.. SPDX-FileCopyrightText: 1992-2026 NWO-I/SRON Space Research Organisation Netherlands .. .. SPDX-License-Identifier: CC-BY-4.0 .. _chap:plasmamodel: Plasma model in SPEX 3.0 ======================== 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 :ref:`sect:newsequences` 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. .. _sect:newsequences: 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: :math:`N`, the number of entries we have (e.g., number of energy levels or transition rates), and :math:`n_{\mathrm max}` the maximum principal quantum number for wich we use data for that ion and process. Note that :math:`n_{\mathrm max}` 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) 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 | +----+----+----+--------+--------+------+--------+------+--------+--------+--------+--------+--------+-----+--------+----+--------+----+--------+----+--------+ 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 | +----+----+----+--------+--------+------+--------+------+--------+--------+--------+--------+--------+-----+--------+----+--------+----+--------+----+--------+ 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 | +----+----+----+--------+--------+-------+--------+------+--------+--------+--------+--------+--------+------+--------+----+--------+----+--------+----+--------+ 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 | +----+----+----+--------+--------+------+--------+------+--------+--------+--------+--------+--------+-----+--------+----+--------+----+--------+----+--------+ 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 | +----+----+----+--------+--------+-------+--------+------+--------+--------+--------+--------+--------+------+--------+----+--------+----+--------+----+--------+ 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 | +----+----+----+--------+--------+-------+--------+------+--------+--------+--------+--------+--------+-------+--------+----+--------+----+--------+----+--------+ 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 | +----+----+----+--------+--------+-------+--------+------+--------+--------+--------+--------+--------+------+--------+----+--------+----+--------+----+--------+ 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 | +----+----+----+--------+--------+-------+--------+------+--------+--------+--------+--------+--------+------+--------+----+--------+----+--------+----+--------+ 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 | +----+----+----+--------+--------+------+--------+------+--------+--------+--------+--------+--------+-----+--------+----+--------+----+--------+----+--------+