Resonance energies of the Cl II-[3s 23p 3( 2D 5/2)] nd and [3s 23p 3( 2P 3/2)] nd, Ar II-3s 23p 4( 1D 2) ns, nd and of the Kr II [4s 24p 4( 1D 2)] ns, nd and 4s 24p 4( 3P 2, 3P 1)] ns, 4s 24p 4( 3D 2)] ns, nd and 4s 24p 4( 3D 2, 1S 0)] ns, nd Rydberg series are reported. Natural widths of the Ar II-[3s 23p 4( 1D 2)] ns, nd series are also reported. Calculations are done in the framework of the Modified Atomic Orbital Theory (MAOT). Excellent agreements are obtained with available theoretical and experimental data. High lying accurate resonance energies up to n = 40 are tabulated. The possibility to use the MAOT formalism report rapidly with an excellent accuracy the position of the excitation resonances as well as their width within simple analytical formulae is demonstrated.
In many astrophysical systems such as stars and nebulae, the main process governing light-atomic species interaction is Photoionization. Of great important ions interesting to investigate are Cl II (Cl+), Ar II (Ar+) and Kr II (Kr+) ions. As far as Cl II is concerned, its interest is connected with it abundance in photoionized astrophysical objects. In the past, various studies have indicated the great importance of Cl II ions abundances for understanding extragalactic HII regions [
In the framework of the modified atomic orbital theory (MAOT), the total energy of a (νl)-given orbital is expressed in the form in Rydberg units
E ( ν l ) = − [ Z − σ ( l ) ] 2 ν 2 (1)
In Equation (1), σ is the screening constant relative to the electron occupying the (νl)-orbital, l denotes the orbital quantum number, ν stands for the principal quantum number and Z represents the atomic number. In general, the doubly excited states (DES) in two electron systems are labelled as ( N l , n l ′ ) L 2 S + 1 π . In this notation, N and n denote respectively the principal quantum numbers of the inner and the outer electron, l and l’ are their respective orbital quantum numbers, S the total spin, L the total angular momentum and πthe parity of the system. For an atomic system of many M electrons, total energy is expressed as follows
E = − ∑ i = 1 M [ Z − σ i ( L 2 S + 1 π ) ] 2 ν i 2 (2)
In the photoionisation study, energy resonances En are generally measured relatively to the E¥ converging limit of a given (2S+1LJ)nl-Rydberg series. For these states [
E n = E ∞ − 1 n 2 { Z − σ 1 ( L 2 S + 1 J ) − σ 2 ( L 2 S + 1 J ) × 1 n − σ 2 α ( P 2 3 / 2 0 , D 1 2 ) × ( n − m ) × ( n − q ) ∑ k 1 f k ( n , m , q , s ) } 2 (3)
In this equation, m and q (m < q) denote the principal quantum numbers of the (2S+1LJ)nl-Rydberg series of the considered atomic system used in the empirical determination of the σ i ( L 2 S + 1 J ) -screening constants, s represents the spin of the nl-electron (s = 1/2), E¥ is the energy value of the series limit generally determined from NIST atomic database, and Z represents the nuclear charge of the considered element. The only problem that one may face by using the
MAOT formalism is linked to the determination of the ∑ k 1 f k ( n , m , q , s ) -term.
The correct expression of this term is determined iteratively by imposing general Equation (3) to give accurate data with a constant quantum defect values along all the considered series. The value of α is fixed to 1 and or 2 during the iteration. The quantum defect is calculated from the standard formula
E n = E ∞ − R Z core 2 ( n − δ ) 2 (4)
In this equation, R is the Rydberg constant, E¥ denotes the converging limit, Zcore represents the electric charge of the core ion, and δ means the quantum defect. As far as the natural widths are concerned, they are given by (in Rydberg units)
Γ n = 1 n 2 { Z − σ ′ 1 ( L 2 S + 1 J ) − σ ′ 2 ( L 2 S + 1 J ) × 1 n − σ 2 α ′ ( P 2 3 / 2 0 , D 1 2 ) × ( n − m ) × ( n − q ) ∑ k 1 f ′ k ( n , m , q , s ) } 2 (5)
In the present work, for all the Rydberg series investigated for both Cl II, Ar II and Kr II, the resonance energies are given by the formula
E n = E ∞ − 1 n 2 { Z − σ 1 ( L 2 S + 1 J ) − σ 2 ( L 2 S + 1 J ) × 1 n − σ 2 2 ( L 2 S + 1 J ) × ( n − m ) 2 [ 1 ( n + s + 2 ) 4 + 1 ( n − 2 s ) 4 ] + σ 2 ( L 2 S + 1 J ) × ( n − m ) 2 [ 1 ( n + m + s ) 4 + 1 ( n + m − s ) 4 ] } 2 (6)
For the [3s23p4(1D2)]ns (j = 1/2) series originating from the 3 s 3 2 p 5 P 2 1 / 2 ° metastable state of Ar II ions, the natural widths are given by (in Rydberg units)
Γ n = 1 n 2 { Z − σ 1 ( L 2 S + 1 J ) − σ 2 ( L 2 S + 1 J ) × 1 n + σ 2 2 ( L 2 S + 1 J ) × ( n − m ) × ( n − q ) × [ 1 ( n + q − m + s + 1 ) 4 + 1 ( n + m + s ) 4 + 1 ( n + q + s ) 4 + 1 ( n + m − s ) 4 ] } 2 (7)
The other expressions for the other series are of type Equation (7).
The σ1-screening constants in Equations (6) and (7) are evaluated empirically using the data from Covington et al., [
h ν + X p + → X ( p + 1 ) + e − ⇒ Z core = ( p + 1 ) (8)
So, for Cl II, Ar II and Kr II, we find respectively.
h ν + Cl + → Cl 2 + + e − ; Z core = 2 ⇒ σ 2 = 15.00
h ν + Ar + → Ar 2 + + e − ; Z core = 2 ⇒ σ 2 = 16.00
h ν + Kr + → Kr 2 + + e − ; Z core = 2 ⇒ σ 2 = 34.00
The resonance energies of the [ 3 s 3 2 p 3 ( D 2 5 / 2 ° ) ]nd Rydberg series originating from the 3 s 3 2 p 4 P 3 2 ° ground state and from the 3 s 3 2 p 4 P 3 1 ° , 3 s 3 2 p 4 P 3 0 ° , 3 s 3 2 p 4 S 1 0 ° and 3 s 3 2 p 4 D 1 2 metastable states of Cl II ions are listed in Tables 1-8. Comparisons of the present MAOT calculations are done with the available Dirac-Coulomb R-matrix (DCR) calculations [
n | MAOT | DCR | ALS | MAOT | DCR | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
6 | 24.348 | 24.353 | 24.348 | 0.362 | 0.30 | 0.38 |
7 | 24.824 | 24.846 | 24.829 | 0.363 | 0.35 | 0.35 |
8 | 25.127 | 25.130 | 25.128 | 0.362 | 0.30 | 0.36 |
9 | 25.331 | 25.334 | 25.335 | 0.361 | 0.34 | 0.34 |
10 | 25.474 | 25.476 | 25.479 | 0.360 | 0.35 | 0.32 |
11 | 25.579 | 25.584 | 25.583 | 0.360 | 0.30 | 0.32 |
12 | 25.658 | 0.359 | ||||
13 | 25.719 | 0.359 | ||||
14 | 25.768 | 0.358 | ||||
15 | 25.806 | 0.358 | ||||
16 | 25.838 | 0.358 | ||||
17 | 25.863 | 0.358 | ||||
18 | 25.885 | 0.358 | ||||
19 | 25.903 | 0.358 | ||||
20 | 25.919 | 0.358 | ||||
21 | 25.932 | 0.359 | ||||
22 | 25.944 | 0.359 | ||||
23 | 25.954 | 0.359 | ||||
24 | 25.963 | 0.359 | ||||
25 | 25.970 | 0.359 | ||||
26 | 25.977 | 0.360 | ||||
27 | 25.983 | 0.360 | ||||
28 | 25.989 | 0.360 | ||||
29 | 25.994 | 0.361 | ||||
30 | 25.998 | 0.361 | ||||
31 | 26.002 | 0.361 | ||||
32 | 26.006 | 0.361 | ||||
33 | 26.009 | 0.362 | ||||
34 | 26.012 | 0.362 | ||||
35 | 26.015 | 0.362 | ||||
36 | 26.017 | 0.363 | ||||
37 | 26.019 | 0.363 | ||||
38 | 26.022 | 0.363 | ||||
39 | 26.024 | 0.363 | ||||
40 | 26.025 | 0.364 | ||||
… | … | … | … | … | … | |
¥ | 26.060 | 26.060 | 26.060 |
n | MAOT | DCR | ALS | MAOT | DCR | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
6 | 24.259 | 24.264 | 24.259 | 0.367 | 0.36 | 0.37 |
7 | 24.737 | 24.762 | 24.750 | 0.368 | 0.30 | 0.33 |
8 | 25.040 | 25.039 | 25.036 | 0.367 | 0.37 | 0.38 |
9 | 25.244 | 25.237 | 25.238 | 0.366 | 0.40 | 0.40 |
10 | 25.388 | 25.385 | 25.384 | 0.365 | 0.40 | 0.42 |
11 | 25.493 | 25.493 | (25.492) | 0.365 | 0.36 | (0.37) |
12 | 25.572 | 0.364 | ||||
13 | 25.633 | 0.363 | ||||
14 | 25.681 | 0.363 | ||||
15 | 25.720 | 0.363 | ||||
16 | 25.751 | 0.363 | ||||
17 | 25.777 | 0.363 | ||||
18 | 25.799 | 0.363 | ||||
19 | 25.817 | 0.363 | ||||
20 | 25.833 | 0.363 | ||||
21 | 25.846 | 0.363 | ||||
22 | 25.858 | 0.364 | ||||
23 | 25.868 | 0.364 | ||||
24 | 25.877 | 0.364 | ||||
25 | 25.884 | 0.364 | ||||
26 | 25.891 | 0.365 | ||||
27 | 25.897 | 0.365 | ||||
28 | 25.903 | 0.365 | ||||
29 | 25.908 | 0.365 | ||||
30 | 25.912 | 0.366 | ||||
31 | 25.916 | 0.366 | ||||
32 | 25.920 | 0.366 | ||||
33 | 25.923 | 0.367 | ||||
34 | 25.926 | 0.367 | ||||
35 | 25.929 | 0.367 | ||||
36 | 25.931 | 0.367 | ||||
37 | 25.933 | 0.368 | ||||
38 | 25.936 | 0.368 | ||||
39 | 25.938 | 0.368 | ||||
40 | 25.939 | 0.369 | ||||
… | … | … | … | … | … | |
¥ | 25.974 | 25.974 | 25.974 |
n | MAOT | DCR | ALS | MAOT | DCR | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
6 | 24.219 | 24.223 | 24.219 | 0.370 | 0.36 | 0.37 |
7 | 24.697 | 24.733 | 0.372 | 0.27 | ||
8 | 25.001 | 24.999 | (25.000) | 0.371 | 0.38 | (0.38) |
9 | 25.205 | 25.198 | 0.370 | 0.40 | ||
10 | 25.349 | 25.345 | 0.369 | 0.40 | ||
11 | 25.455 | 0.368 | ||||
12 | 25.534 | 0.367 | ||||
13 | 25.595 | 0.367 | ||||
14 | 25.643 | 0.367 | ||||
15 | 25.682 | 0.366 | ||||
16 | 25.713 | 0.366 | ||||
17 | 25.739 | 0.366 | ||||
18 | 25.761 | 0.366 | ||||
19 | 25.779 | 0.367 | ||||
20 | 25.795 | 0.367 | ||||
21 | 25.808 | 0.367 | ||||
22 | 25.820 | 0.367 | ||||
23 | 25.830 | 0.367 | ||||
24 | 25.839 | 0.368 | ||||
25 | 25.846 | 0.368 | ||||
26 | 25.853 | 0.368 | ||||
27 | 25.859 | 0.368 | ||||
28 | 25.865 | 0.369 | ||||
29 | 25.870 | 0.369 | ||||
30 | 25.874 | 0.369 | ||||
31 | 25.878 | 0.370 | ||||
32 | 25.882 | 0.370 | ||||
33 | 25.885 | 0.370 | ||||
34 | 25.888 | 0.371 | ||||
35 | 25.891 | 0.371 | ||||
36 | 25.893 | 0.371 | ||||
37 | 25.895 | 0.371 | ||||
38 | 25.898 | 0.372 | ||||
39 | 25.900 | 0.372 | ||||
40 | 25.901 | 0.372 | ||||
… | … | … | … | … | … | |
¥ | 25.936 | 25.936 | 25.936 |
n | MAOT | DCR | ALS | MAOT | DCR | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
6 | 25.749 | 25.755 | (25.745) | 0.459 | 0.46 | (0.47) |
7 | 26.246 | 26.253 | 26.246 | 0.469 | 0.45 | 0.47 |
8 | 26.562 | 26.576 | 26.564 | 0.471 | 0.45 | 0.46 |
9 | 26.774 | 26.780 | 26.778 | 0.471 | 0.44 | 0.45 |
10 | 26.923 | 26.927 | 26.928 | 0.470 | 0.44 | 0.43 |
11 | 27.031 | 27.035 | 27.031 | 0.469 | 0.43 | 0.47 |
12 | 27.113 | 27.115 | (27.114) | 0.468 | 0.44 | (0.45) |
13 | 27.176 | 27.178 | 27.175 | 0.467 | 0.42 | 0.48 |
14 | 27.225 | 0.467 | ||||
15 | 27.264 | 0.466 | ||||
16 | 27.296 | 0.466 | ||||
17 | 27.323 | 0.466 | ||||
18 | 27.345 | 0.466 | ||||
19 | 27.364 | 0.466 | ||||
20 | 27.379 | 0.466 | ||||
21 | 27.393 | 0.466 | ||||
22 | 27.405 | 0.466 | ||||
23 | 27.415 | 0.466 | ||||
24 | 27.424 | 0.467 | ||||
25 | 27.432 | 0.467 | ||||
26 | 27.439 | 0.467 | ||||
27 | 27.445 | 0.467 | ||||
28 | 27.450 | 0.468 | ||||
29 | 27.455 | 0.468 | ||||
30 | 27.460 | 0.468 | ||||
31 | 27.464 | 0.469 | ||||
32 | 27.467 | 0.469 | ||||
33 | 27.471 | 0.470 | ||||
34 | 27.474 | 0.470 | ||||
35 | 27.476 | 0.470 | ||||
36 | 27.479 | 0.471 | ||||
37 | 27.481 | 0.471 | ||||
38 | 27.483 | 0.471 | ||||
39 | 27.485 | 0.472 | ||||
40 | 27.487 | 0.472 | ||||
… | … | … | … | … | … | |
¥ | 27.522 | 27.522 | 27.522 |
n | MAOT | DCR | ALS | MAOT | DCR | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
6 | 25.659 | 25.668 | (25.660) | 0.464 | 0.45 | (0.45) |
7 | 26.157 | 26.162 | 26.157 | 0.474 | 0.46 | 0.47 |
8 | 26.473 | 26.480 | 26.475 | 0.477 | 0.45 | 0.47 |
9 | 26.686 | 26.695 | 26.687 | 0.476 | 0.43 | 0.46 |
10 | 26.835 | 26.842 | 26.833 | 0.475 | 0.42 | 0.49 |
11 | 26.944 | 0.474 | ||||
12 | 27.025 | 0.473 | ||||
13 | 27.088 | 0.472 | ||||
14 | 27.138 | 0.472 | ||||
15 | 27.177 | 0.471 | ||||
16 | 27.209 | 0.471 | ||||
17 | 27.236 | 0.471 | ||||
18 | 27.258 | 0.471 | ||||
19 | 27.276 | 0.471 | ||||
20 | 27.292 | 0.471 | ||||
21 | 27.306 | 0.471 | ||||
22 | 27.318 | 0.471 | ||||
23 | 27.328 | 0.471 | ||||
24 | 27.337 | 0.472 | ||||
25 | 27.345 | 0.472 | ||||
26 | 27.351 | 0.472 | ||||
27 | 27.358 | 0.473 | ||||
28 | 27.363 | 0.473 | ||||
29 | 27.368 | 0.473 | ||||
30 | 27.373 | 0.474 | ||||
31 | 27.377 | 0.474 | ||||
32 | 27.380 | 0.475 | ||||
33 | 27.384 | 0.475 | ||||
34 | 27.387 | 0.475 | ||||
35 | 27.389 | 0.476 | ||||
36 | 27.392 | 0.476 | ||||
37 | 27.394 | 0.476 | ||||
38 | 27.396 | 0.477 | ||||
39 | 27.398 | 0.477 | ||||
40 | 27.400 | 0.477 | ||||
… | … | … | … | … | … | |
¥ | 27.435 | 27.435 | 27.435 |
n | MAOT | DCR | ALS | MAOT | DCR | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
6 | 25.603 | 25.635 | 0.493 | 0.44 | ||
7 | 26.108 | 26.117 | 26.108 | 0.505 | 0.48 | 0.51 |
8 | 26.429 | 26.434 | 26.430 | 0.507 | 0.49 | 0.50 |
9 | 26.644 | 26.650 | 26.648 | 0.507 | 0.47 | 0.49 |
10 | 26.794 | 26.797 | 0.506 | 0.48 | ||
11 | 26.904 | 0.504 | ||||
12 | 26.986 | 0.503 | ||||
13 | 27.050 | 0.502 | ||||
14 | 27.099 | 0.502 | ||||
15 | 27.139 | 0.501 | ||||
16 | 27.171 | 0.501 | ||||
17 | 27.198 | 0.501 | ||||
18 | 27.220 | 0.501 | ||||
19 | 27.239 | 0.501 | ||||
20 | 27.255 | 0.501 | ||||
21 | 27.268 | 0.501 | ||||
22 | 27.280 | 0.501 | ||||
23 | 27.290 | 0.502 | ||||
24 | 27.299 | 0.502 | ||||
25 | 27.307 | 0.502 | ||||
26 | 27.314 | 0.503 | ||||
27 | 27.320 | 0.503 | ||||
28 | 27.326 | 0.504 | ||||
29 | 27.331 | 0.504 | ||||
30 | 27.335 | 0.504 | ||||
31 | 27.339 | 0.505 | ||||
32 | 27.343 | 0.505 | ||||
33 | 27.346 | 0.506 | ||||
34 | 27.349 | 0.506 | ||||
35 | 27.352 | 0.507 | ||||
36 | 27.355 | 0.507 | ||||
37 | 27.357 | 0.507 | ||||
38 | 27.359 | 0.508 | ||||
39 | 27.361 | 0.508 | ||||
40 | 27.363 | 0.509 | ||||
… | … | … | … | … | … | |
¥ | 27.398 | 27.398 | 27.398 |
n | MAOT | DCR | ALS | MAOT | DCR | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
4 | 20.426 | 20.420 | 20.426 | 0.127 | 0.13 | 0.13 |
5 | 21.762 | 21.734 | 21.742 | 0.127 | 0.16 | 0.15 |
6 | 22.477 | 22.459 | 22.463 | 0.126 | 0.16 | 0.15 |
7 | 22.902 | 22.890 | 22.900 | 0.126 | 0.16 | 0.13 |
8 | 23.176 | 23.170 | 23.178 | 0.125 | 0.15 | 0.12 |
9 | 23.363 | 23.361 | 0.125 | 0.14 | ||
10 | 23.496 | 0.125 | ||||
11 | 23.594 | 0.124 | ||||
12 | 23.668 | 0.124 | ||||
13 | 23.726 | 0.124 | ||||
14 | 23.771 | 0.124 | ||||
15 | 23.808 | 0.124 | ||||
16 | 23.838 | 0.124 | ||||
17 | 23.863 | 0.124 | ||||
18 | 23.884 | 0.124 | ||||
19 | 23.901 | 0.124 | ||||
20 | 23.916 | 0.124 | ||||
21 | 23.929 | 0.124 | ||||
22 | 23.940 | 0.124 | ||||
23 | 23.950 | 0.124 | ||||
24 | 23.959 | 0.124 | ||||
25 | 23.966 | 0.124 | ||||
26 | 23.973 | 0.125 | ||||
27 | 23.979 | 0.125 | ||||
28 | 23.984 | 0.125 | ||||
29 | 23.989 | 0.125 | ||||
30 | 23.993 | 0.125 | ||||
31 | 23.997 | 0.125 | ||||
32 | 24.000 | 0.125 | ||||
33 | 24.004 | 0.125 | ||||
34 | 24.007 | 0.125 | ||||
35 | 24.009 | 0.125 | ||||
36 | 24.012 | 0.125 | ||||
37 | 24.014 | 0.125 | ||||
… | … | … | … | … | … | |
¥ | 24.054 | 24.054 | 24.054 |
n | MAOT | DCR | ALS | MAOT | DCR | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
6 | 22.979 | 22.969 | 22.979 | 0.232 | 0.25 | 0.27 |
7 | 23.427 | 23.392 | 0.233 | 0.32 | ||
8 | 23.713 | 23.719 | 23.718 | 0.232 | 0.21 | 0.21 |
9 | 23.907 | 23.907 | 23.907 | 0.232 | 0.23 | 0.23 |
10 | 24.045 | 24.039 | 24.040 | 0.231 | 0.28 | 0.27 |
11 | 24.146 | 24.138 | (24.152) | 0.231 | 0.32 | (0.27) |
12 | 24.222 | 0.230 | ||||
13 | 24.281 | 0.230 | ||||
14 | 24.328 | 0.230 | ||||
15 | 24.366 | 0.230 | ||||
16 | 24.396 | 0.230 | ||||
17 | 24.421 | 0.229 | ||||
18 | 24.443 | 0.229 | ||||
19 | 24.461 | 0.229 | ||||
20 | 24.476 | 0.229 | ||||
21 | 24.489 | 0.229 | ||||
22 | 24.500 | 0.229 | ||||
23 | 24.510 | 0.229 | ||||
24 | 24.519 | 0.230 | ||||
25 | 24.526 | 0.230 | ||||
26 | 24.533 | 0.230 | ||||
27 | 24.539 | 0.230 | ||||
28 | 24.544 | 0.230 | ||||
29 | 24.549 | 0.230 | ||||
30 | 24.554 | 0.230 | ||||
31 | 24.558 | 0.230 | ||||
32 | 24.561 | 0.230 | ||||
33 | 24.564 | 0.230 | ||||
34 | 24.567 | 0.231 | ||||
35 | 24.570 | 0.231 | ||||
36 | 24.572 | 0.231 | ||||
37 | 24.575 | 0.231 | ||||
38 | 24.577 | 0.231 | ||||
39 | 24.579 | 0.231 | ||||
40 | 24.581 | 0.231 | ||||
… | … | … | … | … | … | |
¥ | 24.615 | 24.615 | 24.615 |
n | MAOT | SCUNC | QB | MAOT | SCUNC | QB |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
8 | 27.830 | 27.830 | 27.830 | 1.672 | 1.673 | 1.673 |
9 | 28.169 | 28.173 | 28.173 | 1.695 | 1.682 | 1.682 |
10 | 28.400 | 28.401 | 28.401 | 1.696 | 1.689 | 1.688 |
11 | 28.561 | 28.561 | 28.561 | 1.689 | 1.694 | 1.692 |
12 | 28.678 | 28.676 | 28.677 | 1.679 | 1.697 | 1.695 |
13 | 28.765 | 28.763 | 28.763 | 1.670 | 1.699 | 1.698 |
14 | 28.831 | 28.829 | 28.829 | 1.662 | 1.700 | 1.699 |
15 | 28.883 | 28.881 | 28.881 | 1.656 | 1.701 | 1.701 |
16 | 28.925 | 28.923 | 28.923 | 1.652 | 1.701 | 1.702 |
17 | 28.958 | 28.956 | 1.649 | 1.700 | ||
18 | 28.985 | 28.984 | 1.647 | 1.700 | ||
19 | 29.008 | 29.007 | 1.647 | 1.698 | ||
20 | 29.027 | 29.027 | 1.648 | 1.697 | ||
21 | 29.044 | 29.043 | 1.649 | 1.695 | ||
22 | 29.058 | 29.057 | 1.652 | 1.693 | ||
23 | 29.070 | 29.069 | 1.655 | 1.691 | ||
24 | 29.080 | 29.080 | 1.658 | 1.688 | ||
25 | 29.089 | 29.089 | 1.662 | 1.686 | ||
26 | 29.097 | 29.097 | 1.666 | 1.683 | ||
27 | 29.104 | 29.104 | 1.670 | 1.680 | ||
28 | 29.110 | 29.110 | 1.675 | 1.677 | ||
29 | 29.116 | 29.116 | 1.679 | 1.674 | ||
30 | 29.121 | 29.121 | 1.684 | 1.671 | ||
31 | 29.126 | 1.689 | ||||
32 | 29.130 | 1.694 | ||||
33 | 29.133 | 1.699 | ||||
34 | 29.137 | 1.704 | ||||
35 | 29.140 | 1.708 | ||||
36 | 29.143 | 1.713 | ||||
37 | 29.145 | 1.718 | ||||
38 | 29.148 | 1.723 | ||||
39 | 29.150 | 1.727 | ||||
40 | 29.152 | 1.732 | ||||
… | … | … | … | … | … | |
¥ | 29.189 | 29.189 | 29.189 |
n | MAOT | SCUNC | QB | MAOT | SCUNC | QB |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
8 | 28.211 | 28.211 | 28.211 | 0.540 | 0.540 | 0.540 |
9 | 28.428 | 28.426 | 28.426 | 0.543 | 0.555 | 0.554 |
10 | 28.581 | 28.578 | 28.576 | 0.543 | 0.563 | 0.574 |
11 | 28.691 | 28.689 | 28.691 | 0.542 | 0.568 | 0.546 |
12 | 28.775 | 28.772 | 28.773 | 0.541 | 0.571 | 0.562 |
13 | 28.838 | 28.837 | 28.837 | 0.540 | 0.573 | 0.568 |
14 | 28.889 | 28.887 | 28.887 | 0.539 | 0.573 | 0.572 |
15 | 28.929 | 28.928 | 28.928 | 0.538 | 0.573 | 0.574 |
16 | 28.961 | 28.960 | 0.538 | 0.572 | ||
17 | 28.988 | 28.987 | 0.537 | 0.571 | ||
18 | 29.011 | 29.010 | 0.537 | 0.570 | ||
19 | 29.029 | 29.029 | 0.537 | 0.568 | ||
20 | 29.045 | 29.045 | 0.537 | 0.567 | ||
21 | 29.059 | 29.059 | 0.537 | 0.565 | ||
22 | 29.071 | 29.071 | 0.537 | 0.563 | ||
23 | 29.081 | 29.081 | 0.537 | 0.560 | ||
24 | 29.090 | 29.090 | 0.537 | 0.558 | ||
25 | 29.098 | 29.098 | 0.538 | 0.556 | ||
26 | 29.105 | 29.105 | 0.538 | 0.553 | ||
27 | 29.111 | 29.111 | 0.538 | 0.551 | ||
28 | 29.117 | 29.117 | 0.538 | 0.548 | ||
29 | 29.122 | 29.122 | 0.539 | 0.546 | ||
30 | 29.126 | 29.126 | 0.539 | 0.543 | ||
31 | 29.130 | 0.539 | ||||
32 | 29.134 | 0.540 | ||||
33 | 29.137 | 0.540 | ||||
34 | 29.140 | 0.540 | ||||
35 | 29.143 | 0.541 | ||||
36 | 29.146 | 0.541 | ||||
37 | 29.148 | 0.542 | ||||
38 | 29.150 | 0.542 | ||||
39 | 29.152 | 0.542 | ||||
40 | 29.154 | 0.543 | ||||
… | … | … | … | … | … | |
¥ | 29.189 | 29.189 | 29.189 |
n | MAOT | SCUNC | QB | MAOT | SCUNC | QB |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
8 | 27.821 | 27.821 | 27.821 | 1.693 | 1.693 | 1.692 |
9 | 28.163 | 28.171 | 28.171 | 1.717 | 1.688 | 1.691 |
10 | 28.396 | 28.401 | 28.401 | 1.718 | 1.689 | 1.690 |
11 | 28.558 | 28.561 | 28.561 | 1.710 | 1.692 | 1.689 |
12 | 28.676 | 28.677 | 28.677 | 1.700 | 1.693 | 1.688 |
13 | 28.763 | 28.763 | 28.764 | 1.691 | 1.695 | 1.688 |
14 | 28.830 | 28.830 | 28.830 | 1.683 | 1.695 | 1.688 |
15 | 28.882 | 28.882 | 28.882 | 1.676 | 1.695 | 1.687 |
16 | 28.924 | 28.923 | 28.923 | 1.672 | 1.694 | 1.687 |
17 | 28.957 | 28.957 | 1.669 | 1.692 | ||
18 | 28.985 | 28.984 | 1.667 | 1.691 | ||
19 | 29.008 | 29.007 | 1.667 | 1.688 | ||
20 | 29.027 | 29.027 | 1.668 | 1.686 | ||
21 | 29.043 | 29.043 | 1.669 | 1.683 | ||
22 | 29.057 | 29.057 | 1.672 | 1.679 | ||
23 | 29.069 | 29.069 | 1.675 | 1.676 | ||
24 | 29.080 | 29.080 | 1.678 | 1.672 | ||
25 | 29.089 | 29.089 | 1.682 | 1.668 | ||
26 | 29.097 | 29.097 | 1.686 | 1.663 | ||
27 | 29.104 | 29.104 | 1.691 | 1.659 | ||
28 | 29.110 | 29.111 | 1.695 | 1.655 | ||
29 | 29.116 | 29.116 | 1.700 | 1.650 | ||
30 | 29.121 | 29.121 | 1.705 | 1.645 | ||
31 | 29.126 | 1.710 | ||||
32 | 29.130 | 1.715 | ||||
33 | 29.133 | 1.720 | ||||
34 | 29.137 | 1.725 | ||||
35 | 29.140 | 1.730 | ||||
36 | 29.143 | 1.735 | ||||
37 | 29.145 | 1.740 | ||||
38 | 29.148 | 1.745 | ||||
39 | 29.150 | 1.750 | ||||
40 | 29.152 | 1.754 | ||||
… | … | … | … | … | … | |
¥ | 29.189 | 29.189 | 29.189 |
3s23p4(1D2)ns, nd (j = 1/2) and of the 3s23p4(1D2)nd (j = 3/2) series originating from the 3 s 3 2 p 5 P 2 1 / 2 ° metastable state of the Ar II ions. Comparison indicate an excellent agreements between the present results from the Modified atomic orbital theory (MAOT) and both the Screening constant by unit nuclear charge (SCUNC) results [
n | MAOT | SCUNC | QB | MAOT | SCUNC | QB |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
8 | 28.007 | 28.007 | 28.007 | 1.674 | 1.674 | 1.673 |
9 | 28.346 | 28.351 | 28.351 | 1.698 | 1.681 | 1.682 |
10 | 28.577 | 28.579 | 28.579 | 1.699 | 1.688 | 1.688 |
11 | 28.739 | 28.739 | 28.739 | 1.691 | 1.694 | 1.692 |
12 | 28.856 | 28.854 | 28.854 | 1.681 | 1.698 | 1.696 |
13 | 28.943 | 28.941 | 28.941 | 1.672 | 1.701 | 1.698 |
14 | 29.009 | 29.007 | 29.007 | 1.664 | 1.702 | 1.700 |
15 | 29.061 | 29.059 | 29.059 | 1.658 | 1.702 | 1.701 |
16 | 29.103 | 29.101 | 29.100 | 1.654 | 1.702 | 1.702 |
17 | 29.136 | 29.135 | 1.651 | 1.700 | ||
18 | 29.163 | 29.162 | 1.649 | 1.698 | ||
19 | 29.186 | 29.185 | 1.649 | 1.696 | ||
20 | 29.205 | 29.205 | 1.650 | 1.693 | ||
21 | 29.222 | 29.221 | 1.652 | 1.690 | ||
22 | 29.236 | 29.235 | 1.654 | 1.686 | ||
23 | 29.248 | 29.247 | 1.657 | 1.682 | ||
24 | 29.258 | 29.258 | 1.660 | 1.678 | ||
25 | 29.267 | 29.267 | 1.664 | 1.673 | ||
26 | 29.275 | 29.275 | 1.668 | 1.668 | ||
27 | 29.282 | 29.282 | 1.672 | 1.663 | ||
28 | 29.288 | 29.289 | 1.677 | 1.658 | ||
29 | 29.294 | 29.294 | 1.682 | 1.653 | ||
30 | 29.299 | 29.299 | 1.686 | 1.647 | ||
31 | 29.304 | 1.691 | ||||
32 | 29.308 | 1.696 | ||||
33 | 29.311 | 1.701 | ||||
34 | 29.315 | 1.706 | ||||
35 | 29.318 | 1.711 | ||||
36 | 29.321 | 1.716 | ||||
37 | 29.323 | 1.720 | ||||
38 | 29.326 | 1.725 | ||||
39 | 29.328 | 1.730 | ||||
40 | 29.330 | 1.734 | ||||
… | … | … | … | … | … | |
¥ | 29.367 | 29.367 | 29.367 |
n | MAOT | SCUNC | QB | MAOT | SCUNC | QB |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
8 | 28.389 | 28.389 | 28.389 | 0.540 | 0.540 | 0.540 |
9 | 28.606 | 28.603 | 28.603 | 0.543 | 0.560 | 0.554 |
10 | 28.759 | 28.755 | 28.754 | 0.543 | 0.567 | 0.574 |
11 | 28.869 | 28.867 | 28.869 | 0.542 | 0.572 | 0.546 |
12 | 28.953 | 28.950 | 28.951 | 0.541 | 0.575 | 0.562 |
13 | 29.016 | 29.014 | 29.014 | 0.540 | 0.578 | 0.568 |
14 | 29.067 | 29.065 | 29.065 | 0.539 | 0.581 | 0.572 |
15 | 29.107 | 29.105 | 29.105 | 0.538 | 0.583 | 0.574 |
16 | 29.139 | 29.138 | 0.538 | 0.585 | ||
17 | 29.166 | 29.165 | 0.537 | 0.587 | ||
18 | 29.189 | 29.187 | 0.537 | 0.588 | ||
19 | 29.207 | 29.206 | 0.537 | 0.589 | ||
20 | 29.223 | 29.223 | 0.537 | 0.590 | ||
21 | 29.237 | 29.236 | 0.537 | 0.589 | ||
22 | 29.249 | 29.248 | 0.537 | 0.589 | ||
23 | 29.259 | 29.259 | 0.537 | 0.587 | ||
24 | 29.268 | 29.268 | 0.537 | 0.585 | ||
25 | 29.276 | 29.276 | 0.538 | 0.581 | ||
26 | 29.283 | 29.283 | 0.538 | 0.577 | ||
27 | 29.289 | 29.289 | 0.538 | 0.572 | ||
28 | 29.295 | 29.295 | 0.538 | 0.566 | ||
29 | 29.300 | 29.300 | 0.539 | 0.559 | ||
30 | 29.304 | 29.304 | 0.539 | 0.551 | ||
31 | 29.308 | 0.539 | ||||
32 | 29.312 | 0.540 | ||||
33 | 29.315 | 0.540 | ||||
34 | 29.318 | 0.540 | ||||
35 | 29.321 | 0.541 | ||||
36 | 29.324 | 0.541 | ||||
37 | 29.326 | 0.542 | ||||
38 | 29.328 | 0.542 | ||||
39 | 29.330 | 0.542 | ||||
40 | 29.332 | 0.543 | ||||
… | … | … | … | … | … | |
¥ | 29.367 | 29.367 | 29.367 |
n | MAOT | SCUNC | QB | MAOT | SCUNC | QB |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
8 | 27.999 | 27.999 | 27.999 | 1.693 | 1.693 | 1.692 |
9 | 28.341 | 28.348 | 28.348 | 1.717 | 1.692 | 1.691 |
10 | 28.574 | 28.578 | 28.579 | 1.718 | 1.692 | 1.690 |
11 | 28.736 | 28.739 | 28.739 | 1.710 | 1.693 | 1.689 |
12 | 28.854 | 28.855 | 28.855 | 1.700 | 1.694 | 1.688 |
13 | 28.941 | 28.941 | 28.941 | 1.691 | 1.694 | 1.688 |
14 | 29.008 | 29.008 | 29.098 | 1.683 | 1.695 | 1.688 |
15 | 29.060 | 29.060 | 29.060 | 1.676 | 1.695 | 1.687 |
16 | 29.102 | 29.101 | 29.101 | 1.672 | 1.695 | 1.687 |
17 | 29.135 | 29.135 | 1.669 | 1.695 | ||
18 | 29.163 | 29.162 | 1.667 | 1.695 | ||
19 | 29.186 | 29.185 | 1.667 | 1.694 | ||
20 | 29.205 | 29.205 | 1.668 | 1.694 | ||
21 | 29.221 | 29.221 | 1.669 | 1.693 | ||
22 | 29.235 | 29.235 | 1.672 | 1.692 | ||
23 | 29.247 | 29.247 | 1.675 | 1.691 | ||
24 | 29.258 | 29.258 | 1.678 | 1.690 | ||
25 | 29.267 | 29.267 | 1.682 | 1.689 | ||
26 | 29.275 | 29.275 | 1.686 | 1.688 | ||
27 | 29.282 | 29.282 | 1.691 | 1.687 | ||
28 | 29.288 | 29.288 | 1.695 | 1.686 | ||
29 | 29.294 | 29.294 | 1.700 | 1.684 | ||
30 | 29.299 | 29.299 | 1.705 | 1.683 | ||
31 | 29.304 | 1.710 | ||||
32 | 29.308 | 1.715 | ||||
33 | 29.311 | 1.720 | ||||
34 | 29.315 | 1.725 | ||||
35 | 29.318 | 1.730 | ||||
36 | 29.321 | 1.735 | ||||
37 | 29.323 | 1.740 | ||||
38 | 29.326 | 1.745 | ||||
39 | 29.328 | 1.750 | ||||
40 | 29.330 | 1.754 | ||||
… | … | … | … | … | … | |
¥ | 29.367 | 29.367 | 29.367 |
n | MAOT | SCUNC | QB | MAOT | SCUNC | QB |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
8 | 28.341 | 28.341 | 28.341 | 0.717 | 0.717 | 0.716 |
9 | 28.573 | 28.573 | 28.573 | 0.721 | 0.721 | 0.720 |
10 | 28.735 | 28.734 | (28.774) | 0.721 | 0.724 | (0.422)* |
11 | 28.852 | 28.851 | 28.850 | 0.720 | 0.727 | 0.738 |
12 | 28.939 | 28.939 | 28.937 | 0.718 | 0.729 | 0.745 |
13 | 29.006 | 29.006 | 29.004 | 0.717 | 0.729 | 0.744 |
14 | 29.059 | 29.058 | 29.047 | 0.715 | 0.729 | 0.744 |
15 | 29.100 | 29.100 | 29.099 | 0.714 | 0.728 | 0.744 |
16 | 29.134 | 29.134 | 0.713 | 0.727 | ||
17 | 29.162 | 29.162 | 0.713 | 0.725 | ||
18 | 29.185 | 29.185 | 0.713 | 0.722 | ||
19 | 29.204 | 29.204 | 0.712 | 0.720 | ||
20 | 29.221 | 29.221 | 0.712 | 0.718 | ||
21 | 29.235 | 29.235 | 0.713 | 0.716 | ||
22 | 29.247 | 29.247 | 0.713 | 0.714 | ||
23 | 29.257 | 29.257 | 0.713 | 0.713 | ||
24 | 29.267 | 29.267 | 0.714 | 0.712 | ||
25 | 29.275 | 29.275 | 0.714 | 0.712 | ||
26 | 29.282 | 29.282 | 0.715 | 0.713 | ||
27 | 29.288 | 29.288 | 0.715 | 0.715 | ||
28 | 29.294 | 29.294 | 0.716 | 0.719 | ||
29 | 29.299 | 29.299 | 0.717 | 0.723 | ||
30 | 29.304 | 29.303 | 0.717 | 0.729 | ||
31 | 29.308 | 0.718 | ||||
32 | 29.311 | 0.719 | ||||
33 | 29.315 | 0.719 | ||||
34 | 29.318 | 0.720 | ||||
35 | 29.321 | 0.721 | ||||
36 | 29.323 | 0.722 | ||||
37 | 29.326 | 0.722 | ||||
38 | 29.328 | 0.723 | ||||
39 | 29.330 | 0.724 | ||||
40 | 29.332 | 0.724 | ||||
… | … | … | … | … | … | |
¥ | 29.367 | 29.367 | 29.367 |
*This line is not well identified.
n | [4s24p4(1D2)]ns series | [4s24p4(1D2)]nd series | ||||
---|---|---|---|---|---|---|
MAOT | SCUNC | QB | MAOT | SCUNC | QB | |
G | G | G | G | G | G | |
8 | 103.5 | 103.4 | 103.4 | 0.112 | 0.110 | 0.110 |
9 | 64.9 | 64.8 | 64.8 | 0.072 | 0.070 | 0.070 |
10 | 43.4 | 43.0 | 43.0 | 0.048 | 0.047 | 0.050 |
11 | 30.4 | 30.0 | 30.0 | 0.034 | 0.033 | 0.040 |
12 | 22.1 | 21.7 | 21.8 | 0.024 | 0.024 | 0.030 |
13 | 16.5 | 16.2 | 16.3 | 0.018 | 0.018 | 0.020 |
14 | 12.7 | 12.4 | 12.5 | 0.014 | 0.014 | 0.020 |
15 | 9.9 | 9.8 | 9.8 | 0.011 | 0.011 | 0.020 |
16 | 7.8 | 7.8 | 7.8 | 0.008 | 0.009 | |
17 | 6.3 | 6.4 | 0.007 | 0.008 | ||
18 | 5.1 | 5.3 | 0.005 | 0.006 | ||
19 | 4.2 | 4.5 | 0.004 | 0.005 | ||
20 | 3.5 | 3.8 | 0.004 | 0.005 | ||
21 | 2.9 | 3.3 | 0.003 | 0.004 | ||
22 | 2.5 | 2.9 | 0.003 | 0.003 | ||
23 | 2.1 | 2.5 | 0.002 | 0.003 | ||
24 | 1.8 | 2.2 | 0.002 | 0.003 | ||
25 | 1.5 | 2.0 | 0.002 | 0.002 |
n | [4s24p4(1D2)]ns series | [4s24p4(1D2)]nd series | ||||
---|---|---|---|---|---|---|
MAOT | SCUNC | QB | MAOT | SCUNC | QB | |
G | G | G | G | G | G | |
8 | 0.44 | 0.44 | 0.44 | 25.7 | 25.7 | |
9 | 0.22 | 0.22 | 0.22 | 18.1 | 18.1 | |
10 | 0.13 | 0.11 | 0.13 | 12.9 | 33.8 | |
11 | 0.08 | 0.06 | 0.08 | 9.3 | 8.5 |
12 | 0.05 | 0.03 | 0.08 | 6.9 | 3.8 | |
---|---|---|---|---|---|---|
13 | 0.03 | 0.02 | 0.04 | 5.2 | 5.3 | |
14 | 0.02 | 0.01 | 0.02 | 4.0 | 4.4 | |
15 | 0.01 | 0.01 | 0.02 | 3.1 | 3.6 | |
16 | 2.5 | |||||
17 | 2.1 | |||||
18 | 1.7 | |||||
19 | 1.4 | |||||
20 | 1.2 | |||||
21 | 1.0 | |||||
22 | 0.9 | |||||
23 | 0.8 | |||||
24 | 0.7 | |||||
25 | 0.6 |
n | MAOT | SCUNC | ALS | MAOT | SCUNC | ALS |
---|---|---|---|---|---|---|
E | E | E | δ | δ | δ | |
5 | 24.342 | 24.342 | 24.342 | −0.387 | −0.387 | −0.385 |
6 | 24.882 | 24.878 | 24.878 | −0.386 | −0.375 | −0.370 |
7 | 25.220 | 25.215 | 25.217 | −0.387 | −0.369 | −0.370 |
8 | 25.444 | 25.439 | 25.441 | −0.389 | −0.366 | −0.370 |
9 | 25.600 | 25.596 | 25.598 | −0.390 | −0.365 | −0.360 |
10 | 25.713 | 25.710 | 25.712 | −0.390 | −0.365 | −0.358 |
11 | 25.798 | 25.796 | 25.796 | −0.391 | −0.365 | −0.345 |
12 | 25.863 | 25.861 | (25.880) | −0.391 | −0.366 | (−0.671) |
13 | 25.913 | 25.912 | (25.926) | −0.391 | −0.367 | (−0.663) |
14 | 25.954 | 25.953 | −0.391 | −0.368 | ||
15 | 25.987 | 25.987 | −0.390 | −0.369 | ||
16 | 26.014 | 26.014 | −0.390 | −0.370 | ||
17 | 26.037 | 26.037 | −0.390 | −0.371 | ||
18 | 26.056 | 26.056 | −0.389 | −0.372 | ||
19 | 26.072 | 26.072 | −0.389 | −0.373 | ||
20 | 26.086 | 26.086 | −0.389 | −0.373 | ||
21 | 26.098 | 26.098 | −0.388 | −0.374 | ||
22 | 26.108 | 26.108 | −0.388 | −0.374 | ||
23 | 26.118 | 26.117 | −0.387 | −0.374 | ||
24 | 26.125 | 26.125 | −0.387 | −0.374 |
25 | 26.133 | 26.132 | −0.387 | −0.374 | ||
---|---|---|---|---|---|---|
26 | 26.139 | 26.139 | −0.386 | −0.374 | ||
27 | 26.144 | 26.144 | −0.386 | −0.374 | ||
28 | 26.149 | 26.149 | −0.385 | −0.373 | ||
29 | 26.154 | 26.154 | −0.385 | −0.373 | ||
30 | 26.158 | 26.158 | −0.385 | −0.372 | ||
31 | 26.162 | −0.384 | ||||
32 | 26.165 | −0.384 | ||||
33 | 26.168 | −0.383 | ||||
34 | 26.171 | −0.383 | ||||
35 | 26.174 | −0.383 | ||||
36 | 26.176 | −0.382 | ||||
37 | 26.178 | −0.382 | ||||
38 | 26.180 | −0.382 | ||||
39 | 26.182 | −0.381 | ||||
40 | 26.184 | −0.381 | ||||
… | … | … | … | … | … | |
¥ | 29.367 | 29.367 | 29.367 |
associated ALS quantum defects are equal to (−0.671) and (−0.663) respectively. For the same levels, the MAOT and SCUNC calculations [
n | 4s24p4(3P2)]ns | 4s24p4(3P1)]ns | ||||||
---|---|---|---|---|---|---|---|---|
MAOT | ALS | MAOT | ALS | MAOT | ALS | MAOT | ALS | |
E | E | δ | δ | E | E | δ | δ | |
11 | 23.910 | (23.906) | −0.771 | (−0.716) | ||||
12 | 23.969 | 23.969 | −0.765 | −0.779 | ||||
13 | 24.016 | 24.016 | −0.762 | −0.791 | ||||
14 | 24.053 | (24.059) | −0.761 | (−0.940) | 23.957 | 0.418 | ||
15 | 24.084 | 24.083 | −0.761 | −0.730 | 23.996 | 23.996 | 0.419 | 0.403 |
16 | 24.109 | 24.109 | −0.762 | −0.774 | 24.028 | 0.420 | ||
17 | 24.131 | (24.129) | −0.762 | (−0.686) | 24.054 | 0.420 | ||
18 | 24.148 | (24.147) | −0.763 | (−0.707) | 24.076 | 0.420 | ||
19 | 24.164 | (24.162) | −0.764 | (−0.659) | 24.094 | 0.420 | ||
20 | 24.177 | (24.176) | −0.764 | (−0.731) | 24.110 | 0.420 | ||
21 | 24.188 | −0.765 | 24.124 | 0.420 | ||||
22 | 24.198 | −0.765 | 24.135 | 0.420 | ||||
23 | 24.207 | −0.765 | 24.145 | 0.419 | ||||
24 | 24.214 | −0.766 | 24.154 | 0.419 | ||||
25 | 24.221 | −0.766 | 24.162 | 0.419 | ||||
26 | 24.227 | −0.766 | 24.169 | 0.419 | ||||
27 | 24.232 | −0.766 | 24.175 | 0.419 | ||||
28 | 24.237 | −0.766 | 24.180 | 0.419 | ||||
29 | 24.242 | −0.766 | 24.185 | 0.418 | ||||
30 | 24.246 | −0.766 | 24.190 | 0.418 | ||||
31 | 24.249 | −0.766 | 24.194 | 0.418 | ||||
32 | 24.252 | −0.765 | 24.197 | 0.418 | ||||
33 | 24.255 | −0.765 | 24.201 | 0.418 | ||||
34 | 24.258 | −0.765 | 24.204 | 0.418 | ||||
35 | 24.260 | −0.765 | 24.206 | 0.418 | ||||
36 | 24.263 | −0.765 | 24.209 | 0.418 | ||||
37 | 24.265 | −0.764 | 24.211 | 0.418 | ||||
38 | 24.267 | −0.764 | 24.213 | 0.418 | ||||
39 | 24.269 | −0.764 | 24.215 | 0.418 | ||||
40 | 24.270 | −0.763 | 24.217 | 0.418 | ||||
… | ||||||||
¥ | 24.303 | 24.303 | 24.252 | 24.252 |
n | 4s24p4(3D2)]ns | 4s24p4(3D2)]nd | ||||||
---|---|---|---|---|---|---|---|---|
MAOT | ALS | MAOT | ALS | MAOT | ALS | MAOT | ALS | |
E | E | δ | δ | E | E | δ | δ | |
6 | 23.927 | 23.927 | 0.200 | 0.200 | 24.214 | 24.214 | −0.371 | −0.375 |
7 | 24.368 | (24.366) | 0.200 | (0.205) | 24.553 | 24.551 | −0.369 | −0.371 |
8 | 24.650 | 24.650 | 0.200 | 0.204) | 24.778 | 24.775 | −0.370 | −0.371 |
9 | 24.842 | 24.842 | 0.200 | 0.201 | 24.935 | 24.933 | −0.371 | −0.375 |
10 | 24.978 | - | 0.199 | - | 25.049 | 25.047 | −0.372 | −0.379 |
11 | 25.079 | 25.082 | 0.199 | 0.152 | 25.134 | 25.132 | −0.372 | −0.363 |
12 | 25.154 | 25.158 | 0.199 | 0.139 | 25.199 | 25.196 | −0.373 | −0.349 |
13 | 25.213 | 0.198 | 25.251 | 25.248 | −0.373 | −0.364 | ||
14 | 25.259 | 0.198 | 25.292 | −0.373 | ||||
15 | 25.297 | 0.198 | 25.325 | −0.373 | ||||
16 | 25.327 | 0.198 | 25.352 | −0.373 | ||||
17 | 25.352 | 0.198 | 25.375 | −0.373 | ||||
18 | 25.373 | 0.198 | 25.394 | −0.373 | ||||
19 | 25.391 | 0.198 | 25.410 | −0.373 | ||||
20 | 25.406 | 0.198 | 25.424 | −0.373 | ||||
21 | 25.419 | 0.198 | 25.436 | −0.373 | ||||
22 | 25.431 | 0.198 | 25.446 | −0.372 | ||||
23 | 25.440 | 0.198 | 25.455 | −0.372 | ||||
24 | 25.449 | 0.198 | 25.463 | −0.372 | ||||
25 | 25.457 | 0.198 | 25.470 | −0.372 | ||||
26 | 25.463 | 0.198 | 25.477 | −0.371 | ||||
27 | 25.469 | 0.198 | 25.482 | −0.371 | ||||
28 | 25.475 | 0.198 | 25.487 | −0.371 | ||||
29 | 25.479 | 0.198 | 25.492 | −0.371 | ||||
30 | 25.484 | 0.198 | 25.496 | −0.370 | ||||
31 | 25.488 | 0.198 | 25.500 | −0.370 | ||||
32 | 25.491 | 0.198 | 25.503 | −0.370 | ||||
33 | 25.494 | 0.198 | 25.506 | −0.370 | ||||
34 | 25.497 | 0.198 | 25.509 | −0.369 | ||||
35 | 25.500 | 0.198 | 25.511 | −0.369 | ||||
36 | 25.503 | 0.198 | 25.514 | −0.369 | ||||
37 | 25.505 | 0.199 | 25.516 | −0.369 | ||||
38 | 25.507 | 0.199 | 25.518 | −0.368 | ||||
39 | 25.509 | 0.199 | 25.520 | −0.368 | ||||
40 | 25.511 | 0.199 | 25.522 | −0.368 | ||||
… | ||||||||
¥ | 25.545 | 25.545 | 25.555 | 25.555 |
n | 4 s 4 2 p 5 P 2 1 / 2 ° → 4s24p4(1S0]ns | 4 s 4 2 p 5 P 2 3 / 2 ° → 4s24p4(1S0)]nd | ||||||
---|---|---|---|---|---|---|---|---|
MAOT | ALS | MAOT | ALS | MAOT | ALS | MAOT | ALS | |
E | E | δ | δ | E | E | δ | δ | |
4 | 23.738 | 23.738 | 0.357 | 0.358 | ||||
5 | 25.315 | 25.312 | 0.358 | 0.360 | 25.965 | (25.947) | 0.369 | (0.385) |
6 | 26.132 | 26.124 | 0.355 | 0.368 | 26.780 | 26.780 | 0.380 | 0.379 |
7 | 26.608 | 26.602 | 0.353 | 0.371 | 27.261 | (27.261) | 0.381 | (0.379) |
8 | 26.910 | 26.904 | 0.352 | 0.376 | 27.566 | 27.566 | 0.381 | 0.376 |
9 | 27.112 | 27.108 | 0.351 | 0.377 | 27.771 | 27.771 | 0.379 | 0.378 |
10 | 27.255 | (27.261) | 0.351 | (0.303) | 27.915 | 27.914 | 0.378 | 0.381 |
11 | 27.360 | 27.356 | 0.351 | 0.400 | 28.021 | 28.020 | 0.378 | 0.383 |
12 | 27.439 | 27.435 | 0.351 | 0.412 | 28.100 | 28.099 | 0.377 | 0.381 |
13 | 27.500 | (27.495) | 0.351 | (0.435) | 28.161 | (28.160) | 0.377 | (0.394) |
14 | 27.548 | (27.544) | 0.352 | (0436) | 28.210 | (28.208) | 0.376 | (0.394) |
15 | 27.586 | 0.352 | 28.249 | (28.247) | 0.376 | (0.418) | ||
16 | 27.618 | 0.353 | 28.280 | 0.376 | ||||
17 | 27.644 | 0.354 | 28.306 | 0.376 | ||||
18 | 27.665 | 0.354 | 28.328 | 0.376 | ||||
19 | 27.683 | 0.355 | 28.346 | 0.376 | ||||
20 | 27.699 | 0.356 | 28.362 | 0.376 | ||||
21 | 27.712 | 0.356 | 28.375 | 0.377 | ||||
22 | 27.724 | 0.357 | 28.387 | 0.377 | ||||
23 | 27.734 | 0.358 | 28.397 | 0.377 | ||||
24 | 27.743 | 0.358 | 28.405 | 0.377 | ||||
25 | 27.750 | 0.359 | 28.413 | 0.378 | ||||
26 | 27.757 | 0.359 | 28.420 | 0.378 | ||||
27 | 27.763 | 0.360 | 28.426 | 0.378 | ||||
28 | 27.769 | 0.361 | 28.432 | 0.379 | ||||
29 | 27.774 | 0.361 | 28.437 | 0.379 | ||||
30 | 27.778 | 0.362 | 28.441 | 0.379 | ||||
31 | 27.782 | 0.362 | 28.445 | 0.379 | ||||
32 | 27.786 | 0.363 | 28.449 | 0.380 | ||||
33 | 27.789 | 0.363 | 28.452 | 0.380 | ||||
34 | 27.792 | 0.364 | 28.455 | 0.380 | ||||
35 | 27.795 | 0.364 | 28.458 | 0.381 | ||||
36 | 27.797 | 0.365 | 28.460 | 0.381 | ||||
37 | 27.799 | 0.365 | 28.462 | 0.381 | ||||
38 | 27.802 | 0.366 | 28.465 | 0.382 | ||||
39 | 27.804 | 0.366 | 28.467 | 0.382 | ||||
40 | 27.805 | 0.366 | 28.468 | 0.382 | ||||
… | ||||||||
¥ | 27.840 | 27.840 | 28.503 | 28.503 |
4s24p4(3D2, 1S0)]ns, nd series of the Kr II ions. Here again, the good agreements between the present MAOT and ALS data [
Accurate high lying resonance energy up to n = 40 is reported applying the Modified atomic orbital theory. For both the Cl II, Ar II and Kr II ions investigated, a single formula has been established to reproduce with a very good accuracy high experimental measurements such as those performed at the Advanced Light Source at Lawrence Berkeley National Laboratory. A huge number of results are tabulated as useful reference data for interpreting atomic spectra from astrophysical objects containing chlorine, argon and krypton elements.
The authors declare no conflicts of interest regarding the publication of this paper.
Diallo, A., Ba, M.D., Badiane, J.K., Gning, M.T., Sow, M. and Sakho, I. (2018) Photoionization Study of Cl II, Ar II and Kr II Ions Using the Modified Atomic Orbital Theory. Journal of Modern Physics, 9, 2594-2622. https://doi.org/10.4236/jmp.2018.914162