Relativistic Configuration Interaction Calculations of ...Relativistic configuration interaction calculations of multi-pole … 239 Dirac coupled equations (equations 2 and 3) are

Advanced Studies in Theoretical Physics

Vol. 10, 2016, no. 5, 235 - 266

HIKARI Ltd, www.m-hikari.com

http://dx.doi.org/10.12988/astp.2016.6314

Relativistic Configuration Interaction Calculations

of Multi-Pole Transitions Rates and

Spectra of Ar I and Ar II

Feras Afaneh and Safeia Hamasha

Department of Physics

The Hashemite University, Zarqa 13115. Jordan

Khaldoon Al Khateeb

College of Art and Sciences at Wadi Aldawaser

Prince Sattam Bin Abdulaziz University, Kingdom of Saudi Arabia

Copyright © 2016 Feras Afaneh et al. This article is distributed under the Creative Commons

Attribution License, which permits unrestricted use, distribution, and reproduction in any medium,

provided the original work is properly cited.

Abstract

The relativistic configuration interaction method of the flexible atomic code

(FAC) was used to calculate atomic data for multi-pole transitions in Ar I and Ar

II. Large-scale calculations were performed to produce atomic structure and

spectra data with ∆n ≠ 0 (n=3→4, 5, 6). Energy levels, oscillator strengths and

transition rates are calculated for electric-dipole (E1), electric quadruple (E2),

electric octupole (E3), magnetic dipole (M1), magnetic quadruple (M2) and

magnetic octupole (M3) transitions. The produced atomic data are important in

modeling of M-shell spectra of Ar ions in laser, astrophysics and plasma

diagnostics. Correlation effects to all orders are considered in the calculations by

the configuration interaction expansion, and all relativistic effects are included.

Some calculated energy levels are compared against published values. An

excellent overall agreement is observed.

Keywords: Atomic Structure; Oscillator Strengths; Transition Probabilities;

Multi-pole Configuration Interaction; Ar Ions; Allowed Transitions; Forbidden

Transitions

236 Feras Afaneh et al.

1. Introduction

Argon is widely used in the manufacturing industry, health sector and also used

for lighting and TIG welding purpose. Argon plasma is widely used for

fundamental plasma spectroscopy studies as well as for numerous application

involving technical plasmas, such as gas lasers and spectra-chemical

investigations with inductively coupled plasmas. It is most widely used in plasma

discharge devices for a large amount of applications that range from wavelength

reference standards to controlled fusion experiment. The kinetics modeling of

laboratory as well as astrophysical plasma requires accurate radiative transition

rates [1]. The detailed understanding of the atomic structure and the investigations

of transition rates in multi- charged ions are of great relevance to plasma

diagnostics and astrophysics.

The relative intensities of forbidden transitions are frequently employed as a

sensitive tool for plasma density diagnostics and coronal lines analysis [2]. For

example the magnetic dipole M1 transitions ratios M1/E1 has been used to

determine the electron density of plasma [3]. M1 lines occur at larger wavelengths

than E1 lines while they connect to levels in the same electron configurations. If

the larger lines extend to visible or near UV range then high resolution techniques

can be used to determine detailed information about lines. Due to the weakness of

the electric quadrapole transitions (E2), the lifetime within indicated accuracy is

determined by the M1 transition. The magnetic dipole M1, and electric

quadrupole E2 have been connected to main features in the optical spectra of

aurora and planetary nebulae [4, 5]. In stellar and solar plasma Argon ions lines

are observed as well as in the laboratory plasma [6]. The spectral lines of argon

are used in determination of chemical abundances of elements of stellar plasmas

[7]. Several experimental studies investigated Ar plasma sources [7-12]. Also

many studies focused on the transition parameters in argon ions. E. B. Saloman

compiled all experimental and theoretical atomic data available in literature for all

argon ions starting from Ar II to Ar XVIII [13]. Also they are listed in NIST data

base [14]. Some forbidden transition parameters of some Ar ions were reported in

several studies [15-21]. M1and E2 transition parameters for Ar III were recently

calculated by L. Özdemir et, al. [22]. Several methods of calculations were used to

calculate atomic data for some Ar ions. Multi-configuration Hartree–Fock

relativistic (HFR) approach is used to calculate the weighted oscillator strengths

and lifetimes for the Ar III [23]. S. N. Nahar used the close-coupling

approximation employing the R-matrix method to calculate allowed transitions of

ArV. [24]. Also C. A. Ramsbottom et, al. used R-matrix method to compute

electron impact excitation collision strengths in Ar IV. [25]. Multi- configuration

Dirac Fock (MCDF) method is used for the calculations of M1 transitions in Ar13+

and Ar14+ [26]. Leyla Özdemir, et al [22] calculated forbidden transitions

magnetic dipole, M1, and electric quadrupole, E2 of doubly ionized argon (Ar III)

using the multi-configuration Hartree-Fock approach within the framework of the

Breit-Pauli Hamiltonian.

http://physics.nist.gov/cgi-bin/ASBib1/Elevbib/make_query.cgi?author=E.%20B.%20Saloman&order=1

Relativistic configuration interaction calculations of multi-pole … 237

Because of the critical importance of the forbidden lines in plasma temperature

and density diagnostic, and the above mentioned importance of argon ions atomic

data of allowed and forbidden transitions for astrophysical and laser and

laboratory studies. It is noticed the lack of recent data for Ar I. The only available

study is reported in 1973 [27]. Also there is a lack of atomic data about magnetic

quadruple, magnetic ouctupole, and electric octupole transitions. Most of the

motioned studies focused on one or two Argon ions. In this work we aimed at

providing comprehensive large scale atomic structure and spectra calculations for

multi-pole transitions of Ar (Ar I) and Ar1+ (Ar II). The main objective is to

produce accurate atomic data that will provide direct access to the important

spectroscopic properties of Ar atoms and ions for both allowed and forbidden

transitions. By comparing the produced data with other previously calculated data

we will benchmark the atomic theories of the methods of calculations.

We performed large scale calculations from n=3 to n=4, 5, 6 shell numbers for

allowed and forbidden transitions. The calculated atomic data includes the energy

levels, oscillator strengths and transition rates for allowed transition (electric

dipole E1) and forbidden (multi-pole) transitions, electric quadruple E2, electric

octupole E3, magnetic dipole M1, magnetic quadruple M2, magnetic octupole

M3. To simulate the Ar experimental spectra we produced synthetic spectra of

both allowed and forbidden transitions of the selected Ar ions individually. The

produced data are tabulated and discussed along with their theoretical spectra.

2. Theoretical model

The relativistic multi configuration interaction (RMCI) method is used to perform

large scale calculations from n=3 to n=4, 5 and 6 shell numbers of Argon atom

(Ar I) and singly ionized Ar ion (Ar II or Ar1+). The Flexible Atomic Code (FAC)

[28] is used to perform the calculation. The calculated data of transitions

parameters were used to calculate synthetic spectra for both allowed and

forbidden transitions [29].

Starting with Dirac equations, ground state configuration for Ar I or Ar II ion is

used to construct a fictitious mean configuration with a fractional occupation

number that takes into account the electron screening of involved configurations.

Bound states are calculated in the configuration mixing approximations with

convenient specification of mixing scheme. Modified self-consistent Dirac-Fock-

Slater iteration is performed to derive a local central potential that is used to

derive the radial orbitals for the construction of basis states. The energy levels are

calculated by digonalizing the constructed Hamiltonian. A correction procedure is

applied to reduce errors in the calculated energy levels.

The relativistic Hamiltonian (H) for an atomic ion with n electrons (in atomic

units) is:

H = ∑ HD(i) + ∑1

rij

Ni<j

Ni=1 (1)


where HD (i) is the single electron Dirac Hamiltonian due to nuclear charge

potential. The approximate atomic state functions are: Ψ = ∑ bμμ φµ, where µ are

the basis states which are anti-symmetric sums of the products of the N Dirac

spinors φnkm. Where φnkm =1

r(

𝑖Pnk(r)χkm(θ, ϕ, σ)

Qnk(r)χ−k,m(θ, ϕ, σ)) ; and bµ are the mixing

coefficients obtained by diagonalizing the total Hamiltonian. n is the principle

quantum number, k is the relativistic angular momentum which is equal to (l-

j)(2j+1); m is the magnetic quantum number; l is the orbital angular momentum;

and j is the total angular momentum. km is the spin angular function; Pnk and Qnk

are the large and small components, respectively. Pnk and Qnk satisfy the coupled

Dirac equation for local central field V(r),

(d

dr+

k

r) Pnk = α (ϵnk − V +

2

α2) Qnk (2)

(d

dr−

k

r) Qnk = α(−ϵnk − V)Pnk (3)

Where the fine is structure constant; and ϵnk is the energy eigen values of the

radial orbitals. V(r) is the sum of nuclear charge contribution potential and the

electron- electron interaction potential Ve-e(r).

𝑉(𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛−𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛)(𝑟) = 1

𝑟 ∑ 𝜔𝑛𝑘(𝑃𝑛𝑘2 (𝑟)+𝑄𝑛𝑘

2 (𝑟))𝑛𝑘

{∑ 𝜔𝑛𝑘(𝜔�́�𝑘−́𝛿𝑛𝑘,�́��́�) ∗𝑛𝑘,�́��́�

𝑟 ∫1

𝑟>(𝑃�́��́�

2 (�́�) + 𝑄�́��́�2 (�́́�))𝑑�́� ∗ (𝑃𝑛𝑘

2 (𝑟) + 𝑄𝑛𝑘2 (𝑟)) + ∑ 𝜔𝑛𝑘(𝜔𝑛𝑘 − 1) ∗ ∑ − (1 +𝐾>0𝑛𝑘

1

2𝑗𝑛𝑘) (

𝑗𝑛𝑘 𝐾 𝑗𝑛𝑘

−1

20

1

2

)

2

∗ 𝑟 ∫𝑟<

𝐾

𝑟>𝐾+1 (𝑃𝑛𝑘

2 (�́�) + 𝑄𝑛𝑘2 (�́�))𝑑�́� ∗ (𝑃𝑛𝑘

2 (𝑟) + 𝑄𝑛𝑘2 (𝑟)) +

∑ ∑ −𝜔𝑛𝑘𝜔�́��́�𝐾 (𝑗𝑛𝑘 𝐾 𝑗�́��́�

−1

20

1

2

)

2

∗𝑛𝑘≠�́��́� 𝑟 ∫𝑟<

𝐾

𝑟>𝐾+1 (𝑃𝑛𝑘(�́�)𝑃�́��́�(�́�) + 𝑄𝑛𝑘(�́�)𝑄�́��́�(�́�)) 𝑑�́� ∗

(𝑃𝑛𝑘(𝑟)𝑃�́��́�(𝑟) + 𝑄𝑛𝑘(𝑟)𝑄�́��́�(𝑟) ) } (4)

The electron-electron interaction includes the spherically averaged potential due

to bound electrons, and local approximations to the exchange interactions.

equation (4), which follows the approach of SZ code [30] after excluding the self-

interaction term in order to correct the asymptotic behavior at large r.

where: (𝑗1 𝑗2 𝑗3

𝑚1 𝑚2 𝑚3) is the Wigner 3-j symbol and r< and r> are the less or grater

of r and r’. The electron-electron contribution to average energy Ee-e is:

𝐸𝑒−𝑒 =1

2∑ 𝜔𝑛𝑘𝑛𝑘 ⟨�́��́�|𝑉𝑒−𝑒|𝑛𝑘⟩ =

1

2∑ 𝜔𝑛𝑘𝑛𝑘 ∫ 𝑉𝑒−𝑒 (𝑟) (𝑃𝑛𝑘

2 (𝑟) + 𝑄𝑛𝑘2 (𝑟))𝑑𝑟 (5)

The (½) factor to the left of the summation is introduced in order to prevent

double counting of electron pairs in the summation.


Dirac coupled equations (equations 2 and 3) are solved by constructing a self-

consistent iteration where a radial orbital from a previous step is used to derive the

potential. The standard Numerov method is then used to solve the acquired

differential equation. The radial function covers a large radial distance for a given

number of grid points. Minimum distances on the radial grid are chosen to be

within the nuclear charge distribution. Maximum distances (rmax) cover the excited

states up to shell number 20. And bound energies are less than Coulomb potential

at rmax.

Radiative transition rates are calculated in a single multipole approximation where

the initial state is: ii b , the final state is: ff b , and the

multipole operator isL

MO . The second quantization method is used to solve the

Hamiltonian matrix elements by recoupling the creation and annihilation operators

with the help of Racah algebra. The line strength of the transition is: 2

i

L

Mffi OS (6)

and the weighted oscillator strength is given by:

fi

L

fi SLfg 221)(

(7)

and finally, the weighted transition rates are given by:

fifi fgAg 232 (8)

where, if EE is the transition energy.

The electric dipole E1, electric quadrapole E2, electric octupole E3, magnetic

dipole M1, magnetic quadrapole M2, magnetic octupole M3 transition

probabilities (s-1) for transitions between the excited states and the ground states

are obtained in terms of line strength Sif (a.u.) and wavelength λ (Å) as:

ifEE

fi SJ

A 1

3

181

)12(

100613.2

, if

MM

fi SJ

A 1

3

131

)12(

1069735.2

ifEE

fi SJ

A 2

5

182

)12(

1011995.1

, if

MM

fi SJ

A2

5

132

)12(

1049097.1

ifEE

fi SJ

A 3

7

173

)12(

1014441.3

, if

MM

fi SJ

A3

7

123

)12(

1018610.4

3. Results and Discussion

The calculations started from the ground state electronic configurations to

single excited configurations of Ar atom and Cl- like Ar (Ar1+) separately. The


calculated atomic data includes: energy levels, wavelengths, transition rates, and

oscillator strengths for allowed and forbidden transition. The atomic data are

calculated, tabulated and discussed.

Doppler line profile at low temperatures is used to convolute the calculated data to

synthetic spectra. The spectral lines intensity is normalized to unity in arbitrary

units. The spectra for both allowed and forbidden transitions for Ar I and Ar II are

shown and discussed along with identifications of their strong transition lines.

Argon Atom (ArI)

Argon (Ar I) has eight valance electrons, the ground electronic configuration is

1s2 2s2 2p6 3s2 3p6, the ground state term is 1S0. The atomic structure calculations

of n=3 yield 27 energy levels, n= 4 yield 1177 energy levels, n=5 yield 1606

energy levels and n= 6 yield to 2114 energy levels of even and odd parities. The

3s sub-shell kept closed through the calculations. The included electronic

configurations in the calculations are: 3s2 3p6, 3s2 3d6 nl, 3s2 3p5nl, 3s2 3d5 nl,

where n= 4, 5 and 6, and l spans all the allowed orbital angular momentum for a

given n. Table 1 lists some calculated energy levels of n=4 of Ar atom by RCIM

of FAC code with the listed data in NIST database [14]. The listed data in NIST is

related to the measured energy levels in 1973 [27]. The difference between the

calculated data by RCIM and the listed data in NIST is up to 1.2263 eV. We have

used another method of calculation to check the validation of RCIM calculated

data. We followed the method of multireference many body perturbation theory

(MR-MBPT) [31] to calculate the energy levels of n=4 shell. The MR-MBPT

method and FAC code are both based on relativistic multi configuration

interaction method but the former includes the high order corrections of quantum

electrodynamics effect (QED) as a second order perturbation theory correction.

The maximum difference between energy levels calculated by RCIM of FAC and

MR-MBPT is 0.2443 eV. This gives an indication that the calculated data by

RCIM of FAC and MR-MBPT of a better agreement than the listed data in NIST.

But since NIST Ar I energy levels are related to an old measurement, so we

believe the calculated data by RCIM of FAC or MR-MBPT are more accurate.

Moreover FAC and MR-MBPT methods did very well in producing accurate data

in so many recent published researches as example [31-36].

The calculated optically allowed strong transitions by RCIM of FAC code

(electric dipole E1) are listed in Table (2). The closed sub-shells do not appear in

the tables. The strongest transitions lines are grouped into 3p-nd, 3p-ns, 3d-nf

transitions, where 3d-nf is the dominant group. The strongest optically allowed

transitions lie in a wide spectral range: (236-12705) Å. Figure (1) represents the

calculated synthetic atomic spectrum of Ar I with Doppler line profile at low

temperatures. The intensity is normalized to unity in arbitrary units (a.u.). The

strong transitions lines of the calculated spectrum were identified on it.

The Forbidden transitions (multipole) are much weaker than the electric

dipole transition. The calculated data of forbidden transitions includes the electric


quadruple E2, electric octupole E3, magnetic dipole M1, magnetic quadruple M2,

magnetic octupole M3 transitions. They are summarized in Table 2. The

calculated spectra of E2, E3 is shown in figure 2. In figure 3 the calculated spectra

of M1, M2, and M3 are shown along with the strong lines identifications. All are

identified in the figures 2 and 3. The radiative transition probabilities (A-values)

ratio of E2 transitions compared to E1 transitions are about

Ar(E2)/Ar(E1)~104/108 ~10- 4. The ratio of A values of E3 transitions compared to

E1 transitions are about Ar(E3)/Ar(E1)~101/108 ~10- 7. Also Ar(M1)/Ar(E1)~10-

2/108 ~10-10, Ar(M2)/Ar(E1) ~10-10 and For magnetic quadruple M3,

Ar(M3)/Ar(E1)~10-5/108 ~10-13.

Cl -like Ar (Ar II)

Ar II or Ar1+ has seven valance electrons, the ground electronic configuration is

1s2 2s2 2p6 3s2 3p5, and the ground state level is: 2P3/2. The atomic structure

calculations of for n=3 (3s sub-shell was kept closed) yield 122 energy levels, n=

4 yield 1486 energy level, n=5 yield 1370 energy levels and n= 6 yield to 1837

energy levels of even and odd parities. The included electronic configurations in

the calculation are: 3s2 3p5, 3s2 3p5 nl, 3s2 3p4 nl, 3s2 3d5 nl where n=4, 5 and 6,

and l spans all the allowed orbital angular momentum for a given n. Table (4)

show part of energy levels table that was calculated by FAC code and the MR-

MBPT method compared with available data in NIST database. The maximum

difference between the energy values calculated by FAC and MR-MBPT methods

is less than 0.2 eV, while the difference between the calculated energy by FAC

and the listed data by NIST is less than 0.8 eV. Actually the comparison of energy

levels of our calculated data with NIST data of Cl-like Ar is in better agreement

than the NIST energy levels of Ar I.

The electric dipole E1 transitions rates, wavelengths, and oscillator strengths are

calculated and listed in Table 5 for only strong optically allowed transitions. They

are grouped into 3p-nd, 3s-np and 3d-nf transitions, where 3d -nf is the dominant.

The calculated synthetic atomic spectrum of Ar II with Doppler line profile is

shown in Figure 4. We found the intense lines are related to 3p-6d transitions in

the spectral range ~ (450-600) Å, 3p-4s transitions in the range ~ (650-750) Å

while 3d-nf are the strongest lines in the whole spectral range ~ (450-1550) Å.

The upper spectrum in figure 4 is for the whole spectral range, while the lower

one is for part of the spectra where the lines other than 3d-nf transitions may

appear. All the strong lines in the whole spectral range are identified on figure 4.

Forbidden transitions (multi-pole transitions) are calculated by RCIM of FAC.

They are listed for strong strongest transitions in Table (5). The synthetic spectra

for electric forbidden transitions E2 and E3 are shown in figure 5 while the

synthetic spectra for magnetic forbidden transitions M1, M2 and M3 are shown in

figure 6. The transitions lines for multipole transitions were identified on the

figures 5 and 6. The A-values ratio of E2 transitions compared to E1 transitions


are about Ar(E2)/Ar(E1)~104/109 ~10-5. The ratio of E3 transitions compared to E1

transitions is: Ar(E3)/Ar(E1)~10-1/109 ~10-10. The transition rates ratios for M1,

M2, and M3 to E1 transitions are respectively: Ar(M1)/Ar(E1)~10-1/109 ~10-10,

Ar(M2)/Ar(E1)~10-2/109 ~10-11, and Ar(M3)/Ar(E1)~10-5/109 ~10- 14.

4. Conclusions

The fully relativistic configuration interaction method (RCIM) of the flexible

atomic code is applied to produce atomic data for energy levels and multipole

transitions of Ar I and Ar II ion. RCIM is expected to yield accurate data as it

includes correlation and relativistic effects by following Dirac- Fock method. It

takes in all leading relativistic effects, and treats correlation effects to all orders.

Wavelengths, radiative transition rates, and oscillator strength values for electric

dipole E1, electric quadruple E2, electric octupole E3, magnetic dipole M1,

magnetic quadruple M2 and magnetic octupole M3 were calculated, tabulated and

their synthetic spectra were produced. The strong transitions were identified

where 3d-nf transitions dominated the optically allowed transitions.

There is a good agreement between the energy levels calculated by RCIM of

FAC for Ar I and the NIST database with difference less than 1.2 eV. Also there

is a good agreement with calculated energy levels of Ar II and NIST database, the

energy difference is less than 0.8 eV. The calculated atomic data reported in this

paper should be reasonably unique and accurate for Ar I and Ar II that are very

helpful for Ar plasma diagnostics and modeling and may other applications of Ar

ions.

Acknowledgements. We acknowledge the support from the Hashemite

University.

0 2000 4000 6000 8000 10000 12000

0.0

0.2

0.4

0.6

0.8

1.0

3d5/2

-6f372

4d5/2

-4f5/2

3d5/2

-4p3/2

3d3/2

-5f7/2

3d3/2

-6f5/2

3d5/2

-6f7/2

3d3/2

-5f5/2

3d5/2

-5f5/2

Wavelength (A0)

Rela

tive In

ten

sit

y (

a.u

.)

Figure (1): The produced synthetic spectrum of electric dipole E1 transitions of

Ar I


400 500 600 700 800 900 1000

0.0

0.2

0.4

0.6

0.8

1.0

400 500 600 700 800 900 1000

0.0

0.2

0.4

0.6

0.8

1.0

5d5/2

-3p1/2

5f7/2

-3p3/2

6p3/2

-3p3/2

Wavelength (A0)

Rela

tive In

ten

sit

y (

a.u

.)

E2

5f7/2

-3p3/2

5p3/2

-3p1/2

E3

Figure 2: The produced synthetic spectra of electric quadruple (E2) and electric

quadruple E3 of Ar I

200 300 400 500 600 700 800 900 1000 1100

0.0

0.2

0.4

0.6

0.8

1.0300 400 500 600 700 800 900 1000 1100

0.0

0.2

0.4

0.6

0.8

1.0300 400 500 600 700 800 900 1000 1100

0.0

0.2

0.4

0.6

0.8

1.0

Wavelength (A0)

5p1/2

-3p3/2

5p1/2

-3p3/2

4p3/2

-3p1/2

M3

5p3/2

-3s1/2

4d5/2

-3p1/2

4d3/2

-3p3/2

Rela

tive In

ten

sit

y (

a.u

.)

M2

4d5/2

-3p3/2

M1

Figure 3: The produced synthetic spectra of the magnetic dipole M1, magnetic

quadruple (M2) and magnetic octupole M3 of Ar I


400 500 600 700 800

0.0

0.2

0.4

0.6

0.8

1.0

200 400 600 800 1000 1200 1400 1600 1800 2000

0.0

0.2

0.4

0.6

0.8

1.0

6d5/2

-3p3/2

4d5/2

-3p3/2

4s3/2

-3p1/2

4s3/2

-3p1/2

6d3/2

-3p3/2

Rela

tive In

ten

sit

y (

a.u

.)

Wavelength (A0)

4f5/2

-3d7/2

5f5/2

-3d7/2

4f5/2

-3d7/2

5f3/2

-3d7/2

5f5/2

-3d5/2

3p3/2

-4s1/2

6d3/2

-3p3/2

Figure 4: The produced synthetic spectrum of electric dipole E1 transitions of Cl-

like Ar

350 400 450 500 550 600 650

0.0

0.2

0.4

0.6

0.8

1.0

350 400 450 500 550 600 650

0.0

0.2

0.4

0.6

0.8

1.0

6d3/2

-3p1/2 6f

7/2-3p

1/2

4p1/2

-4p3/2

4f5/2

-3p3/2

4p3/2

-4p1/2

4p3/2

-4p1/2

4p3/2

-4p1/2

E2

6g9/2

-3p3/2

4d5/2

-3p3/2

4d5/2

-3p3/2

4d5/2

-3p3/2

6g9/2

-3p3/2

6g9/2

-3p3/2

E3

Rela

tive In

ten

sit

y (

a. u

.)

Wavelength (A0)

Figure 5: The produced synthetic spectra of the electric quadruple E2 and electric

octupole E3 of Cl-like Ar


400 450 500 550 600 650

0.0

0.2

0.4

0.6

0.8

1.0400 450 500 550 600 650

0.0

0.2

0.4

0.6

0.8

1.0400 450 500 550 600 650

0.0

0.2

0.4

0.6

0.8

1.0

Wavelength (A0)

4p1/2

-3p3/2

4p1/2

-3p3/2

6s1/2

-3p1/2

5s1/2

-3s1/2M1

6d5/2

-3p3/2

4d5/2

-3p3/2

4d5/2

-3p3/2

4d5/2

-3p3/2

4d5/3

-3p1/2

4d3/2

-3p1/2

4d5/2

-3p3/2

M2

Rela

tive In

ten

sit

y (

a. u

.)6d

5/2-3p

3/2

M3

Figure 6: The produced synthetic spectra of the magnetic dipole M1, magnetic

quadruple M2 and magnetic octupole M3 of Cl-like Ar

Table 1: Comparison of some n=4 energy levels (eV) for Ar atom calculated by FAC

code and MR-MBPT method against NIST database

Ar I

Lev.# Relativistic Conf. P J Energy(eV)-FAC MR-MBPT NIST

0 3p 1/22 3p3/2

4 0 0 0 0 0

1 3p3/23 4s 1/2 1 2 10.876 10.731 11.548

2 3p3/23 4 s 1/2 1 1 10.965 10.826 11.623

3 3p 1/24 s 1/2 1 0 11.055 10.908 11.723

4 3p 1/24 s 1/2 1 1 11.224 11.147 11.828

5 3p3/23 4p3/2 0 1 12.154 11.910 12.907

6 3p3/23 4p3/2 0 3 12.337 12.177 13.273

7 3p3/23 4p 1/2 0 2 12.348 12.211 13.075

8 3p3/23 4p 1/2 0 1 12.422 12.290 13.094

9 3p3/23 4p3/2 0 2 12.460 12.352 13.153

10 3p 1/24p3/2 0 2 12.563 12.453 13.171

11 3p 1/24p3/2 0 1 12.571 12.460 13.282

12 3p 1/24p 1/2 0 1 12.607 12.504 13.302

13 3p 1/24p 1/2 0 0 12.608 12.505 13.327

14 3p3/23 4p3/2 0 0 13.516 13.441 13.479


Table 1: (Continued): Comparison of some n=4 energy levels (eV) for Ar atom

calculated by FAC code and MR-MBPT method against NIST database

15 3p3/23 4d3/2 1 0 13.605 13.461 14.093

16 3p3/23 4d3/2 1 1 13.621 13.494 14.71

17 3p3/23 4d3/2 1 3 13.634 13.498 14.012

18 3p3/23 4d3/2 1 2 13.645 13.502 14.742

19 3p3/23 4d5/2 1 4 13.655 13.533 14.757

20 3p3/23 4d5/2 1 2 13.668 13.549 14.809

21 3p3/23 4d5/2 1 3 13.687 13.564 14.824

22 3p3/23 4f5/2 0 1 13.693 13.566 14.901

23 3p3/23 4f7/2 0 2 13.693 13.567 14.901

24 3p3/23 4f7/2 0 5 13.696 13.568 14.903

25 3p3/23 4f5/2 0 4 13.696 13.568 14.903

26 3p3/23 4f7/2 0 3 13.700 13.571 14.906

27 3p3/23 4f5/2 0 2 13.700 13.571 14.906

28 3p3/23 4f5/2 0 3 13.703 13.573 14.909

29 3p3/23 4f7/2 0 4 13.703 13.573 14.909

30 3p3/23 4d5/2 1 1 13.726 13.648 14.952

Table 2: Calculated energy difference ∆E (eV), wavelengths (λ) in Å,

transition rates Ar (s- 1), and weighted oscillator strengths (gf) for the

strongest electric dipole E1 transitions of Ar atom

Ar I

E1 transitions

upper state P

up J up Lower state P lower

J lower

∆E (eV) gf Ar λ (Å)

3s1/2 6p3/2 1 1 3 p 3/24 0 0 52.456 3.89E-04 1.55E+07 236.39

3s1/2 5p3/2 1 1 3 p 3/24 0 0 31.921 1.13E-02 1.66E+08 388.46

3s1/2 4p3/2 1 1 3 p 3/24 0 0 31.036 2.70E-02 3.76E+08 399.53

3p1/2 6d3/2 1 1 3 p 3/24 0 0 14.211 1.95E-02 5.69E+07 872.56

3 p3/23 6d5/2 1 1 3 p 3/2

4 0 0 14.037 1.67E-02 4.75E+07 883.37

3 p3/23 5g9/2 1 1 3 p 3/2

4 0 0 13.998 4.07E-02 1.15E+08 885.83

3p1/2 4d3/2 1 1 3 p 3/24 0 0 13.943 1.99E-01 5.60E+08 889.34

3 p3/23 5d5/2 1 1 3 p 3/2

4 0 0 13.816 2.09E-02 5.76E+07 897.54

3 p3/23 4d5/2 1 1 3 p 3/2

4 0 0 13.648 2.48E-02 6.69E+07 908.54

3p1/2 6s1/2 1 1 3 p 3/24 0 0 13.64 1.44E-02 3.86E+07 909.1

3 p3/23 6s1/2 1 1 3 p 3/2

4 0 0 13.463 2.35E-02 6.16E+07 921.05


Table 2: (Continued): Calculated energy difference ∆E (eV), wavelengths (λ)

in Å, transition rates Ar (s- 1), and weighted oscillator strengths (gf) for the


3p1/2 5s1/2 1 1 3 p 3/24 0 0 12.918 3.15E-02 7.60E+07 959.94

3 p3/23 5s1/2 1 1 3 p 3/2

4 0 0 12.746 3.81E-02 8.96E+07 972.82

3p1/2 4s1/2 1 1 3 p 3/24 0 0 11.147 4.11E-01 7.39E+08 1112.36

3 p3/23 4s1/2 1 1 3 p 3/2

4 0 0 10.826 3.23E-02 5.48E+07 1145.34

3 d3/22 3 d5/2

3 6f5/2 1 4 3 d3/23 3 d5/2

3 0 4 4.345 1.54E-01 1.40E+07 2853.83

3 d3/22 3 d5/2

3 6f7/2 1 4 3 d3/23 3 d5/2

3 0 3 4.343 1.26E-01 1.14E+07 2855.48

3 d3/22 3 d5/2

3 6f7/2 1 5 3 d3/23 3 d5/2

3 0 4 4.341 1.48E-01 1.10E+07 2856.56

3 d3/22 3 d5/2

3 6f5/2 1 0 3d3/2 3 d5/25 0 1 4.34 1.81E-02 1.48E+07 2857.16

3 d3/22 3 d5/2

3 6f5/24 1 7 3 d3/2

2 3 d5/24 0 6 4.289 2.15E-01 1.14E+07 2890.92

3 d3/22 3 d5/2

3 6f7/2 1 5 3 d3/23 3 d5/2

3 0 4 3.505 2.32E-01 1.13E+07 3537.47

3 d3/22 3 d5/2

3 5f5/2 1 1 3 d3/23 3 d5/2

3 0 0 3.433 6.29E-02 1.07E+07 3611.72

3 d3/22 3 d5/2

3 6f5/2 1 1 3 d3/23 3 d5/2

3 0 0 3.386 7.55E-02 1.25E+07 3662.51

3 d3/22 3 d5/2

3 5f5/2 1 3 3 d3/23 3 d5/2

3 0 2 3.241 1.65E-01 1.07E+07 3826.55

3 d3/22 3 d5/2

3 6f5/2 1 3 3 d3/23 3 d5/2

3 0 2 3.211 1.66E-01 1.06E+07 3861.19

3 d3/22 3 d5/2

3 6f5/24 1 7 3 d3/2

3 3 d5/23 0 6 3.084 3.77E-01 1.04E+07 4020.93

3 d3/22 3 d5/2

3 5f5/24 1 7 3 d3/2

3 3 d5/23 0 6 3.069 4.51E-01 1.23E+07 4039.94

3 d3/22 3 d5/2

3 5f7/22 1 6 3 d3/2

2 3 d5/24 0 5 3.066 3.55E-01 1.11E+07 4044.26

3 d3/22 3 d5/2

3 6f5/2 1 2 3 d3/23 3 d5/2

3 1 3 3.053 2.11E-01 1.70E+07 4061.74

3 d3/22 3 d5/2

3 6f5/2 1 3 3 d3/23 3 d5/2

3 0 4 3.05 4.26E-01 2.46E+07 4065.71

3d3/2 3 d5/24 6p3/2 1 1 3 d3/2

2 3 d5/24 0 2 3.05 7.94E-02 1.07E+07 4065.81

3d3/2 3 d5/24 6p3/2 1 1 3d3/2 3 d5/2

5 0 1 3.046 8.54E-02 1.15E+07 4070.27

3 d3/22 3 d5/2

3 5f7/2 1 2 3 d3/23 3 d5/2

3 0 3 3.044 2.17E-01 1.74E+07 4073.75

3 d3/22 3 d5/2

3 5f7/2 1 3 3 d3/23 3 d5/2

3 0 4 3.042 3.33E-01 1.91E+07 4075.82

3 d3/22 3 d5/2

3 5f7/2 1 1 3 d3/22 3 d5/2

4 0 2 3.04 7.80E-02 1.04E+07 4079.61

3 d3/22 3 d5/2

3 5f7/2 1 4 3 d3/23 3 d5/2

3 0 4 3.036 2.64E-01 1.17E+07 4084.24

3 d3/22 3 d5/2

3 5f7/2 1 2 3 d3/22 3 d5/2

4 0 3 3.034 1.48E-01 1.18E+07 4087

3 d3/22 3 d5/2

3 5f7/2 1 1 3 d3/22 3 d5/2

4 0 2 3.034 1.24E-01 1.64E+07 4087.27

3 d3/22 3 d5/2

3 6f7/2 1 4 3 d3/23 3 d5/2

3 0 4 3.034 2.61E-01 1.16E+07 4087.52

3 d3/22 3 d5/2

3 6f7/2 1 1 3 d3/22 3 d5/2

4 0 2 3.034 1.15E-01 1.53E+07 4087.65

3 d3/22 3 d5/2

3 6f7/2 1 2 3 d3/22 3 d5/2

4 0 3 3.033 1.55E-01 1.24E+07 4088.19

3 d3/22 3 d5/2

3 5f7/2 1 0 3d3/2 3 d5/25 0 1 3.03 3.94E-02 1.57E+07 4092.15

3 d3/22 3 d5/2

3 6f5/2 1 0 3d3/2 3 d5/25 0 1 3.03 2.84E-02 1.13E+07 4092.98

3d3/2 3 d5/24 6f5/2 1 3 3 d5/2

2 0 4 3.022 2.14E-01 1.21E+07 4103

3 d3/22 3 d5/2

3 4p3/2 1 4 3 d3/22 3 d5/2

3 4s1/2 0 5 2.912 4.30E-01 1.76E+07 4258.66

3 d3/22 3 d5/2

3 4p3/2 1 2 3 d3/22 3 d5/2

3 4s1/2 0 3 2.908 2.57E-01 1.89E+07 4264.54

3 d3/22 3 d5/2

3 4p3/2 1 3 3 d3/22 3 d5/2

4 0 4 2.907 3.37E-01 1.76E+07 4265.51

3 d3/22 3 d5/2

3 4p3/2 1 3 3 d3/22 3 d5/2

4 0 2 2.897 2.46E-01 1.28E+07 4280.36

3 d3/22 3 d5/2

3 5f7/2 1 5 3 d3/22 3 d5/2

4 0 4 2.876 4.38E-01 1.43E+07 4311.16





3 d3/22 3 d5/2

3 6f7/2 1 5 3 d3/22 3 d5/2

4 0 4 2.875 3.96E-01 1.29E+07 4312.78

3 d3/22 3 d5/2

3 6f5/2 1 1 3 d5/22 0 2 2.866 1.64E-01 1.94E+07 4325.91

3 d3/22 3 d5/2

3 6f5/2 1 2 3 d5/22 0 2 2.858 1.76E-01 1.25E+07 4338.19

3 d3/22 3 d5/2

3 5f5/2 1 1 3 d5/22 0 2 2.854 1.26E-01 1.49E+07 4344.38

3 d3/22 3 d5/2

3 6h7/2 1 0 3d3/2 3 d5/25 0 1 2.854 4.64E-02 1.64E+07 4344.5

3 d3/22 3 d5/2

3 5f7/2 1 0 3d3/2 3 d5/25 0 1 2.844 4.30E-02 1.51E+07 4359.38

3 d3/22 3 d5/2

3 4p3/2 1 4 3 d3/22 3 d5/2

4 0 4 2.816 3.20E-01 1.23E+07 4402.71

3d3/2 3 d5/24 5f7/2 1 3 3 d3/2

3 3 d5/23 0 2 2.808 2.52E-01 1.23E+07 4416.05

3d3/2 3 d5/24 6f7/2 1 3 3 d3/2

3 3 d5/23 0 2 2.777 2.38E-01 1.14E+07 4464.47

3 d3/22 3 d5/2

3 4p3/2 1 5 3 d3/22 3 d5/2

4 0 6 2.765 8.83E-01 2.66E+07 4485.38

3 d3/22 3 d5/2

3 5d5/2 0 7 3 d3/22 3 d5/2

4 1 6 2.707 6.90E-01 1.46E+07 4581.52

3 d3/22 3 d5/2

3 6f7/24 1 7 3 d3/2

2 3 d5/24 0 6 2.706 6.50E-01 1.38E+07 4581.81

3d3/2 3 d5/24 4p3/2 1 0 3 d3/2

3 3 d5/23 0 1 2.625 4.20E-02 1.26E+07 4724.28

3 d3/22 3 d5/2

3 6f7/24 1 7 3 d3/2

2 3 d5/24 0 6 2.592 8.55E-01 1.66E+07 4783.38

3 d3/22 3 d5/2

3 5f7/24 1 7 3 d3/2

2 3 d5/24 0 6 2.59 9.67E-01 1.88E+07 4787.3

3 d3/22 3 d5/2

3 6f5/2 1 5 3 d3/2

3 3 d5/23 0 6 2.59 5.00E-01 1.32E+07 4788.25

3 d3/22 3 d5/2

3 6f5/2 1 4 3 d3/22 3 d5/2

4 0 5 2.588 3.98E-01 1.29E+07 4791.59

3 d3/22 3 d5/2

3 6f5/2 2 1 6 3 d3/2

3 3 d5/23 0 6 2.587 6.86E-01 1.53E+07 4793.29

3 d3/22 3 d5/2

3 5f5/2 1 5 3 d3/23 3 d5/2

3 0 6 2.585 4.47E-01 1.18E+07 4796.71

3 d3/22 3 d5/2

3 4p3/2 2 1 6 3 d3/22 3 d5/2

3 4s1/2 0 5 2.584 5.51E-01 1.23E+07 4798.6

3 d3/22 3 d5/2

3 6f7/2 1 3 3 d3/22 3 d5/2

4 0 4 2.582 3.03E-01 1.25E+07 4803.26

3 d3/22 3 d5/2

3 6f7/2 1 4 3 d3/22 3 d5/2

4 0 4 2.579 4.62E-01 1.48E+07 4807.79

3 d3/22 3 d5/2

3 4p3/2 1 5 3 d3/22 3 d5/2

4 0 4 2.577 4.56E-01 1.19E+07 4811.68

3 d3/22 3 d5/2

3 5f7/22 1 6 3 d3/2

3 3 d5/23 0 6 2.574 6.68E-01 1.48E+07 4816.67

3 d3/22 3 d5/2

3 4p1/2 1 4 3 d3/22 3 d5/2

3 4s1/2 0 3 2.574 3.60E-01 1.15E+07 4816.91

3 d3/22 3 d5/2

3 5f5/2 1 5 3 d3/22 3 d5/2

4 0 5 2.573 7.44E-01 1.94E+07 4819.95

3 d3/22 3 d5/2

3 5f7/2 1 4 3 d3/22 3 d5/2

4 0 4 2.567 5.90E-01 1.87E+07 4829.93

3 d3/22 3 d5/2

3 4p3/2 1 2 3 d3/22 3 d5/2

3 4d5/2 0 3 2.519 2.23E-01 1.23E+07 4922.97

3 d3/22 3 d5/2

3 6f5/2 1 4 3 d3/22 3 d5/2

4 0 4 2.493 5.06E-01 1.52E+07 4974.77

3 d3/22 3 d5/2

3 5f5/2 1 4 3 d3/22 3 d5/2

4 0 4 2.49 5.07E-01 1.52E+07 4979.83

3 d3/22 3 d5/2

3 6f5/2 1 3 3 d3/22 3 d5/2

4 0 4 2.489 2.64E-01 1.02E+07 4981.38

3 d3/22 3 d5/2

3 5f5/2 1 3 3 d3/22 3 d5/2

4 0 4 2.489 2.71E-01 1.04E+07 4981.6

3 d3/22 3 d5/2

3 4p1/2 1 4 3 d3/23 3 d5/2

3 0 4 2.476 4.18E-01 1.24E+07 5008.84

3 d3/22 3 d5/2

3 4p3/2 1 0 3d3/2 3 d5/25 0 1 2.473 5.49E-02 1.46E+07 5013.79

3 d3/22 3 d5/2

3 4p3/2 1 2 3 d3/23 3 d5/2

3 0 1 2.465 2.30E-01 1.21E+07 5030.56

3 d3/22 3 d5/2

3 4p3/2 1 1 3 d5/22 0 0 2.464 1.83E-01 1.61E+07 5032.24

3 d3/22 3 d5/2

3 4p3/2 1 1 3 d3/23 3 d5/2

3 0 1 2.463 1.38E-01 1.21E+07 5035.39

3 d3/22 3 d5/2

3 4p3/2 1 2 3 d3/22 3 d5/2

4 0 2 2.461 6.87E-01 3.61E+07 5037.72





3 d3/23 3 d5/2

2 4p3/2 1 0 3 d3/23 3 d5/2

3 0 1 2.459 1.84E-01 4.82E+07 5041.71

3 d3/22 3 d5/2

3 4p3/2 1 1 3 d3/22 3 d5/2

4 0 2 2.459 2.28E-01 1.99E+07 5042.56

3 d3/22 3 d5/2

3 4f7/2 4 1 7 3 d3/22 3 d5/2

4 0 6 2.438 5.91E-01 1.02E+07 5087

3 d3/22 3 d5/2

3 4f5/2 1 5 3 d3/23 3 d5/2 0 6 2.419 6.18E-01 1.43E+07 5125.53

3 d3/22 3 d5/2

3 4f7/2 1 4 3 d3/22 3 d5/2

4 0 5 2.417 4.72E-01 1.33E+07 5129.99

3 d3/22 3 d5/2

3 6f5/2 1 5 3 d3/22 3 d5/2

4 0 4 2.284 1.06E+00 2.18E+07 5428.83

3 d3/22 3 d5/2

3 4p1/2 1 2 3 d3/22 3 d5/2

4 0 3 2.283 2.84E-01 1.28E+07 5431.14

3 d3/22 3 d5/2

3 5f7/2 1 5 3 d3/22 3 d5/2

42 0 4 2.283 1.12E+00 2.30E+07 5432.41

3 d3/22 3 d5/2

3 5f5/2 1 4 3 d3/23 3 d5/2

3 0 5 2.281 5.79E-01 1.45E+07 5437.3

3d3/2 3 d5/24 4p1/2 1 1 3 d3/2

3 3 d5/23 0 2 2.28 1.87E-01 1.41E+07 5438.66

3 d3/22 3 d5/2

3 6f7/2 1 4 3 d3/22 3 d5/2

4 0 4 2.277 4.55E-01 1.14E+07 5445.84

3 d3/23 3 d5/2

2 4p3/2 1 3 3 d5/22 0 4 2.277 4.01E-01 1.29E+07 5446.36

3 d3/22 3 d5/2

3 5f7/2 1 2 3 d3/22 3 d5/2

4 0 3 2.274 3.60E-01 1.62E+07 5452.26

3 d3/22 3 d5/2

3 5f5/2 1 3 3 d3/22 3 d5/2

4 0 4 2.274 4.10E-01 1.31E+07 5453.1

3 d3/22 3 d5/2

3 6f5/2 1 4 3 d3/22 3 d5/2

4 0 5 2.253 4.11E-01 1.01E+07 5503.37

3 d3/22 3 d5/2

3 6f7/2 1 2 3 d3/22 3 d5/2

4 0 3 2.247 2.63E-01 1.15E+07 5518.78

3d3/2 3 d5/24 5p3/2 1 1 3 d3/2

3 3 d5/23 0 2 2.228 1.58E-01 1.14E+07 5565.67

3 d3/22 3 d5/2

4 0 0 3 d3/22 3 d5/2

3 4p3/2 1 1 2.196 6.78E-02 1.42E+07 5646.48

3 d3/22 3 d5/2

3 4p3/2 1 1 3 d3/23 3 d5/2

3 0 1 2.159 2.08E-01 1.40E+07 5742.19

3 d3/22 3 d5/2

3 5f5/2 1 2 3 d3/23 3 d5/2

3 0 2 2.136 3.05E-01 1.21E+07 5805.58

3 d3/22 3 d5/2

3 5g11/2 0 1 3 d3/23 3 d5/2

3 1 2 2.129 1.71E-01 1.12E+07 5824.64

3 d3/22 3 d5/2

3 6f5/2 1 2 3 d3/23 3 d5/2

3 0 2 2.122 2.64E-01 1.03E+07 5844.69

3 d3/22 3 d5/2

3 4f7/2 1 5 3 d3/22 3 d5/2

4 0 4 2.114 5.76E-01 1.02E+07 5865.63

3 d3/22 3 d5/2

3 6f5/2 1 1 3 d3/23 3 d5/2

3 0 2 2.106 2.17E-01 1.39E+07 5888.55

3 d3/22 3 d5/2

3 4f7/2 1 2 3 d3/22 3 d5/2

3 4s1/2 0 3 2.095 3.05E-01 1.16E+07 5918.17

3 d3/22 3 d5/2

3 4p3/2 1 1 3 d3/22 3 d5/2

4 0 2 2.095 3.22E-01 2.04E+07 5919.13

3 d3/22 3 d5/2

3 5f7/2 1 4 3 d3/23 3 d5/2

3 0 3 2.088 8.93E-01 1.88E+07 5938.78

3 d3/22 3 d5/2

3 5f7/2 1 3 3 d3/23 3 d5/2

3 0 3 2.086 6.14E-01 1.66E+07 5945.82

3 d3/22 3 d5/2

3 6f7/2 1 3 3 d3/22 3 d5/2

4 0 2 2.047 3.85E-01 1.00E+07 6058.19

3 d3/22 3 d5/2

3 6f7/2 1 4 3 d3/23 3 d5/2

3 0 3 1.998 7.70E-01 1.48E+07 6206.66

3 d3/22 3 d5/2

3 6f7/2 1 3 3 d3/23 3 d5/2

3 0 3 1.993 5.78E-01 1.42E+07 6222.81

3 d3/22 3 d5/2

3 5p3/22 1 6 3 d3/2

2 3 d5/242 0 6 1.99 9.47E-01 1.25E+07 6229.67

3 d3/22 3 d5/2

3 4p3/2 1 4 3 d3/22 3 d5/2

4 0 5 1.982 1.13E+00 2.15E+07 6255.22

3d3/2 3 d5/24 4p1/2 1 5 3 d3/2

3 3 d5/23 0 6 1.982 1.41E+00 2.19E+07 6255.43

3 d3/22 3 d5/2

3 4p3/2 1 3 3 d3/22 3 d5/2

4 0 4 1.978 9.04E-01 2.19E+07 6268.57

3 d3/22 3 d5/2

3 6f7/2 2 1 6 3 d3/22 3 d5/2

42 0 6 1.976 1.97E+00 2.57E+07 6276.11

3 d3/22 3 d5/2

3 6f7/2 4 1 7 3 d3/22 3 d5/2

4 0 6 1.972 1.84E+00 2.07E+07 6287.42

3 d3/22 3 d5/2

3 5f7/2 4 1 7 3 d3/22 3 d5/2

46 0 6 1.966 2.50E+00 2.79E+07 6307.18





3 d3/22 3 d5/2

3 5f5/2 2 1 6 3 d3/22 3 d5/2

4 0 6 1.964 1.23E+00 1.58E+07 6313.83

3 d3/22 3 d5/2

3 5s1/2 0 1 3 d3/23 3 d5/2

3 1 0 1.958 5.07E-01 2.81E+07 6333.75

3 d3/22 3 d5/2

3 5f5/2 2 1 6 3 d3/23 3 d5/2

3 0 5 1.946 1.34E+00 1.69E+07 6373.1

3 d3/22 3 d5/2

3 5f7/2 1 4 3 d3/22 3 d5/2

4 0 3 1.943 6.90E-01 1.26E+07 6380.77

3 d3/22 3 d5/2

3 6p1/2 1 3 3 d5/22 0 2 1.923 6.32E-01 1.45E+07 6446.64

3 d3/22 3 d5/2

3 6f5/2 2 1 6 3 d3/2

2 3 d5/24 1 5 1.92 8.24E-01 1.01E+07 6457.26

3 d3/22 3 d5/2

3 6f5/2 1 1 3 d3/23 3 d5/2

3 0 0 1.915 4.32E-01 2.29E+07 6475.92

3 d3/22 3 d5/2

3 4p3/2 1 2 3 d3/23 3 d5/2

3 0 2 1.911 1.13E+00 3.57E+07 6487.81

3 d3/22 3 d5/2

3 5f7/2 1 3 3 d5/22 0 2 1.909 7.57E-01 1.71E+07 6493.86

3 d3/22 3 d5/2

3 4p3/2 1 2 3 d3/23 3 d5/2

3 0 1 1.885 3.85E-01 1.19E+07 6577.67

3 d3/22 3 d5/2

3 5f5/2 1 4 3 d3/22 3 d5/2

4 0 3 1.883 7.64E-01 1.31E+07 6584.56

3 d3/22 3 d5/2

3 5f7/2 1 3 3 d3/22 3 d5/2

4 0 2 1.882 6.21E-01 1.36E+07 6588.2

3 d3/22 3 d5/2

3 6d5/2 0 4 3 d3/22 3 d5/2

4 0 3 1.881 6.05E-01 1.03E+07 6591.68

3 d3/22 3 d5/2

3 6p3/2 1 3 3 d3/22 3 d5/2

4 0 2 1.881 4.99E-01 1.09E+07 6592.64

3 d3/23 3 d5/2

2 5f5/2 1 5 3 d5/22 0 4 1.862 9.07E-01 1.24E+07 6658.51

3 d3/22 3 d5/2

3 5f7/2 1 3 3 d3/22 3 d5/2

4 0 4 1.861 6.67E-01 1.43E+07 6664.71

3 d3/22 3 d5/2

3 4f7/2 1 5 3 d3/22 3 d5/2

4 0 6 1.827 1.50E+00 1.98E+07 6788.9

3 d3/22 3 d5/2

3 4f7/2 2 1 6 3 d3/22 3 d5/2

4 0 6 1.826 2.51E+00 2.79E+07 6790.51

3 d3/22 3 d5/2

3 4f7/2 4 1 7 3 d3/22 3 d5/2

4 0 6 1.819 1.94E+00 1.86E+07 6818.32

3 d3/22 3 d5/2

3 5f5/2 1 3 3 d3/23 3 d5/2

3 0 3 1.818 8.42E-01 1.73E+07 6821.3

3 d3/22 3 d5/2

3 5f5/2 1 2 3 d3/23 3 d5/2

3 0 3 1.817 5.11E-01 1.46E+07 6823.8

3 d3/22 3 d5/2

3 5f7/2 1 2 3 d3/23 3 d5/2

3 0 2 1.809 4.46E-01 1.27E+07 6854.18

3 d3/22 3 d5/2

3 5f5/2 1 3 3 d3/23 3 d5/2

3 0 2 1.807 5.14E-01 1.04E+07 6860.64

3 d3/22 3 d5/2

3 4p3/2 1 4 3 d3/23 3 d5/2

3 0 3 1.805 7.21E-01 1.13E+07 6868.47

3 d3/22 3 d5/2

3 4f7/2 1 3 3 d3/22 3 d5/2

3 4d5/2 0 3 1.801 5.33E-01 1.07E+07 6884.7

3 d3/22 3 d5/2

3 6f5/2 4 1 7 3 d3/23 3 d5/2

3 0 6 1.783 2.03E+00 1.87E+07 6954.98

3 d3/22 3 d5/2

3 6f7/2 2 1 6 3 d3/22 3 d5/2

4 0 5 1.783 1.72E+00 1.83E+07 6955.63

3 d3/22 3 d5/2

3 6f7/2 1 2 3 d3/23 3 d5/2

3 0 2 1.782 4.44E-01 1.22E+07 6957.76

3 d3/22 3 d5/2

3 6f7/2 1 5 3 d3/22 3 d5/2

4 0 4 1.777 8.32E-01 1.04E+07 6977.19

3 d3/22 3 d5/2

3 4f5/2 2 1 6 3 d3/22 3 d5/2

3 4s1/2 0 5 1.772 9.64E-01 1.01E+07 6998.75

3 d3/22 3 d5/2

3 5f5/2 4 1 7 3 d3/23 3 d5/2

3 0 6 1.762 2.90E+00 2.60E+07 7038.02

3 d3/22 3 d5/2

3 5f7/2 2 1 6 3 d3/22 3 d5/2

4 0 5 1.761 2.45E+00 2.54E+07 7039.58

3 d3/22 3 d5/2

3 5f7/2 2 1 6 3 d3/23 3 d5/2

3 0 6 1.76 1.27E+00 1.32E+07 7045.89

3 d3/22 3 d5/2

3 5f5/2 1 5 3 d3/22 3 d5/2

4 0 4 1.754 1.20E+00 1.46E+07 7068.75

3 d3/22 3 d5/2

3 5f7/2 1 4 3 d3/22 3 d5/2

4 0 4 1.753 6.79E-01 1.01E+07 7072.77

3 d3/23 3 d5/2

2 4p3/2 1 4 3 d3/22 3 d5/2

3 4s1/2 0 5 1.75 9.82E-01 1.45E+07 7084.27

3 d3/22 3 d5/2

3 4f7/2 1 3 3 d3/22 3 d5/2

4 0 4 1.749 5.62E-01 1.07E+07 7090.33

3 d3/22 3 d5/2

3 4p3/2 1 2 3 d3/22 3 d5/2

3 4s1/2 0 3 1.748 4.84E-01 1.28E+07 7092





3 d3/22 3 d5/2

3 6f5/2 1 2 3 d3/23 3 d5/2

3 0 3 1.736 6.49E-01 1.70E+07 7140.95

3 d3/22 3 d5/2

3 6f5/2 1 4 3 d3/23 3 d5/2

3 0 3 1.722 7.01E-01 1.00E+07 7199.82

3 d3/22 3 d5/2

3 4f5/2 1 3 3 d3/22 3 d5/2

4 0 2 1.688 1.01E+00 1.79E+07 7344.29

3 d3/22 3 d5/2

3 4f5/2 1 0 3 d3/23 3 d5/2

3 0 1 1.64 8.57E-02 1.00E+07 7562.38

3 d3/22 3 d5/2

3 4p3/2 1 2 3 d3/22 3 d5/2

4 0 3 1.623 6.25E-01 1.43E+07 7639.62

3 d3/22 3 d5/2

3 4p1/2 1 3 3 d3/23 3 d5/2

3 0 4 1.623 1.19E+00 1.94E+07 7641.59

3 d3/22 3 d5/2

3 4p3/2 1 5 3 d3/22 3 d5/2

4 0 6 1.621 1.79E+00 1.86E+07 7650.18

3 d3/22 3 d5/2

3 4f7/2 2 1 6 3 d3/23 3 d5/2

3 0 6 1.621 1.63E+00 1.43E+07 7651.04

3 d3/22 3 d5/2

3 4p3/2 1 1 3d3/2 3 d5/25 0 1 1.62 2.83E-01 1.07E+07 7654.25

3 d3/22 3 d5/2

3 4f7/2 1 5 3 d3/22 3 d5/2

4 0 5 1.62 1.39E+00 1.44E+07 7655.71

3 d3/22 3 d5/2

3 4f5/2 4 1 7 3 d3/23 3 d5/2

3 0 6 1.614 2.98E+00 2.25E+07 7680.66

3 d3/22 3 d5/2

3 4f7/2 2 1 6 3 d3/22 3 d5/2

4 0 5 1.614 2.47E+00 2.14E+07 7684.39

3 d3/22 3 d5/2

3 4f7/2 1 5 3 d3/22 3 d5/2

4 0 4 1.608 2.11E+00 2.16E+07 7711.49

3 d3/22 3 d5/2

3 5f5/2 1 4 3 d5/22 0 4 1.589 8.80E-01 1.07E+07 7802.88

3 d3/22 3 d5/2

3 4f5/2 1 3 3 d3/22 3 d5/2

3 4d5/2 0 3 1.537 1.02E+00 1.49E+07 8068.13

3 d3/22 3 d5/2

3 4f5/2 1 2 3 d3/22 3 d5/2

3 4d5/2 0 3 1.527 5.35E-01 1.08E+07 8121.86

3 d3/22 3 d5/2

3 4p3/2 1 3 3 d3/22 3 d5/2

4 0 4 1.505 1.40E+00 1.96E+07 8237.07

3 d3/23 3 d5/2

2 4p3/2 1 2 3 d3/23 3 d5/2

3 0 3 1.455 6.45E-01 1.18E+07 8524.73

3 d3/22 3 d5/2

3 4p1/2 1 0 3 d3/22 3 d5/2

4 0 1 1.453 1.48E-01 1.36E+07 8531.61

3 d3/22 3 d5/2

3 4p3/2 1 1 3 d3/22 3 d5/2

4 0 2 1.43 6.97E-01 2.06E+07 8668.53

3 d3/22 3 d5/2

3 4p3/2 1 5 3 d3/23 3 d5/2

3 0 4 1.415 1.32E+00 1.04E+07 8762.59

3 d3/22 3 d5/2

3 4f7/2 1 1 3 d3/22 3 d5/2

4 0 0 1.259 6.70E-01 1.54E+07 9846.61

3 d3/22 3 d5/2

3 5f7/2 1 1 3 d3/22 3 d5/2

4 0 0 1.245 1.03E+00 2.31E+07 9957.1

3 d3/22 3 d5/2

3 6f5/2 1 5 3 d3/23 3 d5/2

3 0 4 1.124 2.21E+00 1.10E+07 11033.66

3 d3/22 3 d5/2

3 5f7/2 1 4 3 d3/23 3 d5/2

3 0 3 1.122 2.21E+00 1.34E+07 11049.22

3 d3/22 3 d5/2

3 5f5/2 1 5 3 d3/23 3 d5/2

3 0 4 1.121 3.24E+00 1.61E+07 11064.41

3 d3/22 3 d5/2

3 5f7/2 1 3 3 d3/22 3 d5/2

4 0 2 1.12 1.41E+00 1.10E+07 11071.54

3 d3/22 3 d5/2

3 6f7/2 1 1 3 d3/22 3 d5/2

4 0 0 1.119 1.23E+00 2.23E+07 11077.61

3 d3/22 3 d5/2

3 4f5/2 1 5 3 d3/23 3 d5/2

3 0 4 0.976 2.75E+00 1.03E+07 12705.82

Table 3: Energy difference ∆E (eV), wavelengths (λ) in Å, transition rates

(Ar) in s- 1, and oscillator strength (gf) for the strongest multipole E2, E3,

M1, M2, M3 transitions of Ar atom

Ar :E2 transitions

upper state

P (up)

J (up)

Lower state

P (lower)

J (lower)

∆E (eV)

gf Ar (s-1)

λ ( Å)

3s1/2 5d5/2 0 2 3p3/2

4 0 0 32.393 3.17E-07 2.89E+03 382.8

3s1/2 4d5/2 0 2 3p3/2

4 0 0 32.124 1.42E-06 1.28E+04 386


Table 3: (Continued): Energy difference ∆E (eV), wavelengths (λ) in Å,

transition rates (Ar) in s- 1, and oscillator strength (gf) for the strongest

multipole E2, E3, M1, M2, M3 transitions of Ar atom

3s1/2 5f5/2 1 3 3p3/2

4 0 0 32.442 1.59E-10 1.03E+00 382.22

3p1/2 6d5/2 1 3 3p3/2

4 0 0 14.189 2.17E-09 2.70E+00 873.9

3p1/2 6g7/2 1 3 3p3/2

4 0 0 14.179 1.85E-08 2.31E+01 874.51

3p1/2 5g7/2 1 3 3p3/2

4 0 0 14.059 3.90E-09 4.77E+00 882

3p3/23 6d5/2 1 3 3p3/2

4 0 0 14.02 1.76E-09 2.14E+00 884.46

3p3/23 6d3/2 1 3 3p3/2

4 0 0 14.007 2.71E-09 3.30E+00 885.24

3p3/23 6g7/2 1 3 3p3/2

4 0 0 13.997 1.38E-08 1.68E+01 885.88

3p3/23 6g9/2 1 3 3p3/2

4 0 0 13.996 2.46E-08 2.98E+01 885.95

3p3/23 5g7/2 1 3 3p3/2

4 0 0 13.877 2.94E-09 3.51E+00 893.55

3p3/23 5g9/2 1 3 3p3/2

4 0 0 13.876 5.18E-09 6.19E+00 893.66

3p1/2 6f5/2 0 2 3p3/2

4 0 0 14.224 2.36E-06 4.14E+03 871.77

3p3/23 6f5/2 0 2 3p3/2

4 0 0 14.042 2.44E-06 4.17E+03 883.07

3p3/23 6f7/2 0 2 3p3/2

4 0 0 14.04 2.79E-06 4.77E+03 883.2

3p1/2 5f5/2 0 2 3p3/2

4 0 0 14.03 1.98E-06 3.39E+03 883.81

3p1/2 4f5/2 0 2 3p3/2

4 0 0 13.882 1.81E-06 3.03E+03 893.26

3p3/23 5f5/2 0 2 3p3/2

4 0 0 13.849 1.99E-06 3.30E+03 895.4

3p1/2 6p3/2 0 2 3p3/2

4 0 0 13.848 3.36E-05 5.59E+04 895.43

3p3/23 5f7/2 0 2 3p3/2

4 0 0 13.845 2.43E-06 4.03E+03 895.64

3p3/23 4f5/2 1 2 3p3/2

4 0 0 13.7 1.86E-06 3.03E+03 905.13

3p3/23 4f7/2 1 2 3p3/2

4 0 0 13.693 2.35E-06 3.82E+03 905.59

3p3/23 6p3/2 0 2 3p3/2

4 0 0 13.675 2.38E-05 3.86E+04 906.78

3p3/23 6p1/2 0 2 3p3/2

4 0 0 13.664 3.93E-05 6.37E+04 907.51

3p1/2 5p3/2 0 2 3p3/2

4 0 0 13.484 7.09E-06 1.12E+04 919.61

3p3/23 5p3/2 0 2 3p3/2

4 0 0 13.326 5.43E-06 8.38E+03 930.5

3p3/23 5p1/2 0 2 3p3/2

4 0 0 13.295 6.76E-06 1.04E+04 932.71

Ar :E3 transitions

Upper state

P (up)

J (up)

Lower state

P (lower)

J (lower)

∆E (eV) gf Ar(s-1) λ ( Å)

Ar :M1 transitions

upper state

P (up)

J (up)

Lower state

P (lower)

J (lower) ∆E (eV) gf Ar(s-1) λ ( Å)

3s1/2 6s1/2 0 1 3p3/2

4 0 0 32.089 8.11E-14 1.21E-03 386.43

3p1/2 6p3/2 0 1 3p3/2

4 0 0 13.845 4.03E-12 1.12E-02 895.6

3p3/23 6p1/2 0 1 3p3/2

4 0 0 13.672 1.55E-12 4.18E-03 906.94

3p3/23 6p3/2 0 1 3p3/2

4 0 0 13.642 2.19E-12 5.90E-03 908.97

3p1/2 5p3/2 0 1 3p3/2

4 0 0 13.484 9.44E-12 2.48E-02 919.63

3p1/2 5p1/2 0 1 3p3/2

4 0 0 13.475 2.03E-12 5.33E-03 920.19

3p3/23 5p1/2 0 1 3p3/2

4 0 0 13.317 3.74E-12 9.59E-03 931.12

3p3/23 5p3/2 0 1 3p3/2

4 0 0 13.243 2.86E-12 7.26E-03 936.34

3p1/2 4p1/2 0 1 3p3/2

4 0 0 12.607 1.15E-11 2.64E-02 983.57

3p1/2 4p3/2 0 1 3p3/2

4 0 0 12.571 3.72E-11 8.51E-02 986.44

3p3/23 4p1/2 0 1 3p3/2

4 0 0 12.422 9.13E-12 2.04E-02 998.26 3p3/2

3 4p3/2 0 1 3p3/24 0 0 12.154 2.41E-12 5.15E-03 1020.30


Table 3: (Continued): Energy difference ∆E (eV), wavelengths (λ) in Å,

transition rates (Ar) in s- 1, and oscillator strength (gf) for the strongest

multipole E2, E3, M1, M2, M3 transitions of Ar atom

Ar :M2 transitions

upper state P (up)

J (up)

Lower state

P (lower)

J (lower)


3s1/2 6p3/2 1 2 3p3/2

4 0 0 32.277 3.52E-12 3.19E-02 384.17

3s1/2 5p3/2 1 2 3p3/2

4 0 0 31.878 3.12E-12 2.75E-02 388.98

3s1/2 4p3/2 1 2 3p3/2

4 0 0 30.814 3.84E-12 3.16E-02 402.42

3p1/2 6d5/2 1 2 3p3/2

4 0 0 14.187 7.90E-13 1.38E-03 874.02

3p3/23 6d5/2 1 2 3p3/2

4 0 0 14.015 3.06E-12 5.22E-03 884.77

3p3/23 6d3/2 1 2 3p3/2

4 0 0 14.01 2.46E-12 4.19E-03 885.09

3p1/2 5d5/2 1 2 3p3/2

4 0 0 13.963 1.24E-12 2.10E-03 888.06

3p1/2 4d3/2 1 2 3p3/2

4 0 0 13.872 7.78E-13 1.30E-03 893.87

3p1/2 4d5/2 1 2 3p3/2

4 0 0 13.813 1.25E-12 2.07E-03 897.72

3p3/23 5d3/2 1 2 3p3/2

4 0 0 13.795 4.68E-12 7.72E-03 898.86

3p3/23 5d5/2 1 2 3p3/2

4 0 0 13.786 6.02E-12 9.93E-03 899.45

3p3/23 4d5/2 1 2 3p3/2

4 0 0 13.668 1.78E-11 2.89E-02 907.25

3p3/23 4d3/2 1 2 3p3/2

4 0 0 13.645 4.86E-12 7.85E-03 908.75

3p3/23 6s1/2 1 2 3p3/2

4 0 0 13.471 1.24E-12 1.95E-03 920.48

3p3/23 4s1/2 1 2 3p3/2

4 0 0 10.876 1.16E-11 1.19E-02 1140.1

Ar: M3 transitions

upper state

P (up)

J (up)

Lower state

P (lower)

J (lower)


3s1/2 5d5/2 0 3 3p3/2

4 0 0 32.382 1.70E-16 1.10E-06 382.92

3s1/2 4d5/2 0 3 3p3/2

4 0 0 32.106 7.49E-16 4.78E-06 386.22

3p1/2 6f7/2 0 3 3p3/2

4 0 0 14.224 2.18E-16 2.73E-07 871.79

3p3/23 6f5/2 0 3 3p3/2

4 0 0 14.043 9.44E-17 1.15E-07 883.01

3p3/23 6f7/2 0 3 3p3/2

4 0 0 14.042 6.34E-16 7.75E-07 883.07

3p1/2 5f7/2 0 3 3p3/2

4 0 0 14.03 1.81E-16 2.21E-07 883.82

3p1/2 4f7/2 0 3 3p3/2

4 0 0 13.882 1.38E-16 1.65E-07 893.27

3p3/23 5f7/2 0 3 3p3/2

4 0 0 13.848 5.33E-16 6.33E-07 895.41

3p3/23 4f7/2 0 3 3p3/2

4 0 0 13.7 5.00E-16 5.82E-07 905.14

3p3/23 6p3/2 0 3 3p3/2

4 0 0 13.657 9.31E-15 1.08E-05 907.95

3p3/23 5p3/2 0 3 3p3/2

4 0 0 13.287 1.76E-15 1.92E-06 933.27


Table 4: Comparison of some n=4 energy levels (eV) for Cl- like Ar

calculated by FAC code and MR-MBPT method against NIST database

Cl- like Ar

Level Relativistic Conf P J Energy(eV)- FAC MR-MBPT NIST

0 3p3/23 1 1.5 0 0 0

1 3p 1/2 1 0.5 0.17656 0.1845 0.17749

2 3p3/22 4s 1/2 0 2.5 16.01626 15.8648 16.6438

3 3p 1/2 3p3/2

3 4s 1/2 0 1.5 16.11333 15.9688 16.7485

4 3p 1/2 3p3/2

3 4s 1/2 0 0.5 16.20023 16.0402 16.8124

5 3p3/22 4s 1/2 0 1.5 16.68399 16.6230 17.14

6 3p 1/2 3p3/2

3 4s 1/2 0 0.5 16.81739 16.7524 17.2658

7 3p 1/2 3p3/2

3 4s 1/2 0 2.5 18.12026 18.0924 18.4265

8 3p 1/2 3p3/2

3 4s 1/2 0 1.5 18.1237 18.0957 18.4541

9 3p3/22 4p3/2 1 2.5 18.4511 18.2573 19.2229

10 3p3/22 4p 1/2 1 1.5 18.48686 18.2977 19.261

11 3p 1/2 3p3/2

3 4p 1/2 1 0.5 18.53811 18.3428 19.3053

12 3p3/22 4p3/2 1 3.5 18.74778 18.6050 19.4945

13 3p 1/2 3p3/2

3 4p3/2 1 2.5 18.79605 18.6678 19.549

14 3p 1/2 3p3/2

3 4p 1/2 1 1.5 18.87018 18.7289 19.6103

15 4p 1/2 1 0.5 18.92014 18.7663 19.6425

16 3p 1/2 3p3/2

3 4p3/2 1 2.5 19.0111 18.9140 19.68

17 3p 1/2 3p3/2

3 4p3/2 1 1.5 19.11683 19.0192 19.7622

18 3p3/22 4p3/2 1 0.5 19.22763 19.1363 19.801

19 3p 1/2 3p3/2

3 4p3/2 1 1.5 19.28399 19.2303 19.8671

20 3p 1/2 3p3/2

3 4p3/2 1 1.5 19.33965 19.2390 19.9674

21 3p 1/2 3p3/2

3 4p3/2 1 0.5 19.37414 19.2939 19.9725

22 3p 1/2 3p3/2

3 4p 1/2 1 2.5 20.57763 20.5235 21.127

23 3p 1/2 3p3/2

3 4p3/2 1 3.5 20.58491 20.5321 21.143

24 3p3/22 4s 1/2 0 0.5 20.89198 20.9772 20.7435

25 3p 1/2 3p3/2

3 4p3/2 1 1.5 20.97195 20.9904 21.3517

26 3p 1/2 3p3/2

3 4p3/2 1 2.5 20.97854 20.9991 21.4264

27 3p 1/2 3p3/2

3 4p 1/2 1 1.5 21.52717 21.5439 21.3517

28 3p 1/2 3p3/2

3 4p3/2 1 0.5 21.59093 21.6013 21.4264


Table (5): The calculated energy difference ∆E (eV), wavelengths (λ) in Å,

transition rates Ar(s- 1), and weighted oscillator strengths (gf) for the

strongest electric dipole E1 transitions of Cl- like Ar

Cl- like Ar

E1 transitions

upper state P up J up Lower state P lower J lower ∆E (eV) gf Ar λ (Å)

3p3/22 6d5/2 0 2.5 3p3/2

3 1 1.5 29.222 1.48E-02 9.16E+07 424.34

3p3/22 6d3/2 0 1.5 3p1/2 1 0.5 29.041 1.04E-02 9.55E+07 426.99

3p3/22 6s1/2 0 0.5 3p3/2

3 1 1.5 28.002 4.60E-03 7.82E+07 442.82

3p3/22 4d3/2 0 1.5 3p3/2

3 1 1.5 26.755 1.77E-02 1.38E+08 463.47

3p3/22 4d5/2 0 2.5 3p3/2

3 1 1.5 26.74 1.59E-01 8.24E+08 463.73

3p3/22 4d3/2 0 1.5 3p1/2 1 0.5 26.578 1.13E-01 8.64E+08 466.54

3p1/2 3p3/2

3 6d3/2 0 0.5 3p3/23 1 1.5 26.505 2.29E-02 3.48E+08 467.84

3p1/2 3p3/2

3 6d5/2 0 1.5 3p3/23 1 1.5 26.501 3.86E-02 2.93E+08 467.91

3p1/2 3p3/2

3 6d5/2 0 2.5 3p3/23 1 1.5 26.49 3.65E-02 1.85E+08 468.1

3p1/2 3p3/2

3 6d5/2 0 0.5 3p3/23 1 1.5 26.49 4.93E-03 7.51E+07 468.11

3p1/2 3p3/2

3 6d5/2 0 0.5 3p1/2 1 0.5 26.324 2.16E-02 3.24E+08 471.06

3p1/2 3p3/2

3 6d3/2 0 1.5 3p1/2 1 0.5 26.32 2.22E-02 1.67E+08 471.13

3p1/2 3p3/2

3 6d5/2 0 1.5 3p1/2 1 0.5 26.309 9.83E-03 7.38E+07 471.33

3p1/2 3p3/2

3 6d3/2 0 0.5 3p1/2 1 0.5 26.295 6.24E-03 9.37E+07 471.58

3p1/2 3p3/2

3 6s1/2 0 2.5 3p3/23 1 1.5 25.23 2.45E-02 1.13E+08 491.48

3p1/2 3p3/2

3 6s1/2 0 1.5 3p1/2 1 0.5 25.049 1.49E-02 1.01E+08 495.04

6d5/2 0 2.5 3p3/23 1 1.5 24.86 8.14E-02 3.63E+08 498.8

3p3/22 6g7/2 0 1.5 3p3/2

3 1 1.5 24.743 7.61E-03 5.05E+07 501.15

3p1/2 3p3/2

3 6d3/2 0 1.5 3p3/23 1 1.5 24.743 3.19E-02 2.12E+08 501.15

3p1/2 3p3/2

3 6d5/2 0 1.5 3p1/2 1 0.5 24.72 5.61E-02 3.71E+08 501.62

6d5/2 0 2.5 3p3/23 1 1.5 24.709 2.69E-02 1.19E+08 501.84

3p1/2 3p3/2

3 6d3/2 0 0.5 3p3/23 1 1.5 24.697 5.67E-03 7.51E+07 502.08

3p1/2 3p3/2

3 6d3/2 0 0.5 3p1/2 1 0.5 24.528 9.86E-03 1.29E+08 505.55

3p1/2 3p3/2

3 4d5/2 0 0.5 3p3/23 1 1.5 24.477 8.45E-02 1.09E+09 506.59

3p1/2 3p3/2

3 4d3/2 0 1.5 3p3/23 1 1.5 24.369 5.82E-01 3.75E+09 508.85

3p3/22 4d5/2 0 2.5 3p3/2

3 1 1.5 24.333 6.96E-01 2.98E+09 509.59


Table (5): (Continued): The calculated energy difference ∆E (eV),

wavelengths (λ) in Å, transition rates Ar(s- 1), and weighted oscillator

strengths (gf) for the strongest electric dipole E1 transitions of Cl- like Ar

3p1/2 3p3/2

3 4d5/2 0 0.5 3p1/2 1 0.5 24.262 2.28E-01 2.91E+09 511.09

3p1/2 3p3/2

3 4d5/2 0 1.5 3p1/2 1 0.5 24.222 5.10E-01 3.25E+09 511.94

3p1/2 3p3/2

3 4d5/2 0 0.5 3p3/23 1 1.5 24.112 1.84E-01 2.32E+09 514.27

3p1/2 3p3/2

3 4d5/2 0 0.5 3p1/2 1 0.5 23.935 6.79E-02 8.44E+08 518.06

6s1/2 0 0.5 3p3/23 1 1.5 23.578 6.79E-03 8.19E+07 525.92

3p1/2 3p3/2

3 6s1/2 0 1.5 3p3/23 1 1.5 23.458 2.10E-02 1.26E+08 528.62

6s1/2 0 0.5 3p1/2 1 0.5 23.396 1.19E-02 1.41E+08 530

3p3/22 6s1/2 0 1.5 3p3/2

3 1 1.5 23.366 2.48E-02 1.47E+08 530.69

3p1/2 3p3/2

3 6s1/2 0 0.5 3p1/2 1 0.5 23.312 5.70E-03 6.71E+07 531.9

3p1/2 3p3/2

3 4d5/2 0 2.5 3p3/23 1 1.5 22.802 5.24E-01 1.97E+09 543.82

3p1/2 3p3/2

3 4d5/2 0 1.5 3p3/23 1 1.5 22.753 2.70E-02 1.52E+08 544.99

3p1/2 3p3/2

3 4d5/2 0 1.5 3p1/2 1 0.5 22.576 2.65E-01 1.46E+09 549.26

3p1/2 3p3/2

3 4d5/2 0 1.5 3p3/23 1 1.5 22.529 1.41E-01 7.77E+08 550.4

3p3/22 4d5/2 0 0.5 3p3/2

3 1 1.5 22.409 2.24E-02 2.44E+08 553.35

3p3/22 4d5/2 0 0.5 3p1/2 1 0.5 22.233 3.30E-02 3.54E+08 557.74

3p3/22 4s1/2 0 0.5 3p3/2

3 1 1.5 20.892 8.08E-02 7.65E+08 593.53

3p3/22 4s1/2 0 0.5 3p1/2 1 0.5 20.715 4.97E-02 4.63E+08 598.59

3p1/2 3p3/2

3 4s1/2 0 2.5 3p3/23 1 1.5 18.124 4.07E-01 9.67E+08 684.19

3p1/2 3p3/2

3 4s1/2 0 1.5 3p3/23 1 1.5 18.12 2.96E-02 1.06E+08 684.32

3p1/2 3p3/2

3 4s1/2 0 1.5 3p1/2 1 0.5 17.947 2.47E-01 8.62E+08 690.92

3p1/2 3p3/2

3 4s1/2 0 0.5 3p3/23 1 1.5 16.817 1.39E-01 8.56E+08 737.33

3p3/22 4s1/2 0 1.5 3p3/2

3 1 1.5 16.684 6.79E-01 2.05E+09 743.23

3p1/2 3p3/2

3 4s1/2 0 0.5 3p1/2 1 0.5 16.641 2.58E-01 1.55E+09 745.16

3p3/22 4s1/2 0 1.5 3p1/2 1 0.5 16.507 1.16E-01 3.42E+08 751.18

3d 3/2 2 3d 5/2

2 5f 7/2 1 5.5 3d 3/2 2 3d 5/2

3 0 4.5 10.733 1.26E+00 5.23E+08 1155.29

3d 3/2 3d 5/23 5f 5/2 1 1.5 3d 3/2

2 3d 5/23 0 2.5 10.427 8.68E-01 1.02E+09 1189.23

3d 3/2 3d 5/23 5f 5/2 1 2.5 3d 3/2

2 3d 5/23 0 2.5 10.426 1.30E+00 1.02E+09 1189.31

3d 3/2 2 3d 5/2

2 5f 7/2 1 3.5 3d 3/2 2 3d 5/2

3 0 2.5 10.425 1.74E+00 1.02E+09 1189.43





3d 3/2 2 3d 5/2

2 4f 7/2 1 5.5 3d 3/2 2 3d 5/2

3 0 4.5 9.581 1.35E+00 4.49E+08 1294.24

3d 3/2 2 3d 5/2

2 4f 5/2 1 4.5 3d 3/2 3d 5/2 4 0 3.5 9.578 1.09E+00 4.35E+08 1294.64

3d 3/2 2 3d 5/2

2 5f 7/2 1 6.5 3d 3/2 2 3d 5/2

3 0 6.5 9.484 1.77E+00 4.94E+08 1307.5

3d 3/2 2 3d 5/2

2 5f 5/2 1 5.5 3d 3/2 2 3d 5/2

3 0 5.5 9.479 1.51E+00 4.92E+08 1308.15

3d 3/2 2 3d 5/2

2 5f 7/2 1 7.5 3d 3/2 2 3d 5/2

3 0 6.5 9.463 2.03E+00 4.92E+08 1310.33

3d 3/2 2 3d 5/2

2 5f 5/2 1 6.5 3d 3/2 2 3d 5/2

3 0 5.5 9.459 1.77E+00 4.91E+08 1310.97

3d 3/2 3d 5/23 4f 5/2 1 2.5 3d 3/2

2 3d 5/23 0 2.5 9.118 1.66E+00 9.99E+08 1359.97

3d 3/2 2 3d 5/2

2 4f 7/2 1 3.5 3d 3/2 2 3d 5/2

3 0 2.5 9.116 2.21E+00 9.97E+08 1360.18

3d 3/2 3d 5/23 5f 7/2 1 7.5 3d 3/2

2 3d 5/23 0 6.5 8.758 2.26E+00 4.70E+08 1415.77

3d 3/2 2 3d 5/2

2 5f 7/2 1 6.5 3d 3/2 2 3d 5/2

3 0 5.5 8.752 1.96E+00 4.65E+08 1416.87

3d 3/2 2 3d 5/2

2 5f 5/2 1 5.5 3d 3/2 2 3d 5/2

3 0 4.5 8.685 1.77E+00 4.82E+08 1427.74

3d 3/2 2 3d 5/2

2 5f 5/2 1 0.5 3d 3/23 3d 5/2

2 0 0.5 8.601 2.93E-01 4.70E+08 1441.64

3d 3/23 3d 5/2 5f 7/2 1 1.5 3d 3/2

3 3d 5/2 2 0 0.5 8.601 5.84E-01 4.69E+08 1441.67

3d 3/2 2 3d 5/2

2 4f 7/2 1 3.5 3d 3/2 2 3d 5/2

3 0 4.5 8.591 1.04E+00 4.16E+08 1443.43

3d 3/2 3d 5/23 4f 5/2 1 4.5 3d 3/2

2 3d 5/23 0 5.5 8.59 1.35E+00 4.33E+08 1443.52

3d 3/2 2 3d 5/2

2 4f 5/2 1 2.5 3d 3/2 2 3d 5/2

3 0 3.5 8.588 7.78E-01 4.15E+08 1443.88

3d 3/2 3d 5/23 5f 5/2 1 2.5 3d 3/2

2 3d 5/23 0 1.5 8.586 8.86E-01 4.72E+08 1444.22

3d 3/2 2 3d 5/2

2 4f 7/2 1 1.5 3d 3/2 2 3d 5/2

3 0 2.5 8.584 5.74E-01 4.59E+08 1444.54

3d 3/2 3d 5/23 5f 7/2 1 4.5 3d 3/2

2 3d 5/23 0 3.5 8.575 1.51E+00 4.81E+08 1446.04

3d 5/2 4 5f 7/2 1 3.5 3d 5/2 0 2.5 8.573 1.28E+00 5.12E+08 1446.36

3d 3/2 3d 5/23 4f 7/2 1 5.5 3d 3/2

2 3d 5/23 0 5.5 8.546 1.57E+00 4.15E+08 1451.04

3d 3/2 2 3d 5/2

2 5f 7/2 1 4.5 3d 3/2 2 3d 5/2

3 0 3.5 8.45 1.53E+00 4.76E+08 1467.52

3d 3/2 3d 5/23 5f 7/2 1 5.5 3d 3/2 3d 5/2 4 0 4.5 8.328 1.93E+00 4.84E+08 1488.9

3d 3/2 2 3d 5/2

2 5f 7/2 1 4.5 3d 3/2 2 3d 5/2

3 0 3.5 8.328 1.59E+00 4.78E+08 1489.03

3d 3/2 2 3d 5/2

2 4f 7/2 1 6.5 3d 3/2 2 3d 5/2

3 0 6.5 8.299 2.21E+00 4.71E+08 1494.09

3d 3/2 2 3d 5/2

2 4f 5/2 1 5.5 3d 3/2 2 3d 5/2

3 0 5.5 8.295 1.89E+00 4.70E+08 1494.82

3d 3/2 2 3d 5/2

2 4f 7/2 1 7.5 3d 3/2 2 3d 5/2

3 0 6.5 8.28 2.82E+00 5.24E+08 1497.67

3d 3/2 2 3d 5/2

2 4f 5/2 1 6.5 3d 3/2 2 3d 5/2

3 0 5.5 8.276 2.47E+00 5.24E+08 1498.35

3d 3/2 3d 5/23 5f 5/2 1 6.5 3d 3/2

2 3d 5/23 0 5.5 8.205 2.23E+00 4.66E+08 1511.2





3d 3/2 3d 5/23 4f 5/2 1 2.5 3d 3/2

2 3d 5/23 0 1.5 7.64 1.01E+00 4.28E+08 1623.02

3d 5/2 4 4f 7/2 1 3.5 3d 5/2 5 0 2.5 7.631 1.44E+00 4.54E+08 1624.87

3d 3/2 3d 5/23 4f 7/2 1 7.5 3d 3/2

2 3d 5/23 0 6.5 7.59 2.78E+00 4.35E+08 1633.75

3d 3/2 2 3d 5/2

2 4f 7/2 1 6.5 3d 3/2 2 3d 5/2

3 0 5.5 7.584 2.41E+00 4.30E+08 1635.1

3d 3/2 3d 5/23 5f 7/2 1 0.5 3d 3/2 3d 5/2 4 0 1.5 7.388 4.12E-01 4.88E+08 1678.35

3d 3/2 2 3d 5/2

2 4f 5/2 1 5.5 3d 3/2 2 3d 5/2

3 0 4.5 7.056 2.33E+00 4.20E+08 1757.49

3d 3/2 3d 5/23 4f 5/2 1 6.5 3d 3/2

2 3d 5/23 0 5.5 7.054 2.88E+00 4.44E+08 1757.75

3d 3/2 2 3d 5/2

2 4f 7/2 1 4.5 3d 3/2 2 3d 5/2

3 0 3.5 7.052 1.88E+00 4.06E+08 1758.3

3d 3/23 3d 5/2 4f 7/2 1 3.5 3d 3/2

2 3d 5/23 0 2.5 7.047 1.52E+00 4.08E+08 1759.64

3d 3/2 3d 5/23 5f 5/2 1 3.5 3d 3/2

2 3d 5/23 0 2.5 6.945 2.17E+00 5.66E+08 1785.44

3d 3/2 3d 5/23 5f 7/2 1 2.5 3d 3/2 3d 5/2 4 0 1.5 6.943 1.50E+00 5.24E+08 1785.87

3d 3/2 3d 5/23 4f 5/2 1 1.5 3d 3/2

2 3d 5/23 0 2.5 6.574 1.05E+00 4.92E+08 1886.09

3d 3/2 3d 5/23 4f 7/2 1 0.5 3d 3/2 3d 5/2 4 0 1.5 6.572 5.83E-01 5.46E+08 1886.79

3d 3/2 3d 5/23 4f 5/2 1 3.5 3d 3/2

2 3d 5/23 0 2.5 6.128 2.62E+00 5.35E+08 2023.62

3d 3/2 3d 5/23 4f 7/2 1 2.5 3d 3/2 3d 5/2 4 0 1.5 6.125 1.83E+00 4.98E+08 2024.4

3p3/22 6d5/2 0 2.5 3p3/2

3 1 1.5 29.222 1.48E-02 9.16E+07 424.34

3p3/22 6d3/2 0 1.5 3p1/2 1 0.5 29.041 1.04E-02 9.55E+07 426.99

3p3/22 6s1/2 0 0.5 3p3/2

3 1 1.5 28.002 4.60E-03 7.82E+07 442.82

3p3/22 4d3/2 0 1.5 3p3/2

3 1 1.5 26.755 1.77E-02 1.38E+08 463.47

3p3/22 4d5/2 0 2.5 3p3/2

3 1 1.5 26.74 1.59E-01 8.24E+08 463.73

3p3/22 4d3/2 0 1.5 3p1/2 1 0.5 26.578 1.13E-01 8.64E+08 466.54

3p1/2 3p3/2

3 6d3/2 0 0.5 3p3/23 1 1.5 26.505 2.29E-02 3.48E+08 467.84

3p1/2 3p3/2

3 6d5/2 0 1.5 3p3/23 1 1.5 26.501 3.86E-02 2.93E+08 467.91

3p1/2 3p3/2

3 6d5/2 0 2.5 3p3/23 1 1.5 26.49 3.65E-02 1.85E+08 468.1

3p1/2 3p3/2

3 6d5/2 0 0.5 3p3/23 1 1.5 26.49 4.93E-03 7.51E+07 468.11

3p1/2 3p3/2

3 6d5/2 0 0.5 3p1/2 1 0.5 26.324 2.16E-02 3.24E+08 471.06

3p1/2 3p3/2

3 6d3/2 0 1.5 3p1/2 1 0.5 26.32 2.22E-02 1.67E+08 471.13

3p1/2 3p3/2

3 6d5/2 0 1.5 3p1/2 1 0.5 26.309 9.83E-03 7.38E+07 471.33

3p1/2 3p3/2

3 6d3/2 0 0.5 3p1/2 1 0.5 26.295 6.24E-03 9.37E+07 471.58




strengths (gf) for the strongest electric dipole E1 transitions of Cl- like Ar 3p1/2

3p3/23 6s1/2 0 2.5 3p3/2

3 1 1.5 25.23 2.45E-02 1.13E+08 491.48

3p1/2 3p3/2

3 6s1/2 0 1.5 3p1/2 1 0.5 25.049 1.49E-02 1.01E+08 495.04

6d5/2 0 2.5 3p3/23 1 1.5 24.86 8.14E-02 3.63E+08 498.8

3p3/22 6g7/2 0 1.5 3p3/2

3 1 1.5 24.743 7.61E-03 5.05E+07 501.15

3p1/2 3p3/2

3 6d3/2 0 1.5 3p3/23 1 1.5 24.743 3.19E-02 2.12E+08 501.15

3p1/2 3p3/2

3 6d5/2 0 1.5 3p1/2 1 0.5 24.72 5.61E-02 3.71E+08 501.62

6d5/2 0 2.5 3p3/23 1 1.5 24.709 2.69E-02 1.19E+08 501.84

3p1/2 3p3/2

3 6d3/2 0 0.5 3p3/23 1 1.5 24.697 5.67E-03 7.51E+07 502.08

3p1/2 3p3/2

3 6d3/2 0 0.5 3p1/2 1 0.5 24.528 9.86E-03 1.29E+08 505.55

3p1/2 3p3/2

3 4d5/2 0 0.5 3p3/23 1 1.5 24.477 8.45E-02 1.09E+09 506.59

3p1/2 3p3/2

3 4d3/2 0 1.5 3p3/23 1 1.5 24.369 5.82E-01 3.75E+09 508.85

3p3/22 4d5/2 0 2.5 3p3/2

3 1 1.5 24.333 6.96E-01 2.98E+09 509.59

3p1/2 3p3/2

3 4d5/2 0 0.5 3p1/2 1 0.5 24.262 2.28E-01 2.91E+09 511.09

3p1/2 3p3/2

3 4d5/2 0 1.5 3p1/2 1 0.5 24.222 5.10E-01 3.25E+09 511.94

3p1/2 3p3/2

3 4d5/2 0 0.5 3p3/23 1 1.5 24.112 1.84E-01 2.32E+09 514.27

3p1/2 3p3/2

3 4d5/2 0 0.5 3p1/2 1 0.5 23.935 6.79E-02 8.44E+08 518.06

6s1/2 0 0.5 3p3/23 1 1.5 23.578 6.79E-03 8.19E+07 525.92

3p1/2 3p3/2

3 6s1/2 0 1.5 3p3/23 1 1.5 23.458 2.10E-02 1.26E+08 528.62

6s1/2 0 0.5 3p1/2 1 0.5 23.396 1.19E-02 1.41E+08 530

3p3/22 6s1/2 0 1.5 3p3/2

3 1 1.5 23.366 2.48E-02 1.47E+08 530.69

Table (6): Calculated energy difference ∆E (eV), wavelengths (λ) in Å,

transition rates (Ar) in s-1, and oscillator strength (gf) for the strongest

multipole E2, E3, M1, M2, M3 transitions of Cl- like Ar

Cl- like Ar

E2 transitions

upper state P up J up Lower state

P lower

J lower

∆E (eV)

gf Ar λ (Å)

3s1/2 6d5/2 0 2 3p3/2

4 0 0 32.638 4.03E-07 3.73E+03 379.925

3s1/2 5 d

5/2 0 2 3p3/24 0 0 32.393 6.70E-07 6.10E+03 382.800


Table (6): (Continued): Calculated energy difference ∆E (eV), wavelengths

(λ) in Å, transition rates (Ar) in s-1, and oscillator strength (gf) for the

strongest multipole E2, E3, M1, M2, M3 transitions of Cl- like Ar

3s1/2 4d5/2 0 2 3p3/2

4 0 0 32.124 1.24E-06 1.11E+04 386.004

3s1/2 4d5/2 0 2 3p3/2

4 0 0 32.124 1.24E-06 1.11E+04 386.004

3p1/2 3p3/2

3 6f7/2 1 2.5 3p3/23 1 1.5 26.689 4.92E-07 2.54E+03 464.613

3p1/2 3p3/2

3 6f5/2 1 0.5 3p3/23 1 1.5 26.673 3.44E-07 5.31E+03 464.881

3p1/2 3p3/2

3 6f7/2 1 1.5 3p3/23 1 1.5 26.673 3.27E-07 2.52E+03 464.883

3p1/2 3p3/2

3 6f7/2 1 1.5 3p1/2 1 0.5 26.492 3.64E-07 2.77E+03 468.062

3p1/2 3p3/2

3 6p3/2 1 3.5 3p3/23 1 1.5 25.660 6.36E-07 2.27E+03 483.240

3p3/22 6f7/2 1 2.5 3p3/2

3 1 1.5 24.806 6.78E-07 3.02E+03 499.886

3p3/22 6f7/2 1 3.5 3p3/2

3 1 1.5 24.799 1.26E-06 4.22E+03 500.019

3p1/2 3p3/2

3 6f7/2 1 2.5 3p1/2 1 0.5 24.740 4.82E-07 2.13E+03 501.217

3p3/22 6p1/2 1 2.5 3p3/2

3 1 1.5 23.802 5.13E-07 2.10E+03 520.974

3p3/22 4p1/2 1 0.5 3p3/2

3 1 1.5 23.608 7.60E-07 9.18E+03 525.236

3p3/22 4f7/2 1 3.5 3p3/2

3 1 1.5 23.007 3.22E-06 9.23E+03 538.969

3p1/2 3p3/2

3 4p3/2 1 3.5 3p3/23 1 1.5 20.585 5.88E-06 1.35E+04 602.383

3p1/2 3p3/2

3 4p1/2 1 2.5 3p1/2 1 0.5 20.401 3.72E-06 1.12E+04 607.811

3p1/2 3p3/2

3 4p3/2 1 0.5 3p3/23 1 1.5 19.374 9.53E-07 7.76E+03 640.028

3p1/2 3p3/2

3 4p3/2 1 1.5 3p1/2 1 0.5 19.163 2.41E-06 9.62E+03 647.077

3p1/2 3p3/2

3 4p3/2 1 1.5 3p3/23 1 1.5 19.117 3.71E-06 1.47E+04 648.643

3p1/2 3p3/2

3 4p3/2 1 2.5 3p3/23 1 1.5 19.011 6.55E-06 1.71E+04 652.251

3p1/2 3p3/2

3 4p3/2 1 1.5 3p1/2 1 0.5 18.940 1.86E-06 7.24E+03 654.689

E3 transitions


P lower

J lower

∆E (eV)

gf Ar λ (Å)

3p3/22 6g9/2 0 4.5 3p3/2

3 1 1.5 29.403 3.75E-11 1.41E-01 421.727

3p3/22 6g7/2 0 3.5 3p1/2 1 0.5 29.222 2.41E-11 1.12E-01 424.342

3p3/22 4d3/2 0 1.5 3p3/2

3 1 1.5 26.755 2.97E-12 2.30E-02 463.467

3p3/22 4d5/2 0 2.5 3p3/2

3 1 1.5 26.740 1.99E-12 1.03E-02 463.725

3p1/2 3p3/2

3 6g7/2 0 2.5 3p3/23 1 1.5 26.630 1.55E-11 7.94E-02 465.647

3p1/2 3p3/2

3 6g9/2 0 2.5 3p3/23 1 1.5 26.621 1.86E-11 9.51E-02 465.799

3p1/2 3p3/2

3 6g7/2 0 1.5 3p3/23 1 1.5 26.621 2.88E-11 2.21E-01 465.799

3p3/22 4d5/2 0 2.5 3p1/2 1 0.5 26.563 2.94E-12 1.50E-02 466.808





3p1/2 3p3/2

3 6g7/2 0 2.5 3p1/2 1 0.5 26.448 1.34E-11 6.79E-02 468.837

3p1/2 3p3/2

3 6g9/2 0 2.5 3p1/2 1 0.5 26.440 2.66E-11 1.35E-01 468.992

3p3/22 6g9/2 0 4.5 3p3/2

3 1 1.5 24.735 2.33E-11 6.18E-02 501.308

3p1/2 3p3/2

3 6g9/2 0 3.5 3p1/2 1 0.5 24.679 1.91E-11 6.30E-02 502.462

3p1/2 3p3/2

3 4d5/2 0 4.5 3p3/23 1 1.5 23.713 1.05E-11 2.57E-02 522.920

3p1/2 3p3/2

3 4d3/2 0 3.5 3p1/2 1 0.5 23.532 6.46E-12 1.94E-02 526.938

3p3/22 4d3/2

1 0 1.5 3p3/23 1 1.5 22.753 3.80E-12 2.13E-02 544.993

3p3/22 4d3/2

2 0 2.5 3p1/2 1 0.5 22.625 3.63E-12 1.34E-02 548.066

3p3/22 4d3/2 0 2.5 3p3/2

3 1 1.5 22.302 4.00E-12 1.44E-02 556.004

3p3/22 4d3/2 0 3.5 3p3/2

3 1 1.5 22.191 5.71E-12 1.53E-02 558.785

M1 transitions


P lower

J lower

∆E (eV)

gf Ar λ (Å)

3p3/22 6p1/2 1 0.5 3p3/2

3 1 1.5 28.462 4.79E-12 8.42E-02 436.00

3p3/22 6p3/2 1 1.5 3p1/2 1 0.5 28.282 4.55E-12 3.95E-02 438.00

3p1/2 3p3/2

3 6p3/2 1 2.5 3p3/23 1 1.5 25.720 8.22E-12 3.93E-02 482.00

3p1/2 3p3/2

3 6p1/2 1 1.5 3p3/23 1 1.5 25.720 9.62E-12 6.90E-02 482.00

3p1/2 3p3/2

3 6p1/2 1 1.5 3p1/2 1 0.5 25.539 6.73E-12 4.76E-02 486.00

3p3/22 6p3/2 1 1.5 3p3/2

3 1 1.5 23.937 9.48E-12 5.90E-02 518.00

3p1/2 3p3/2

3 6s1/2 1 2.5 3p3/23 1 1.5 23.899 9.27E-12 3.83E-02 519.00

3p3/22 6p3/2 1 1.5 3p1/2 1 0.5 23.773 5.49E-12 3.37E-02 522.00

3p3/22 6p1/2 1 1.5 3p3/2

3 1 1.5 23.763 1.35E-11 8.25E-02 522.00

6s1/2 1 0.5 3p1/2 1 0.5 23.727 4.93E-12 6.02E-02 523.00

3p3/22 4p1/2 1 0.5 3p3/2

3 1 1.5 23.609 3.60E-11 4.35E-01 525.00

3p3/22 4p3/2 1 1.5 3p1/2 1 0.5 23.407 4.09E-11 2.43E-01 530.00

3p1/2 3p3/2

3 4p3/2 1 2.5 3p3/23 1 1.5 20.979 6.46E-11 2.05E-01 591.00

3p1/2 3p3/2

3 4p3/2 1 1.5 3p3/23 1 1.5 20.972 1.04E-10 4.97E-01 591.00

3p1/2 3p3/2

3 4p3/2 1 1.5 3p1/2 1 0.5 20.795 3.08E-11 1.45E-01 596.00

3p1/2 3p3/2

3 4p3/2 1 1.5 3p3/23 1 1.5 19.284 1.09E-10 4.41E-01 643.00

3p3/22 4p1/2 1 2.5 3p3/2

3 1 1.5 18.796 1.20E-10 3.08E-01 660.00

3p3/22 4p1/2 1 1.5 3p1/2 1 0.5 18.694 3.75E-11 1.42E-01 663.00





3p3/22 4p1/2 1 1.5 3p3/2

3 1 1.5 18.487 4.64E-11 1.72E-01 671.00

3p3/22 4p1/2 1 0.5 3p1/2 1 0.5 18.362 2.76E-11 2.02E-01 675.00

M2 transitions


P lower

J lower

∆E (eV)

gf Ar λ (Å)

3p3/22 4d5/2 0 2.5 3p3/2

3 1 1.5 26.740 1.95E-10 1.01E+00 463.72

3p1/2 3p3/2

3 4d3/2 0 0.5 3p3/23 1 1.5 24.439 3.15E-11 4.09E-01 507.39

3p1/2 3p3/2

3 4d3/2 0 1.5 3p3/23 1 1.5 24.398 9.29E-11 6.00E-01 508.24

3p1/2 3p3/2

3 4d3/2 0 1.5 3p3/23 1 1.5 24.369 7.48E-11 4.82E-01 508.84

3p1/2 3p3/2

3 4d5/2 0 0.5 3p3/23 1 1.5 24.112 9.10E-11 1.15E+00 514.27

3p3/22 4d5/2 0 2.5 3p1/2 1 0.5 22.625 1.33E-10 4.91E-01 548.07

3p3/22 4d5/2 0 1.5 3p1/2 1 0.5 22.576 7.13E-11 3.94E-01 549.26

3p3/22 4d5/2 0 0.5 3p3/2

3 1 1.5 22.409 1.28E-10 1.39E+00 553.35

3p3/22 4d5/2 0 1.5 3p1/2 1 0.5 22.353 8.17E-11 4.43E-01 554.74

3p3/22 4d5/2 0 3.5 3p3/2

3 1 1.5 21.599 3.52E-10 8.90E-01 574.10

M3 transitions


P lower

J lower

∆E (eV)

gf Ar λ (Å)

3s1/2 5 d

5/2 0 3 3p3/24 0 0 32.382 1.69E-16 1.10E-06 382.93

3s1/2 4d5/2 0 3 3p3/2

4 0 0 32.106 7.48E-16 4.78E-06 386.22

3s1/2 4d5/2 0 3 3p3/2

4 0 0 32.106 7.48E-16 4.78E-06 386.22

3p3/22 6f7/2 1 3.5 3p3/2

3 1 1.5 29.465 4.16E-15 1.96E-05 420.84

3p3/22 6f7/2 1 3.5 3p1/2 1 0.5 29.284 1.30E-15 6.07E-06 423.44

3p3/22 6p3/2 1 1.5 3p3/2

3 1 1.5 28.463 1.02E-14 8.95E-05 435.65

3p3/22 4f7/2 1 3.5 3p3/2

3 1 1.5 27.691 4.20E-16 1.75E-06 447.80

3p1/2 3p3/2

3 6f7/2 1 2.5 3p3/23 1 1.5 26.689 8.58E-15 4.42E-05 464.61

3p1/2 3p3/2

3 6h11/2 1 3.5 3p3/23 1 1.5 26.626 2.17E-15 8.33E-06 465.71

3p1/2 3p3/2

3 6p3/2 1 2.5 3p3/23 1 1.5 25.72 2.33E-15 1.11E-05 482.12

3p1/2 3p3/2

3 6p3/2 1 3.5 3p3/23 1 1.5 25.66 4.57E-15 1.63E-05 483.24

3p1/2 3p3/2

3 6p3/2 1 3.5 3p1/2 1 0.5 25.479 7.45E-15 2.62E-05 486.68





3p3/22 6p3/2 1 3.5 3p3/2

3 1 1.5 23.775 3.34E-15 1.02E-05 521.56

3p1/2 3p3/2

3 6p3/2 1 2.5 3p1/2 1 0.5 23.718 1.81E-15 7.36E-06 522.81

3p3/22 4p3/2 1 3.5 3p3/2

3 1 1.5 18.748 7.00E-16 1.33E-06 661.40

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Received: April 12, 2016; Published: May 19, 2016


http://dx.doi.org/10.1140/epjd/e2006-00214-0

http://dx.doi.org/10.1086/506602



http://dx.doi.org/10.1088/0031-8949/81/01/015301


http://iopscience.iop.org/journal/1402-4896

http://dx.doi.org/10.1088/0031-8949/79/06/065301

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