User guide
1. Introduction
ADAMANT (Applicable DAta of Many-electron Atom eNergies and Transitions) is devoted to spectrosckopic data of atoms and ions (energy levels, radiative transition parameters (line strengths, oscillator strengths, transition probabilities). This database contains parameters, involving free-electrons, such as autoionization probabilities, electron-impact collision strengths, cross-sections and rates, dielectronic recombination rates that are needed in modeling both high temperature plasma (astrophysical, nuclear fusion) and low temperature plasma, such as planetary nebulae, working material of spectroscopic and medical devices. Huge amount of spectroscopic data for different atoms and ions has been produced so far. Unfortunately, it is rather complex task to apply these data for modeling purposes, because they are calculated in different approximations, with different computer code suites and atomic data accuracy. Therefore, it becomes difficult to match one set of data, e.g., energy levels, radiative transition probabilities, with another set of data involving free electrons, e.g. electron-impact excitation or ionization rates. In ADAMANT, the atomic data sets for specific atom were produced by using the same computer code suites, applying the same approximation for inclusion of relativistic and correlation effects. They are generated using identical multireference wavefunction basis. Such an approach to produce data significantly reduces workload for data application, making it possible an automatic data parsing in plasma modeling codes. ADAMANT database is constantly updated and extended with new results.
2. Data presented in ADAMANT
Spectroscopic parameters:
- energy levels,
- weights of the wavefunctions of levels,
- radiative transition wavelengths,
- weighted oscillator strengths,
- transition probabilities,
- level lifetimes,
- Lande factors,
- matrix element of a multipole transition operator,
- line strengths.
Electron-atom(ion) interaction parameters:
- electron-impact excitation cross sections, collision strengths and rates,
- electron-impact ionization cross sections, collision strengths and rates,
- level autoionization probabilities,
- dielectronic recombination rates.
In ADAMANT, a various approaches are used to produce the data (parameters). A general descrition of them can be found below and in the data base as 'info'.
3 The steps to search and obtain data
ADAMANT opens with Periodic table with differently colored boxes of chemical elements. The yellow color indicates the available data sets. The green color shows that the data are absent.
Clicking on the element opens a table consisting of a number of columns. The first column is for the degree of ionization (zero indicates neutral atom). The next columns are for the data calculated in different approximations. The abbreviations QRHF and DFS mean Quasirelativistic-Hartree-Fock and Dirac-Fock-Slater, respectively. CI indicates that correlation effects were included by using configuration interaction method.
There are two links in each column. The links 'data' and 'info' opens a table for the spectroscopic parameters and the description of the methohs and approaches used to obtain the presented parameters, respectively. The set of spectroscopy parameters can be reached by clicking on the link 'data'. The window with a number of boxes indicating the sets of spectroscopic parameters opens.
Another possibility to obtain data is the click on the triangles in the middle of the field. The available data from the isoelectronic sequences be obtained by clicking on the yellow boxes.3.1 Energy level parameters
The values of the energy levels can be reached by clicking on the box 'Energy levels'. In the opened window the user can change the atom or ion, choose the ionization degree, approach used for calculation, output type, interval for energy values, and units. The definitions used in the tables of output data are explained Table 1. In this table also an exhaustive explanations of some other notations used for energy levels are presented.
Table 1: The notations used for energy levels
| Notations used in ADAMANT | Explanation of notations in ADAMANT |
|---|---|
| nlN | The shell $nl^{N}$ of $N$ equivalent electrons |
| nljN, nl+N, nl$-$N | The subshell $nl\,_{j}^{N}$ (or $nl\,_{\pm}^{N}$, when $j=l\pm1/2$) . nl+N (nl$-$N) is used when j=l+1/2 (j=l$-$1/2) |
| Term | L S denotes a term $^{2S+1}\mathrm{L}$ |
| Level | L S J denotes a level $^{2S+1}\mathrm{L}$$_{J}$ |
| nl(N) 2S+1 L gama J | Determines $nl^{N}$$\,^{2S+1}\mathrm{_{\gamma}L}_{J}$. Gama ($\gamma$ ) denotes a seniority number. Total angular momentum J is given in a separate column |
| nljNJ, nl+N(2J), nl--N(2J) | Determines $nl\,_{j}^{N}\,\gamma\, J\,$ ($nl\,_{\pm}^{N}$$\,\gamma\, J$) |
| Configuration | n1l1N1 n2l2N2 ... is a label of level associated with the non-relativistic configuration $n_{1}l_{1}^{N_{1}}\, n_{2}l_{2}^{N_{2}}...$. E.g., for C-like elements, the configuration $1s^{2}\,2s^{2}\,2p^{2}$is denoted as 2p2. Closed shells 1s2 and 2s2 are not listed |
| Wavefunction | In intermediate coupling, a wavefunction of a level is given by $\Psi(\alpha J)=\sum_{i} c_{i}^{\alpha} \Phi_{i}(C_{i}\, J).$ $\Phi_{i}(C_{i}J)$ is a basis function. The closed shells in $C_{i}$ are omitted |
| Level label (LS-coupling) | n1l1(N1) 2S1+1 L1 $\gamma_{1}$.n2l2(N2) 2S2+1 L2 $\gamma_{2}$\_2S'+1 L' .n3l3(N3)$\gamma_{3}$... L S determines the label of level for $\scriptsize{ CJ\equiv {n_1} {l_1}^{N_1} \, {n_2} {l_2}^{N_2}\,{n_3} {l_3}^{N_3}...\,\,_{\gamma_1}^{2S_1+1}{L_1}\,\,_{\gamma_2}^{2S_2+1}{L_2}\,\left(\,\,^{2S'+1}L'\right)\,\,_{\gamma_3}^{2S_3+1}{L_3}\,....^{2S+1}\mathrm{L}_J }$ in LS-coupling. When N=1, the notation of term 2S+1 L $\gamma$ is omitted. Total angular momentum J is placed in separate column. For example, 3s(1).3p(4)3P2\_4P, J=3/2 denotes $\scriptsize{ CJ\equiv3s\,3p^{4}\,{}_{1}^{2}S\,\,_{2}^{3}P\,\,^{4}P_{3/2} }$ |
| Level label (jj-coupling) | n1l1$\pm$N1 (2J1) 2J1 n2l2$\pm$N2 (2J2) 2J' n3l3$\pm$N3 (2J3) 2J''...2J determines the label of a level for $\scriptsize{CJ\equiv n_{1}l_{\pm}^{N_{1}}\, n_{2}l_{\pm}^{N_{2}}\, n_{3}l_{\pm}^{N_{3}}\,\gamma_{1\,}J_{1}\,\gamma_{2}\, J_{2}\,\left(\, J'\right)\,\gamma_{3}J_{3}\,(J'')...J}$ in jj-coupling. The number immediately after the parentheses indicate the 2J value when all preceding shells are coupled. If it is not necessary, the symbol $\gamma_{i}$ is suppressed in $CJ$. Only open subshells are given. For example, 2s+1(1)1 2p+2(4)5 3d-1(3)4 denotes $\scriptsize{ CJ\equiv 2s_{+}(2p_{+}^{2}(2))(5/2)(3d_{-}(3/2))2}$ |
| Contributions | Squared expansion coefficients $c_{i}^{\alpha}$ of $\Psi(\,\alpha\, J)$ are expressed as percentages. Only the leading contributions are presented. For example, in ADAMANT notations the expansion of $\Psi(\,\alpha\,5/2)$ looks as 81 3s.3p(4)3P2\_4P 13 3p(2)3P2.3d\_4P . $c_{i}^{\alpha}$ gives 81% (${\scriptstyle \mathsf{{\displaystyle \Phi}_{i}}}(3s\,3p^{4}\,{}_{1}^{2}S\,{}_{2}^{3}P\,\,^{4}P_{5/2}\,)$ ), while $c_{j}^{\alpha}$ gives 13% (${\scriptstyle \mathsf{{\displaystyle \Phi_{j}}}}(3p^{2}\,3d\,{}_{2}^{3}P\,{}_{1}^{2}D\,^{4}P_{5/2})$. Total angular momentum $J=5/2$ is placed in separate column. In the case of N=1, the notation of N is omitted. |
| N | Level index. Positive integer number assigned to an energy level and the corresponding wavefunction for a task considered |
| E0 | The energy level of the lowest level |
| E | The energy of the level for $\Psi(\,\alpha\, J)$ calculated from E0 |
| J | The total (final) angular momentum J of $\Psi(\,\alpha\, J)$ |
| p | The parity of $\Psi(\,\alpha\, J)$. $p=o$ denotes an odd (ODD) parity. $p=e$ denotes an even (EVEN) parity |
| T | Radiative lifetime $\tau$ of a level |
| g | The Lande factor $g_{\alpha\, J}$ of a level $J$ |
3.2 Radiative transitions
The explanations of notations used in the output files is presented in Table 2.
Table 2. The notations used for the radiative transitions.
| Notations used in ADAMANT | Explanation of notations |
|---|---|
| Type | Type of a radiative transition: EK or MK. EK (MK) is electric (magnetic) transition of the multipolity K. For example, E1 denotes electric dipole transition, while M2 denotes magnetic quadrupole transition |
| Ni | The level index of initial (upper) level |
| Ji | The total angular momentum J of an initial (upper) level |
| Nf | The level index of final (lower) level |
| Jf | The total angular momentum J of a final (upper) level |
| Wavelength | The transition wavelength$\lambda_{i\rightarrow f}$$\,$between the initial Ni and final Nf levels. Wavelength (in vacuum) is given in selected units. |
| S | The transition line strength $S_{i\rightarrow f}^{EK,MK}$ in selected units, e.g. a.u. |
| M | M denotes $M_{i\rightarrow j}^{EK,MK}$ transition matrix element of $EK,\, MK$ transitions operator |
| gf | The weighted oscillator strength $g_{i}f_{i\rightarrow f}^{EK,MK}=g_{j}f_{f\rightarrow i}^{EK,MK}$. $gf=(2K+1)^{-1}\omega\,(\alpha\omega)^{2K-2}S\,,$where $\omega=E_{i}-E_{f}$ in Hatree a.u. and $\alpha$ is fine structure constant. |
| A | The radiative transition probability $A_{i\rightarrow f}^{EK,MK}(1/s)$. In a.u. $A=2\,\alpha^{3}\,\omega^{2}\,$ f |
3.3 Electron-impact excitation
Three boxes titled by 'Electron-impact excitation collision strenght', 'Electron-impact excitation cross section', and 'Electron-impact excitation rates' are devoted to the parameters describing the excitation of atoms by electrons process. The explanations of the notations are given in Table 3.
Table 3. The notations used for electron-impact excitations (EIE).
| Notations used in ADAMANT | Explanation of notations |
|---|---|
| CS | The electron-impact excitation collisions strength $\Omega_{i\rightarrow j}$ |
| sigma | The electron-impact excitation cross section $\sigma_{i\rightarrow f}$ in Mb |
| vsigma | The electron-impact excitation collision rate $\lt v\sigma \gt_{i\rightarrow j}$ in cm$^3$/s |
| ECS | The effective excitation collision strength $\upsilon_{i\rightarrow j}$ |
| Temperatures | Electron temperature T in eV |
| Eex | The excitation energy $\Delta E_{i\rightarrow j}$ from Ni to Nf. Eex is given in eV |
| Eejected | The ejected electron energy in eV |
| Eel | The electron impact (incident) energy Eel=Ki*Eex (Ki is a numerical coefficient) or Eel=E+Eejected. E is given in eV |
3.4 Electron-impact ionization
Three boxes titled by 'Electron-impact excitation ionization strenght', 'Electron-impact ionization cross section', and 'Electron-impact ionization rates' helps to obtain the parameters describing the ionization of atoms by electrons. The explanations of the notations are given in Table 4.
Table 4. The notations used for electron-impact ionization (EI).
| Notations used in ADAMANT | Explanation of notations |
|---|---|
| IS | The electron-impact ionization strength $\Omega$ |
| sigma | The electron-impact ionization cross section $\sigma$ in Mb |
| vsigma | The electron-impact ionization rate $\lt v\sigma \gt $ in cm$^3$/s |
| Temperatures | Electron temperature T in eV |
| Ei | The ionization energy $\Delta E_{i\rightarrow j}$. E is given in eV |
| E2 | The ejected electron energy in eV |
| E1 | The electron impact (incident) energy E1=Ei+E2 E2 is given in eV |
3.5 Level autoionization
For the autoionization probabilities, the explanations of the notations are given in Table 5.
Table 5: The notations of level autoionization (AI) quantities.
| Notations used in ADAMANT | Explanation of notations |
|---|---|
| A | Autoionization transition probability $A_{i\rightarrow f}(1/s)$ from the initial level Ni |
| Ni | The level index of initial (upper) level |
| Ji | The total angular momentum J of an initial (upper) level |
| Nf | The level index of final (lower) level |
| Jf | The total angular momentum J of a final (upper) level |
3.6 Dielectronic recombination
The dielectronic recombination rates are presented in section ``Dielectronic recombination''. The explanation of the notations are given in Table 6.
Table 6: The notations of level dielectronic recombination rates
| Notations used in ADAMANT | Explanation of notations in ADAMANT |
|---|---|
| DR | Dielectronic recombination rate to the level Nf in cm$^3/$s |
| Nf | The level index of a final level |
| Jf | The total angular momentum J of a final level |