 10% with the available calculated [11] values. In the far UV 1034.869 - 1557.121 Ǻ, the calculated transition probabilities is in agreement with the calculated values [11] within the range 0.22% - 8.8% accuracy. The transition probabilities in the near infra red and mid-infra red regions 10,557.487 - 132,266.211 Ǻ show an agreement within 57% - 65% with the calculated [11] results. The calculated transition probability of the spectral line 49,449.846 Ǻ of the 1s210s2S1/2 - 1s210p2P3/2 transition shows 59% discrepancy with the calculated results [11] . Since in the present work, the COWAN code [17] , taking into account the relativistic and configuration interaction effects has been used. There is a difference in the present results using the Breit-Pauli approximation and the Breit-Pauli R-matrix (BPRM) method in the near infra red and mid infra red regions. This discrepancy may due to the close coupling (CC) approximation using R-matrix method which may not accurate in the infra red regions. The data of transition probabilities for a great number of lines for Ar XVI is not available. Therefore, there is an urgent needs to the experimental data to be compared with the theoretical results. This experimental support will show the best methods that give accurate results.
4. Conclusion
Calculations have been carried out for fine structure energy levels, wavelengths and allowed transition probabilities in lithium-like Ar XVI including the relativistic effect using the Breit-Pauli approximation. Fine structure energy levels obtained from Breit-Pauli are assessed to be more accurate by 0.15% than the observed and calculated values. The transition probabilities show a good agreement in the soft X-rays, EUV and far UV regions with almost all available calculated values. A slight discrepancy appears in the near infra red and mid infra red regions in the calculated results. No experimental data for the transition probabilities exist in literatures for comparison. However, the present results show that there is an urgent need for experimental data in order to identify the spectral lines from astrophysics and the controlled thermonuclear fusion research.
Cite this paper
A. I.Refaie, (2015) Fine Structure Calculations of Atomic Data for Ar XVI. Journal of Modern Physics,06,1609-1630. doi: 10.4236/jmp.2015.611163
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