8.1.2. Plasma model in SPEX 3.0¶
8.1.2.1. The core of the plasma model¶
The old plasma code used by SPEX in version 2.0 and below is essentially the same plasma code as developed originally by Rolf Mewe and colleagues, with relatively minor updates to the atomic data (like wavelength improvements, corrections of a few typo’s, improvements for Fe XVII).
Its basis were pre-calculated and parametrized line emissivities for each spectral line, as a function of temperature, with for relevant lines empirical density corrections. For some transitions, like the He-like triplets, the calculations were rather complex and required several correction factors to account for the full density dependence.
In the new approach presented here, the basic plasma processes are evaluated for each individual level, and then the occupation numbers of the excited states are calculated for the full ion, solving a matrix equation. This has the great advantage that with the same effort a multitude of processes can be taken into account, including effects of photo-excitation and photo-ionisation. From the occupation numbers and the radiative transition probabilities it is then straightforward to calculate the emitted spectrum.
In order to keep the code fast and flexible, we have chosen for a procedure to parametrise all relevant processes, and using simple analytical formulae with a limited number of parameters for each process. This is beneficial both in terms of computation time and storage demands and formed the basis for the succes of Mewe’s original work.
The production of the relevant files is not yet complete, but in the first release of version 3.0 we incorporate the data for the H, He, and Li iso-electronic sequences, and some data for the other sequences, including the Fe-L ions. For an overview of what is in the code see Section Ions for which updated calculations are available below.
By default, the plasma code is the old version 2.0 code, but by giving the command “var calc new”, for the ions for which new data are available, the new code is used. This leads in principle to higher accuracy and many more spectral lines. A disadvantage is of course that the computations become somewhat slower. For spectral fitting, one could envision a procedure where in a first run the old code is used to get close to the best parameters, and then to refine using the new plasma core.
If you want to use the new plasma model, it is important to make sure the ionisation balance is the new u17 balance. This new balance has improved collisional ionisation rates and allows to calculate properly inner-shell transitions that are needed for the new calculations. See Urdampilleta et al. (2017) for details.
Finally, it is advised that the users have a look to the various ascii-output options that are available for the plasma models, allowing to get deeper insight into the physical process and parameters that are being used.
8.1.2.2. Ions for which updated calculations are available¶
Below we list for each iso-electronic sequence what data is available
for the new plasma calculations. Each line corresponds to one ion, with
ii, iz and jz corresponding to the iso-electronic sequence, nuclear
charge and ionisation stage, respectively. Then for a number of process
we list two quantities: 
, the number of entries we have (e.g.,
number of energy levels or transition rates), and 
the maximum principal quantum number for wich we use data for that ion
and process. Note that refers to the highest level
included for a transition between two levels.
The processes incorporated and shown in the table are:
levels – Energy levels
Arad – Radiative transition probabilities (Einstein coefficients)
Atwo – Two-photon processes
El col – Electron collisional excitation
Pr col – Proton collisional excitation
Aug – Auger rates (auto-ionisation, needed for dielectronic recombination)
CX – Charge exchange recombination
RR – Radiative recombination
II – Inner-shell processes (this is merely the number of quantum states after ionisation; the number of fluorescent lines will be larger)
8.1.2.3. Iso-electronic sequence: 1¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
1 |
1 |
1 |
256 |
16 |
325 |
16 |
1 |
2 |
31 |
16 |
1 |
2 |
0 |
0 |
1 |
1 |
19 |
16 |
0 |
0 |
1 |
2 |
2 |
256 |
16 |
325 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
0 |
0 |
19 |
16 |
0 |
0 |
1 |
3 |
3 |
256 |
16 |
325 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
0 |
0 |
19 |
16 |
0 |
0 |
1 |
4 |
4 |
256 |
16 |
326 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
1 |
3 |
19 |
16 |
0 |
0 |
1 |
5 |
5 |
256 |
16 |
327 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
1 |
4 |
19 |
16 |
0 |
0 |
1 |
6 |
6 |
284 |
20 |
431 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
7 |
7 |
19 |
16 |
0 |
0 |
1 |
7 |
7 |
284 |
20 |
436 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
8 |
6 |
19 |
16 |
0 |
0 |
1 |
8 |
8 |
284 |
20 |
438 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
11 |
9 |
19 |
16 |
0 |
0 |
1 |
9 |
9 |
256 |
16 |
335 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
11 |
8 |
19 |
16 |
0 |
0 |
1 |
10 |
10 |
284 |
20 |
444 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
15 |
8 |
19 |
16 |
0 |
0 |
1 |
11 |
11 |
256 |
16 |
337 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
18 |
10 |
19 |
16 |
0 |
0 |
1 |
12 |
12 |
284 |
20 |
446 |
20 |
1 |
2 |
15 |
18 |
1 |
2 |
0 |
0 |
21 |
10 |
19 |
16 |
0 |
0 |
1 |
13 |
13 |
256 |
16 |
339 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
24 |
11 |
19 |
16 |
0 |
0 |
1 |
14 |
14 |
284 |
20 |
451 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
29 |
12 |
19 |
16 |
0 |
0 |
1 |
15 |
15 |
256 |
16 |
345 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
29 |
13 |
19 |
16 |
0 |
0 |
1 |
16 |
16 |
284 |
20 |
456 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
32 |
14 |
19 |
16 |
0 |
0 |
1 |
17 |
17 |
256 |
16 |
351 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
35 |
14 |
19 |
16 |
0 |
0 |
1 |
18 |
18 |
284 |
20 |
461 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
39 |
15 |
19 |
16 |
0 |
0 |
1 |
19 |
19 |
256 |
16 |
355 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
41 |
15 |
19 |
16 |
0 |
0 |
1 |
20 |
20 |
284 |
20 |
467 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
42 |
15 |
19 |
16 |
0 |
0 |
1 |
21 |
21 |
256 |
16 |
359 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
42 |
15 |
19 |
16 |
0 |
0 |
1 |
22 |
22 |
284 |
20 |
470 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
43 |
15 |
19 |
16 |
0 |
0 |
1 |
23 |
23 |
256 |
16 |
362 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
43 |
15 |
19 |
16 |
0 |
0 |
1 |
24 |
24 |
284 |
20 |
473 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
44 |
15 |
19 |
16 |
0 |
0 |
1 |
25 |
25 |
256 |
16 |
364 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
37 |
15 |
19 |
16 |
0 |
0 |
1 |
26 |
26 |
284 |
20 |
476 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
44 |
15 |
19 |
16 |
0 |
0 |
1 |
27 |
27 |
256 |
16 |
367 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
44 |
15 |
19 |
16 |
0 |
0 |
1 |
28 |
28 |
284 |
20 |
479 |
20 |
1 |
2 |
15 |
17 |
1 |
2 |
0 |
0 |
44 |
15 |
19 |
16 |
0 |
0 |
1 |
29 |
29 |
256 |
16 |
371 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
44 |
15 |
19 |
16 |
0 |
0 |
1 |
30 |
30 |
256 |
16 |
401 |
16 |
1 |
2 |
13 |
10 |
1 |
2 |
0 |
0 |
44 |
15 |
19 |
16 |
0 |
0 |
8.1.2.4. Iso-electronic sequence: 2¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
2 |
2 |
1 |
511 |
16 |
794 |
16 |
1 |
2 |
3 |
6 |
1 |
2 |
0 |
0 |
0 |
0 |
10 |
8 |
0 |
0 |
2 |
3 |
2 |
558 |
16 |
878 |
16 |
1 |
2 |
5 |
7 |
1 |
2 |
11 |
3 |
0 |
0 |
10 |
8 |
2 |
2 |
2 |
4 |
3 |
558 |
16 |
892 |
16 |
1 |
2 |
27 |
7 |
1 |
2 |
11 |
3 |
0 |
0 |
10 |
8 |
2 |
2 |
2 |
5 |
4 |
558 |
16 |
903 |
16 |
1 |
2 |
27 |
7 |
1 |
2 |
11 |
3 |
1 |
2 |
10 |
8 |
2 |
2 |
2 |
6 |
5 |
678 |
16 |
1236 |
16 |
1 |
2 |
59 |
10 |
1 |
2 |
38 |
5 |
8 |
4 |
10 |
8 |
2 |
2 |
2 |
7 |
6 |
678 |
16 |
1251 |
16 |
1 |
2 |
59 |
10 |
1 |
2 |
38 |
5 |
12 |
7 |
10 |
8 |
2 |
2 |
2 |
8 |
7 |
678 |
16 |
1266 |
16 |
1 |
2 |
59 |
10 |
1 |
2 |
38 |
5 |
14 |
6 |
10 |
8 |
2 |
2 |
2 |
9 |
8 |
678 |
16 |
1229 |
16 |
1 |
2 |
56 |
7 |
1 |
2 |
38 |
5 |
2 |
5 |
10 |
8 |
2 |
2 |
2 |
10 |
9 |
678 |
16 |
1281 |
16 |
1 |
2 |
59 |
10 |
1 |
2 |
38 |
5 |
24 |
8 |
10 |
8 |
2 |
2 |
2 |
11 |
10 |
678 |
16 |
1261 |
16 |
1 |
2 |
55 |
7 |
1 |
2 |
38 |
5 |
28 |
9 |
10 |
8 |
2 |
2 |
2 |
12 |
11 |
678 |
16 |
1308 |
16 |
1 |
2 |
59 |
10 |
1 |
2 |
38 |
5 |
35 |
10 |
10 |
8 |
2 |
2 |
2 |
13 |
12 |
678 |
16 |
1300 |
16 |
1 |
2 |
55 |
7 |
1 |
2 |
38 |
5 |
42 |
10 |
10 |
8 |
2 |
2 |
2 |
14 |
13 |
678 |
16 |
1335 |
16 |
1 |
2 |
59 |
10 |
1 |
2 |
38 |
5 |
47 |
11 |
10 |
8 |
2 |
2 |
2 |
15 |
14 |
678 |
16 |
1329 |
16 |
1 |
2 |
56 |
7 |
1 |
2 |
38 |
5 |
0 |
0 |
10 |
8 |
2 |
2 |
2 |
16 |
15 |
678 |
16 |
1357 |
16 |
1 |
2 |
58 |
10 |
1 |
2 |
38 |
5 |
3 |
10 |
10 |
8 |
2 |
2 |
2 |
17 |
16 |
678 |
16 |
1344 |
16 |
1 |
2 |
55 |
7 |
1 |
2 |
38 |
5 |
3 |
10 |
10 |
8 |
2 |
2 |
2 |
18 |
17 |
678 |
16 |
1369 |
16 |
1 |
2 |
58 |
10 |
1 |
2 |
38 |
5 |
4 |
11 |
10 |
8 |
2 |
2 |
2 |
19 |
18 |
678 |
16 |
1355 |
16 |
1 |
2 |
55 |
7 |
1 |
2 |
38 |
5 |
4 |
11 |
10 |
8 |
2 |
2 |
2 |
20 |
19 |
678 |
16 |
1375 |
16 |
1 |
2 |
58 |
10 |
1 |
2 |
38 |
5 |
4 |
12 |
10 |
8 |
2 |
2 |
2 |
21 |
20 |
678 |
16 |
1359 |
16 |
1 |
2 |
55 |
7 |
1 |
2 |
38 |
5 |
4 |
12 |
10 |
8 |
2 |
2 |
2 |
22 |
21 |
678 |
16 |
1379 |
16 |
1 |
2 |
57 |
10 |
1 |
2 |
38 |
5 |
5 |
13 |
10 |
8 |
2 |
2 |
2 |
23 |
22 |
678 |
16 |
1362 |
16 |
1 |
2 |
54 |
7 |
1 |
2 |
38 |
5 |
4 |
12 |
10 |
8 |
2 |
2 |
2 |
24 |
23 |
678 |
16 |
1383 |
16 |
1 |
2 |
58 |
10 |
1 |
2 |
38 |
5 |
5 |
14 |
10 |
8 |
2 |
2 |
2 |
25 |
24 |
678 |
16 |
1363 |
16 |
1 |
2 |
53 |
7 |
1 |
2 |
38 |
5 |
5 |
14 |
10 |
8 |
2 |
2 |
2 |
26 |
25 |
678 |
16 |
1384 |
16 |
1 |
2 |
58 |
10 |
1 |
2 |
38 |
5 |
56 |
15 |
10 |
8 |
2 |
2 |
2 |
27 |
26 |
678 |
16 |
1362 |
16 |
1 |
2 |
55 |
7 |
1 |
2 |
38 |
5 |
5 |
14 |
10 |
8 |
2 |
2 |
2 |
28 |
27 |
678 |
16 |
1386 |
16 |
1 |
2 |
58 |
10 |
1 |
2 |
38 |
5 |
5 |
15 |
10 |
8 |
2 |
2 |
2 |
29 |
28 |
678 |
16 |
1367 |
16 |
1 |
2 |
55 |
7 |
1 |
2 |
38 |
5 |
6 |
16 |
10 |
8 |
2 |
2 |
2 |
30 |
29 |
678 |
16 |
1368 |
16 |
1 |
2 |
56 |
7 |
1 |
2 |
38 |
5 |
5 |
16 |
10 |
8 |
2 |
2 |
8.1.2.5. Iso-electronic sequence: 3¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
3 |
4 |
2 |
815 |
16 |
1978 |
16 |
0 |
0 |
10 |
5 |
0 |
0 |
56 |
3 |
0 |
0 |
5 |
8 |
1 |
2 |
3 |
5 |
3 |
815 |
16 |
1895 |
16 |
0 |
0 |
9 |
4 |
0 |
0 |
60 |
3 |
0 |
0 |
5 |
8 |
1 |
2 |
3 |
6 |
4 |
885 |
16 |
1368 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
232 |
5 |
1 |
2 |
5 |
8 |
1 |
2 |
3 |
7 |
5 |
885 |
16 |
1357 |
16 |
0 |
0 |
35 |
6 |
0 |
0 |
232 |
5 |
1 |
3 |
5 |
8 |
1 |
2 |
3 |
8 |
6 |
885 |
16 |
1373 |
16 |
0 |
0 |
35 |
5 |
0 |
0 |
232 |
5 |
1 |
2 |
5 |
8 |
1 |
2 |
3 |
9 |
7 |
271 |
16 |
349 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
1 |
4 |
5 |
8 |
1 |
2 |
3 |
10 |
8 |
885 |
16 |
1389 |
16 |
0 |
0 |
35 |
5 |
0 |
0 |
232 |
5 |
1 |
4 |
5 |
8 |
1 |
2 |
3 |
11 |
9 |
271 |
16 |
352 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
1 |
5 |
5 |
8 |
1 |
2 |
3 |
12 |
10 |
885 |
16 |
1414 |
16 |
0 |
0 |
35 |
5 |
0 |
0 |
232 |
5 |
1 |
5 |
5 |
8 |
1 |
2 |
3 |
13 |
11 |
271 |
16 |
357 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
2 |
8 |
5 |
8 |
1 |
2 |
3 |
14 |
12 |
885 |
16 |
1452 |
16 |
0 |
0 |
35 |
5 |
0 |
0 |
232 |
5 |
2 |
8 |
5 |
8 |
1 |
2 |
3 |
15 |
13 |
271 |
16 |
360 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
2 |
8 |
5 |
8 |
1 |
2 |
3 |
16 |
14 |
885 |
16 |
1462 |
16 |
0 |
0 |
34 |
5 |
0 |
0 |
234 |
5 |
2 |
8 |
5 |
8 |
1 |
2 |
3 |
17 |
15 |
271 |
16 |
365 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
2 |
9 |
5 |
8 |
1 |
2 |
3 |
18 |
16 |
885 |
16 |
1461 |
16 |
0 |
0 |
34 |
5 |
0 |
0 |
234 |
5 |
2 |
9 |
5 |
8 |
1 |
2 |
3 |
19 |
17 |
271 |
16 |
371 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
2 |
9 |
5 |
8 |
1 |
2 |
3 |
20 |
18 |
885 |
16 |
1458 |
16 |
0 |
0 |
34 |
5 |
0 |
0 |
234 |
5 |
2 |
9 |
5 |
8 |
1 |
2 |
3 |
21 |
19 |
271 |
16 |
375 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
2 |
10 |
5 |
8 |
1 |
2 |
3 |
22 |
20 |
885 |
16 |
1452 |
16 |
0 |
0 |
34 |
5 |
0 |
0 |
234 |
5 |
2 |
10 |
5 |
8 |
1 |
2 |
3 |
23 |
21 |
271 |
16 |
379 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
3 |
13 |
5 |
8 |
1 |
2 |
3 |
24 |
22 |
885 |
16 |
1436 |
16 |
0 |
0 |
34 |
5 |
0 |
0 |
234 |
5 |
2 |
11 |
5 |
8 |
1 |
2 |
3 |
25 |
23 |
271 |
16 |
382 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
3 |
14 |
5 |
8 |
1 |
2 |
3 |
26 |
24 |
2944 |
20 |
20560 |
20 |
0 |
0 |
43 |
5 |
0 |
0 |
1186 |
20 |
3 |
14 |
5 |
8 |
1 |
2 |
3 |
27 |
25 |
271 |
16 |
385 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
3 |
14 |
5 |
8 |
1 |
2 |
3 |
28 |
26 |
885 |
16 |
1408 |
16 |
0 |
0 |
34 |
5 |
0 |
0 |
234 |
5 |
3 |
14 |
5 |
8 |
1 |
2 |
3 |
29 |
27 |
271 |
16 |
387 |
16 |
0 |
0 |
3 |
4 |
0 |
0 |
0 |
0 |
3 |
15 |
5 |
8 |
1 |
2 |
3 |
30 |
28 |
885 |
16 |
1410 |
16 |
0 |
0 |
34 |
5 |
0 |
0 |
234 |
5 |
3 |
15 |
5 |
8 |
1 |
2 |
8.1.2.6. Iso-electronic sequence: 4¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
4 |
6 |
3 |
753 |
16 |
1386 |
16 |
0 |
0 |
74 |
6 |
0 |
0 |
48 |
5 |
0 |
0 |
10 |
8 |
8 |
2 |
4 |
7 |
4 |
778 |
16 |
1696 |
16 |
0 |
0 |
101 |
6 |
0 |
0 |
48 |
5 |
1 |
2 |
10 |
8 |
8 |
2 |
4 |
8 |
5 |
727 |
16 |
1121 |
16 |
0 |
0 |
79 |
6 |
0 |
0 |
48 |
5 |
3 |
7 |
10 |
8 |
8 |
2 |
4 |
9 |
6 |
578 |
16 |
953 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
2 |
5 |
10 |
8 |
4 |
2 |
4 |
10 |
7 |
753 |
16 |
1352 |
16 |
0 |
0 |
76 |
5 |
0 |
0 |
48 |
5 |
2 |
5 |
10 |
8 |
8 |
2 |
4 |
11 |
8 |
578 |
16 |
978 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
2 |
5 |
10 |
8 |
4 |
2 |
4 |
12 |
9 |
753 |
16 |
1456 |
16 |
0 |
0 |
77 |
5 |
0 |
0 |
48 |
5 |
2 |
5 |
10 |
8 |
8 |
2 |
4 |
13 |
10 |
578 |
16 |
1012 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
2 |
5 |
10 |
8 |
4 |
2 |
4 |
14 |
11 |
753 |
16 |
1491 |
16 |
0 |
0 |
76 |
5 |
0 |
0 |
48 |
5 |
3 |
8 |
10 |
8 |
8 |
2 |
4 |
15 |
12 |
578 |
16 |
1044 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
3 |
8 |
10 |
8 |
4 |
2 |
4 |
16 |
13 |
753 |
16 |
1540 |
16 |
0 |
0 |
77 |
5 |
0 |
0 |
48 |
5 |
3 |
9 |
10 |
8 |
8 |
2 |
4 |
17 |
14 |
578 |
16 |
1073 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
3 |
9 |
10 |
8 |
4 |
2 |
4 |
18 |
15 |
753 |
16 |
1543 |
16 |
0 |
0 |
76 |
5 |
0 |
0 |
48 |
5 |
3 |
10 |
10 |
8 |
8 |
2 |
4 |
19 |
16 |
577 |
16 |
1102 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
3 |
10 |
10 |
8 |
4 |
2 |
4 |
20 |
17 |
753 |
16 |
1563 |
16 |
0 |
0 |
76 |
5 |
0 |
0 |
48 |
5 |
4 |
11 |
10 |
8 |
8 |
2 |
4 |
21 |
18 |
578 |
16 |
1130 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
4 |
11 |
10 |
8 |
4 |
2 |
4 |
22 |
19 |
753 |
16 |
1577 |
16 |
0 |
0 |
76 |
5 |
0 |
0 |
48 |
5 |
4 |
12 |
10 |
8 |
8 |
2 |
4 |
23 |
20 |
578 |
16 |
1151 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
4 |
12 |
10 |
8 |
4 |
2 |
4 |
24 |
21 |
753 |
16 |
1584 |
16 |
0 |
0 |
76 |
5 |
0 |
0 |
48 |
5 |
5 |
13 |
10 |
8 |
8 |
2 |
4 |
25 |
22 |
578 |
16 |
1164 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
4 |
12 |
10 |
8 |
4 |
2 |
4 |
26 |
23 |
1191 |
16 |
3929 |
16 |
0 |
0 |
115 |
7 |
1 |
2 |
342 |
7 |
5 |
14 |
10 |
8 |
8 |
2 |
4 |
27 |
24 |
578 |
16 |
1175 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
5 |
14 |
10 |
8 |
4 |
2 |
4 |
28 |
25 |
753 |
16 |
1597 |
16 |
0 |
0 |
75 |
5 |
0 |
0 |
46 |
5 |
5 |
14 |
10 |
8 |
8 |
2 |
4 |
29 |
26 |
578 |
16 |
1185 |
16 |
0 |
0 |
14 |
3 |
0 |
0 |
0 |
0 |
5 |
14 |
10 |
8 |
4 |
2 |
4 |
30 |
27 |
753 |
16 |
1599 |
16 |
0 |
0 |
74 |
5 |
0 |
0 |
48 |
5 |
5 |
15 |
10 |
8 |
8 |
2 |
8.1.2.7. Iso-electronic sequence: 5¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
5 |
6 |
2 |
719 |
16 |
1844 |
16 |
0 |
0 |
20 |
5 |
0 |
0 |
249 |
5 |
0 |
0 |
5 |
8 |
16 |
2 |
5 |
7 |
3 |
973 |
16 |
2162 |
16 |
0 |
0 |
50 |
5 |
0 |
0 |
249 |
5 |
0 |
0 |
5 |
8 |
16 |
2 |
5 |
8 |
4 |
973 |
16 |
2228 |
16 |
0 |
0 |
46 |
5 |
0 |
0 |
249 |
5 |
1 |
2 |
5 |
8 |
16 |
2 |
5 |
9 |
5 |
744 |
16 |
1661 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
0 |
0 |
1 |
3 |
5 |
8 |
8 |
2 |
5 |
10 |
6 |
973 |
16 |
2258 |
16 |
0 |
0 |
24 |
5 |
0 |
0 |
249 |
5 |
1 |
3 |
5 |
8 |
16 |
2 |
5 |
11 |
7 |
744 |
16 |
1697 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
0 |
0 |
1 |
4 |
5 |
8 |
8 |
2 |
5 |
12 |
8 |
973 |
16 |
2222 |
16 |
0 |
0 |
25 |
5 |
0 |
0 |
249 |
5 |
1 |
4 |
5 |
8 |
16 |
2 |
5 |
13 |
9 |
744 |
16 |
1610 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
0 |
0 |
1 |
5 |
5 |
8 |
8 |
2 |
5 |
14 |
10 |
972 |
16 |
2238 |
16 |
0 |
0 |
23 |
5 |
0 |
0 |
249 |
5 |
1 |
5 |
5 |
7 |
16 |
2 |
5 |
15 |
11 |
744 |
16 |
1713 |
16 |
0 |
0 |
35 |
5 |
0 |
0 |
0 |
0 |
2 |
8 |
5 |
7 |
8 |
2 |
5 |
16 |
12 |
973 |
16 |
2277 |
16 |
0 |
0 |
25 |
5 |
0 |
0 |
249 |
5 |
2 |
8 |
5 |
7 |
16 |
2 |
5 |
17 |
13 |
744 |
16 |
1717 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
0 |
0 |
2 |
8 |
5 |
7 |
8 |
2 |
5 |
18 |
14 |
973 |
16 |
2262 |
16 |
0 |
0 |
23 |
5 |
0 |
0 |
249 |
5 |
2 |
8 |
5 |
7 |
16 |
2 |
5 |
19 |
15 |
744 |
16 |
1659 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
0 |
0 |
2 |
9 |
5 |
7 |
8 |
2 |
5 |
20 |
16 |
973 |
16 |
2228 |
16 |
0 |
0 |
25 |
5 |
0 |
0 |
249 |
5 |
2 |
9 |
5 |
7 |
16 |
2 |
5 |
21 |
17 |
744 |
16 |
1671 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
0 |
0 |
2 |
9 |
5 |
7 |
8 |
2 |
5 |
22 |
18 |
973 |
16 |
2244 |
16 |
0 |
0 |
24 |
5 |
0 |
0 |
249 |
5 |
2 |
9 |
5 |
7 |
16 |
2 |
5 |
23 |
19 |
744 |
16 |
1672 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
0 |
0 |
2 |
10 |
5 |
7 |
8 |
2 |
5 |
24 |
20 |
973 |
16 |
2211 |
16 |
0 |
0 |
24 |
5 |
0 |
0 |
249 |
5 |
2 |
10 |
5 |
7 |
16 |
2 |
5 |
25 |
21 |
972 |
16 |
1806 |
16 |
0 |
0 |
49 |
5 |
0 |
0 |
248 |
5 |
3 |
13 |
5 |
7 |
15 |
2 |
5 |
26 |
22 |
2034 |
16 |
11210 |
7 |
0 |
0 |
176 |
6 |
0 |
0 |
3212 |
7 |
2 |
11 |
5 |
7 |
16 |
2 |
5 |
27 |
23 |
973 |
16 |
1796 |
16 |
0 |
0 |
49 |
5 |
0 |
0 |
249 |
5 |
3 |
14 |
5 |
7 |
16 |
2 |
5 |
28 |
24 |
973 |
16 |
2170 |
16 |
0 |
0 |
23 |
5 |
0 |
0 |
249 |
5 |
3 |
14 |
5 |
7 |
16 |
2 |
5 |
29 |
25 |
744 |
16 |
1621 |
16 |
0 |
0 |
36 |
5 |
0 |
0 |
0 |
0 |
3 |
14 |
5 |
7 |
8 |
2 |
5 |
30 |
26 |
973 |
16 |
2136 |
16 |
0 |
0 |
49 |
5 |
0 |
0 |
249 |
5 |
3 |
14 |
5 |
7 |
16 |
2 |
8.1.2.8. Iso-electronic sequence: 6¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
6 |
6 |
1 |
1230 |
7 |
2395 |
5 |
0 |
0 |
163 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
6 |
0 |
0 |
6 |
7 |
2 |
1223 |
6 |
2412 |
5 |
0 |
0 |
193 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
4 |
5 |
20 |
2 |
6 |
8 |
3 |
1218 |
5 |
2429 |
5 |
0 |
0 |
201 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
10 |
5 |
1218 |
5 |
2428 |
5 |
0 |
0 |
203 |
5 |
0 |
0 |
1228 |
5 |
3 |
5 |
5 |
5 |
20 |
2 |
6 |
12 |
7 |
1218 |
5 |
2490 |
5 |
0 |
0 |
204 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
14 |
9 |
1218 |
5 |
2432 |
5 |
0 |
0 |
203 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
16 |
11 |
1218 |
5 |
2442 |
5 |
0 |
0 |
204 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
18 |
13 |
1218 |
5 |
2416 |
5 |
0 |
0 |
207 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
20 |
15 |
1218 |
5 |
2472 |
5 |
0 |
0 |
208 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
22 |
17 |
1218 |
5 |
2424 |
5 |
0 |
0 |
208 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
24 |
19 |
1218 |
5 |
2326 |
5 |
0 |
0 |
208 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
26 |
21 |
3098 |
7 |
19841 |
7 |
0 |
0 |
621 |
5 |
0 |
0 |
16980 |
7 |
0 |
0 |
9 |
7 |
20 |
2 |
6 |
28 |
23 |
1218 |
5 |
2265 |
5 |
0 |
0 |
208 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
6 |
30 |
25 |
1218 |
5 |
2238 |
5 |
0 |
0 |
208 |
5 |
0 |
0 |
1228 |
5 |
0 |
0 |
5 |
5 |
20 |
2 |
8.1.2.9. Iso-electronic sequence: 7¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
7 |
8 |
2 |
1706 |
10 |
7708 |
10 |
0 |
0 |
76 |
3 |
0 |
0 |
1690 |
4 |
0 |
0 |
5 |
8 |
16 |
2 |
7 |
10 |
4 |
2073 |
10 |
16329 |
10 |
0 |
0 |
34 |
3 |
0 |
0 |
2932 |
10 |
0 |
0 |
3 |
5 |
16 |
2 |
7 |
12 |
6 |
2073 |
10 |
15961 |
10 |
0 |
0 |
33 |
3 |
0 |
0 |
2432 |
10 |
0 |
0 |
3 |
5 |
16 |
2 |
7 |
14 |
8 |
2073 |
10 |
16480 |
10 |
0 |
0 |
32 |
3 |
0 |
0 |
2090 |
10 |
0 |
0 |
3 |
5 |
16 |
2 |
7 |
16 |
10 |
1798 |
10 |
7720 |
10 |
0 |
0 |
70 |
3 |
0 |
0 |
1880 |
4 |
0 |
0 |
3 |
5 |
16 |
2 |
7 |
18 |
12 |
1735 |
10 |
7244 |
10 |
0 |
0 |
72 |
3 |
0 |
0 |
1743 |
4 |
0 |
0 |
3 |
5 |
16 |
2 |
7 |
20 |
14 |
1712 |
10 |
7187 |
10 |
0 |
0 |
74 |
3 |
0 |
0 |
1698 |
4 |
0 |
0 |
3 |
5 |
16 |
2 |
7 |
22 |
16 |
1716 |
10 |
7448 |
10 |
0 |
0 |
79 |
3 |
0 |
0 |
1694 |
4 |
0 |
0 |
3 |
5 |
16 |
2 |
7 |
24 |
18 |
2073 |
10 |
15643 |
10 |
0 |
0 |
72 |
3 |
0 |
0 |
1692 |
4 |
0 |
0 |
3 |
5 |
16 |
2 |
7 |
26 |
20 |
3702 |
10 |
37884 |
10 |
0 |
0 |
658 |
10 |
0 |
0 |
4310 |
6 |
0 |
0 |
5 |
7 |
16 |
2 |
7 |
28 |
22 |
2073 |
10 |
15475 |
10 |
0 |
0 |
66 |
10 |
0 |
0 |
1692 |
4 |
0 |
0 |
3 |
5 |
16 |
2 |
8.1.2.10. Iso-electronic sequence: 8¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
8 |
12 |
5 |
554 |
4 |
1938 |
4 |
0 |
0 |
185 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
4 |
0 |
0 |
8 |
14 |
7 |
552 |
4 |
1988 |
4 |
0 |
0 |
184 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
4 |
0 |
0 |
8 |
16 |
9 |
554 |
4 |
2020 |
4 |
0 |
0 |
185 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
4 |
0 |
0 |
8 |
18 |
11 |
553 |
4 |
2056 |
4 |
0 |
0 |
184 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
4 |
0 |
0 |
8 |
20 |
13 |
554 |
4 |
2125 |
4 |
0 |
0 |
185 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
4 |
0 |
0 |
8 |
26 |
19 |
4217 |
10 |
25034 |
10 |
0 |
0 |
427 |
6 |
0 |
0 |
5858 |
6 |
0 |
0 |
17 |
8 |
0 |
0 |
8 |
28 |
21 |
2760 |
10 |
11582 |
10 |
0 |
0 |
157 |
5 |
0 |
0 |
1754 |
5 |
0 |
0 |
17 |
8 |
0 |
0 |
8.1.2.11. Iso-electronic sequence: 9¶
ii |
iz |
jz |
levels |
Arad |
Atwo |
El Col |
Pr col |
Aug |
CX |
RR |
II |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
N |
n(max) |
|||
9 |
12 |
4 |
500 |
5 |
1906 |
5 |
0 |
0 |
51 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
7 |
5 |
0 |
0 |
9 |
14 |
6 |
501 |
5 |
1938 |
5 |
0 |
0 |
52 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
7 |
5 |
0 |
0 |
9 |
16 |
8 |
501 |
5 |
1916 |
5 |
0 |
0 |
52 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
7 |
5 |
0 |
0 |
9 |
18 |
10 |
501 |
5 |
1912 |
5 |
0 |
0 |
52 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
7 |
5 |
0 |
0 |
9 |
20 |
12 |
662 |
6 |
1754 |
6 |
0 |
0 |
117 |
6 |
0 |
0 |
270 |
4 |
0 |
0 |
10 |
6 |
0 |
0 |
