# AtomPy: An Open Atomic Data Curation Environment for Astrophysical Applications

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## Abstract

**:**

## 1. Introduction

## 2. Virtual Research Communities

## 3. Community-Driven Data Curation

**Figure 2.**Three-level data curation model proposed for e-Science specifications. Image source: Figure 10 of [58].

## 4. AtomPy

#### 4.1. AtomPy Spreadsheet Structure

`elements`—lists the names, symbols and atomic weights for chemical elements indexed with the atomic number $Z\le 118$;

`ions`—lists the symbol, ground electronic configuration, ground spectroscopic term, total angular momentum (J) and ionization potential (in eV) for each ionic species indexed with the atomic number and electron number tuple $(Z,N)$, where $1\le Z\le 110$ and $1\le N\le Z$;

`isotopes`—lists symbols, atomic weights and fractions for isotopes indexed with the atomic number and mass number tuple $(Z,M)$ for $Z\le 118$.

`ions`sheet where it may be appreciated that, for each ionization potential, its value and uncertainty are both given. The source reference, in this case nist, is also specified and hyperlinked.

`zz_nn.Xi`, where

`zz`and

`nn`are two-character strings respectively associated to the atomic and electron numbers.

`X`denotes the spreadsheets included in this workbook:

`E`—contains the level energies of the atomic model;`A`—contains the radiative transition probabilities (A-values) and, in some cases, f-values;`O`—lists energy tabulations of collision strengths;`U`—lists temperature tabulations of effective collision strengths.

`i=0,1...`where

`i=0`is the default); for example, when $LS$ and intermediate-coupling atomic models are both considered or when allowed and forbidden transitions are analyzed separately. Each ionic workbook is displayed in both the

`IsonuclearSequences/zz`and

`IsoelectronicSequences/nn`subdirectories of AtomPy. An important point here is the selected atomic model for each species that is mainly determined by astrophysical requirements, and is limited to a set of levels for which both radiative and collisional data have been reported.

`02_02`. In Figure 4 we show: (i) the

`02_02.E0`spreadsheet listing level energies for a 49-level atomic model and (ii)

`02_02.A0`with A-values for transitions with upper level $k\le 7$. The key advantage of AtomPy in data evaluation with respect to regular atomic databases is that for each atomic attribute—e.g., level energies $E(Z,N,i)$ or radiative transition probabilities $A(Z,N,k,i)$ (see indexing in

`E0`and

`A0`)—it displays side by side values from several sources, which can then be statistically or graphically compared using the versatile functions of spreadsheets and DataFrames. Furthermore, the general policy is not to replace older datasets as new ones appear, thus contributing to data preservation for future reuse.

**Figure 3.**Google reference sheet

`ions`of

`AtomPy`listing NIST ionization potentials (IP) for elements with $Z\le 110$ (only those with $Z\le 8$ are displayed). Note that IP uncertainties are also included.

**Figure 4.**Workbook

`02_02`for the $(2,2)$ ionic system (i.e., He i) showing the

`02_02.E0`sheet with a 49-level atomic model (only the first 15 levels are depicted) and the

`02_02.A0`sheet with A-values for transitions with upper level $k\le 7$.

#### 4.2. Google Sheets

- Simultaneous distributed editing;
- URL access;
- Dynamic embedding in websites and blogs.

#### 4.3. Pandas DataFrames

#### 4.4. API

Data from theIn [1]: import atompyInitializing AtomPy...AtomPy ready!

`elements`,

`ions`and

`isotopes`reference sheets (see Section 4.1) can be addressed with commands of the type

to list the name and symbol of the chemical element with atomic number $Z=2$ , or its atomic weightIn [2]: atompy.element(2)Out[2]: ('Helium', 'He')

In [3]: atompy.elementaw(2)Out[3]: (4.002602, 2e-06)

`ions`would provide

the latter tuple giving its ionization potential.In [4]: atompy.ion(2,2)Out[4]: (′He I′, ′1s2′, ′1Se′, 0.0)In [5]: atompy.ionip(2,2)Out[5]: (24.587387936, 2.5e-08)

`02_02`, for instance, can be downloaded to a local DataFrame (

`df`) with the command

In [6]: df=atompy.getdata(2,2)Retrieving workbook: 02_02Finished workbook: 02_02Ion: Z = 02, N = 02E0: Fine-Structure Energy Levels for He IE1: LS Energy Terms for He IA0: A-values for fine-structure transitions in He IA1: A-values for LS Transitions in He IIU0: Effective Collision Strengths for LS Transitions of He INo O sheets found...

`df`DataFrame now contains data for four spreadsheets, namely

`E0`,

`A0`,

`A1`and

`U0`. Attributes for the first 10 levels of

`E0`, for example, can be listed with the Pandas command

Each level in theIn [7]: df.E(0)[:10]Out[7]:Conf Term 2S+1 L Pi J E_S1 E_S2Z N i2 2 1 1s2 1S 1 0 0 0 0.000000 0.02 1s.2s 3S 3 0 0 1 159855.974330 159831.03 1s.2s 1S 1 0 0 0 166277.440141 166259.04 1s.2p 3P* 3 1 1 2 169086.766472 169064.95 1s.2p 3P* 3 1 1 1 169086.842898 169065.06 1s.2p 3P* 3 1 1 0 169087.830813 169066.07 1s.2p 1P* 1 1 1 1 171134.896946 171113.88 1s.3s 3S 3 0 0 1 183236.791700 183216.99 1s.3s 1S 1 0 0 0 184864.829320 184848.010 1s.3p 3P* 3 1 1 2 185564.561920 185546.5

`E0`DataFrame is indexed with the tuple $(Z,N,i)$ , which allows further data selection; for instance, the energies of the first five levels from source S1 (spectroscopic values) are listed with the command

In [8]: df.E(0).ix[(2,2,1):(2,2,5)][′E_S1′]Out[8]:Z N i2 2 1 0.0000002 159855.9743303 166277.4401414 169086.7664725 169086.842898Name: E_S1, dtype: float64

In [9]: df.A(0).ix[(2,2,1):(2,2,7)][′AE1_S5′]Out[9]:Z N k i2 2 2 1 NaN3 1 NaN4 1 NaN2 1.021300e+075 1 1.775780e+022 1.021300e+073 2.689700e-026 2 1.021300e+077 1 1.798320e+092 1.548935e+003 1.974850e+06Name: AE1_S5, dtype: float64

`NaN`. Furthermore, the metadata for the source references in

`A0`can also be obtained with a similar command

In [10]: df.A(0,sources=True)S4: comprehensive tabulation by Wiese, W.L.; Fuhr, J.R.http://adsabs.harvard.edu/abs/2009JPCRD..38..565WS2: Atomic structure calculations using MCHF and BSR. Zatsarinny, O.;Froese Fischer, C.http://adsabs.harvard.edu/abs/2009CoPhC.180.2041ZS5: Relativistic calculations by Morton, D.C.; Drake, G.W.F.http://adsabs.harvard.edu/abs/2011PhRvA..83d2503Mand Morton, D.C.; Moffatt, P.; Drake, G.W.F.http://adsabs.harvard.edu/abs/2011CaJPh..89..129MS8: Calculation with correlated variational wave functions of the Hylleraastype. Drake, G.W.F.http://adsabs.harvard.edu/abs/1986PhRvA..34.2871DLevel indices relative to E0

#### 4.5. IPython Notebook

`myfile.ipynb`, say) can be imported and run locally in the IPython shell with the command

or displayed as a static web page with the IPython Notebook Viewer [76].ipython notebook myfile

#### 4.6. GitHub

#### 4.7. API Installation

`pip`[80] command

that resolves further module dependencies; alternatively, it can also be accessed from the GitHub repository withpip install atompy

AtomPy updating requires uninstalling the current version on the user local disk before proceeding with the above commands, that ispip install git+https://github.com/AtomPy/AtomPy

pip uninstall atompy

which should take care of all the prerequisites for the Notebook option.pip install ipython

## 5. Radiative Data Assessment

#### 5.1. H Sequence

`IsoelectronicSequences/01`subdirectory.

Ion | $A(Z,N)$ | E1 | E2 | E3 | M1 | M2 | M3 |
---|---|---|---|---|---|---|---|

H i | $A(1,1)$ | 6 | 6 | 6 | 500 | 6 | 6 |

He ii | $A(2,1)$ | 4 | 2 | 2 | 90 | 2 | 2 |

Li iii | $A(3,1)$ | 5 | 1 | 2 | 85 | 2 | 2 |

Be iv | $A(4,1)$ | 3 | 1 | 2 | 62 | 1 | 1 |

B v | $A(5,1)$ | 2 | 1 | 2 | 13 | 1 | 1 |

C vi | $A(6,1)$ | 2 | 1 | 1 | 12 | 1 | 1 |

N vii | $A(7,1)$ | 1 | 1 | 1 | 3 | 1 | 1 |

**Table 2.**Problematic A-values (s${}^{-1}$) for E3, M2 and M1 forbidden transitions in H i. jb: standard reference [100,101]. grasp: computed with grasp [98]. norad: computed with superstructure [96] and listed in the norad database. autos: computed with autostructure in the present work. Note: $a\mathrm{E}\pm n\equiv a\times {10}^{\pm b}$.

$A(Z,N,k,i)$ | jb | grasp | norad | autos |
---|---|---|---|---|

$A{(1,1,{3\mathrm{d}}_{5/2},{2\mathrm{p}}_{1/2})}_{\mathrm{E}3}$ | 1.2575E−05 | 1.2582E−05 | 1.96E−05 | 1.258E−05 |

$A{(1,1,{3\mathrm{d}}_{5/2},{2\mathrm{p}}_{1/2})}_{\mathrm{M}2}$ | 3.9297E−05 | 3.9319E−05 | 1.57E−04 | 3.932E−05 |

$A{(1,1,{4\mathrm{p}}_{1/2},{3\mathrm{d}}_{5/2})}_{\mathrm{M}2}$ | 4.6585E−08 | 4.6610E−08 | 1.87E−07 | 4.661E−08 |

$A{(1,1,{4\mathrm{d}}_{5/2},{2\mathrm{p}}_{1/2})}_{\mathrm{M}2}$ | 2.2848E−05 | 2.2861E−05 | 9.14E−05 | 2.286E−05 |

$A{(1,1,{4\mathrm{d}}_{5/2},{3\mathrm{p}}_{1/2})}_{\mathrm{M}2}$ | 5.2400E−07 | 5.2429E−07 | 2.10E−06 | 5.243E−07 |

$A{(1,1,{4\mathrm{f}}_{7/2},{3\mathrm{d}}_{3/2})}_{\mathrm{M}2}$ | 1.2319E−06 | 1.2326E−06 | 4.93E−06 | 1.233E−06 |

$A{(1,1,{3\mathrm{p}}_{1/2},{2\mathrm{p}}_{3/2})}_{\mathrm{M}1}$ | 1.2886E−08 | 1.2897E−08 | 1.42E−08 | 1.416E−08 |

$A{(1,1,{3\mathrm{d}}_{3/2},{1\mathrm{s}}_{1/2})}_{\mathrm{M}1}$ | 6.9292E−09 | 6.7907E−09 | 1.93E−08 | 1.036E−08 |

$A{(1,1,{3\mathrm{d}}_{3/2},{2\mathrm{s}}_{1/2})}_{\mathrm{M}1}$ | 1.0479E−10 | 1.0501E−10 | 2.02E−10 | 1.339E−10 |

$A{(1,1,{3\mathrm{p}}_{3/2},{2\mathrm{p}}_{1/2})}_{\mathrm{M}1}$ | 3.3801E−09 | 3.3816E−09 | 2.95E−09 | 2.949E−09 |

$A{(1,1,{4\mathrm{p}}_{1/2},{2\mathrm{p}}_{3/2})}_{\mathrm{M}1}$ | 7.5163E−09 | 7.5361E−09 | 8.45E−09 | 8.452E−09 |

$A{(1,1,{4\mathrm{p}}_{1/2},{3\mathrm{p}}_{3/2})}_{\mathrm{M}1}$ | 5.3686E−10 | 5.3726E−10 | 5.58E−10 | 5.580E−10 |

$A{(1,1,{4\mathrm{s}}_{1/2},{1\mathrm{s}}_{1/2})}_{\mathrm{M}1}$ | 5.3029E−07 | 5.1953E−07 | 5.32E−07 | 5.305E−07 |

$A{(1,1,{4\mathrm{d}}_{3/2},{1\mathrm{s}}_{1/2})}_{\mathrm{M}1}$ | 4.3213E−09 | 4.8205E−09 | 1.23E−08 | 6.533E−09 |

$A{(1,1,{4\mathrm{d}}_{3/2},{2\mathrm{s}}_{1/2})}_{\mathrm{M}1}$ | 6.0462E−11 | 6.1245E−11 | 1.31E−10 | 8.091E−11 |

$A{(1,1,{4\mathrm{d}}_{3/2},{3\mathrm{s}}_{1/2})}_{\mathrm{M}1}$ | 5.3957E−13 | 5.4042E−13 | 8.59E−13 | 6.385E−13 |

$A{(1,1,{4\mathrm{d}}_{3/2},{3\mathrm{d}}_{5/2})}_{\mathrm{M}1}$ | 5.4500E−11 | 5.4461E−11 | 5.95E−11 | 5.948E−11 |

$A{(1,1,{4\mathrm{p}}_{3/2},{2\mathrm{p}}_{1/2})}_{\mathrm{M}1}$ | 1.7386E−09 | 1.7351E−09 | 1.45E−09 | 1.446E−09 |

$A{(1,1,{4\mathrm{p}}_{3/2},{3\mathrm{p}}_{1/2})}_{\mathrm{M}1}$ | 1.9206E−10 | 1.9206E−10 | 1.83E−10 | 1.833E−10 |

$A{(1,1,{4\mathrm{d}}_{5/2},{3\mathrm{d}}_{3/2})}_{\mathrm{M}1}$ | 1.4421E−11 | 1.4318E−11 | 1.23E−11 | 1.232E−11 |

$A{(1,1,{4\mathrm{f}}_{5/2},{2\mathrm{p}}_{3/2})}_{\mathrm{M}1}$ | 4.3994E−11 | 4.3919E−11 | 9.17E−11 | 5.231E−11 |

$A{(1,1,{4\mathrm{f}}_{5/2},{3\mathrm{p}}_{3/2})}_{\mathrm{M}1}$ | 1.4489E−12 | 1.4493E−12 | 2.40E−12 | 1.620E−12 |

#### 5.2. He Sequence

`02_02`AtomPy workbook, the IC energies computed with the combined R-matrix–mchf method in [118] for He i are on average $-18\pm 2$ cm${}^{-1}$ from those listed in the nist tables. Also, their A-values for E1 transitions are within 2% of the standard [88] except for intercombination transitions with very small rates, $logA{(2,2,k,i)}_{\mathrm{E}1}<3$, for which the differences are somewhat larger ($\lesssim 10$%); e.g., $A{(2,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}},2{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})}_{\mathrm{E}1}$, $A{(2,2,2{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}},2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})}_{\mathrm{E}1}$, $A{(2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{D}}_{2},3{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}})}_{\mathrm{E}1}$ and $A{(2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}},4{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{D}}_{2})}_{\mathrm{E}1}$. In general, this may be regarded as outstanding agreement.

**Table 3.**A-values (s${}^{-1}$) for E1 transitions in He i that show discrepancies larger than 10% with respect to the critical compilation of [88] (wf). norad: rates from the norad database computed with the R-matrix method in a 10-state approximation [95]. op: results from the OP [129] listed in TOPbase. Wavelengths are determined from the nist term values.

$A(Z,N,k,i)$ | λ (Å) | wf | norad | op |
---|---|---|---|---|

$A(2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}^{\mathrm{o}},4{\phantom{\rule{0.166667em}{0ex}}}^{1}\mathrm{D})$ | 2.1619E+06 | 5.6862E+01 | 5.706E+01 | 6.73E+01 |

$A(2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}^{\mathrm{o}},5{\phantom{\rule{0.166667em}{0ex}}}^{1}\mathrm{D})$ | 4.1370E+06 | 2.2222E+01 | 2.230E+01 | 2.71E+01 |

$A(2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}^{\mathrm{o}},5{\phantom{\rule{0.166667em}{0ex}}}^{1}\mathrm{S})$ | 3.5849E+05 | 1.8738E+04 | 1.890E+04 | 1.65E+04 |

$A(2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}^{\mathrm{o}},4{\phantom{\rule{0.166667em}{0ex}}}^{1}\mathrm{S})$ | 1.8100E+05 | 5.8221E+04 | 5.876E+04 | 5.10E+04 |

$A(2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{F}}^{\mathrm{o}},4{\phantom{\rule{0.166667em}{0ex}}}^{3}\mathrm{D})$ | 4.0377E+04 | 2.3336E+06 | 2.586E+06 | |

$A(2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{3}\mathrm{D},4{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{F}}^{\mathrm{o}})$ | 4.0564E+04 | 4.5778E+04 | 5.153E+04 | |

$A(2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{F}}^{\mathrm{o}},3{\phantom{\rule{0.166667em}{0ex}}}^{3}\mathrm{D})$ | 1.8691E+04 | 1.2220E+07 | 1.384E+07 | |

$A(2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{F}}^{\mathrm{o}},4{\phantom{\rule{0.166667em}{0ex}}}^{1}\mathrm{D})$ | 4.0409E+04 | 1.8294E+06 | 2.587E+06 | |

$A(2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}\mathrm{D},4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{F}}^{\mathrm{o}})$ | 4.0545E+04 | 3.3200E+04 | 5.113E+04 | |

$A(2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{F}}^{\mathrm{o}},3{\phantom{\rule{0.166667em}{0ex}}}^{1}\mathrm{D})$ | 1.8702E+04 | 8.9780E+06 | 1.383E+07 |

`06_02, 07_02`and

`08_02`workbooks). norad and OP term energies for these systems are again found to be on average below those in the nist spectroscopic database: for the former, $\langle \text{\Delta}E(6,2)\rangle =-6400\pm 300$, $\langle \text{\Delta}E(7,2)\rangle =-7600\pm 500$ and $\langle \text{\Delta}E(8,2)\rangle =-8700\pm 700$ cm${}^{-1}$ in comparison with the slightly better OP differences of $\langle \text{\Delta}E(6,2)\rangle =-4500\pm 200$, $\langle \text{\Delta}E(7,2)\rangle =-5500\pm 400$ and $\langle \text{\Delta}E(8,2)\rangle =-6600\pm 600$ cm${}^{-1}$ resulting from the more effective target approximations. In general, the norad and OP $A{(6-8,2)}_{\mathrm{E}1}$ values are well within 5% of the standard, except for $\text{\Delta}n=0$ transitions with very small $\text{\Delta}E(Z,N,k,i)$ that undergo strong cancellation effects.

**Figure 5.**Level energy differences in Ne ix between the theoretical values of [121] and the experimental data listed in the nist database (v5.1). Such differences are mostly bound to the interval $\pm 1000$ cm${}^{-1}$ except for six levels whose spectroscopic positions are open for a revision.

**Table 4.**Comparison of the $A(2-10,2,3{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{D}}_{2},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ (s${}^{-1}$) electric quadrupole (E2) rate showing the incorrectly assigned data in the nist database (v5.1) for $6\le Z\le 8$. GV: [108] computed with the mchf method. CT: [112] using explicitly correlated functions. SJS: [121] computed with a relativistic CI method. Excellent agreement is otherwise found among the computed A-values. Wavelengths are determined from the nist level energies.

Z | λ (Å) | nist | gv | ct | sjs |
---|---|---|---|---|---|

2 | 5.3733E+02 | 1.2990E+03 | 1.293E+03 | 1.299E+03 | |

3 | 1.7817E+02 | 8.2665E+04 | 8.254E+04 | 8.267E+04 | |

4 | 8.8381E+01 | 9.2668E+05 | 9.253E+05 | 9.267E+05 | |

5 | 5.2720E+01 | 5.1458E+06 | 5.139E+06 | 5.146E+06 | |

6 | 3.4995E+01 | 1.2960E+07 | 1.944E+07 | 1.946E+07 | 1.936E+07 |

7 | 2.4914E+01 | 3.8470E+07 | 5.770E+07 | 5.775E+07 | 5.715E+07 |

8 | 1.8638E+01 | 9.6560E+07 | 1.448E+08 | 1.450E+08 | 1.423E+08 |

**Table 5.**Average differences (${10}^{3}$ cm${}^{-1}$) between the spectroscopic level energies of the nist database (v5.1) and those computed with grasp (${}^{a}$ [124], ${}^{b}$ [123], ${}^{c}$ [122], ${}^{d}$ [125]) and superstructure (

^{e}[128], ${}^{f}$ [126], ${}^{g}$ [127]). grasp1: excludes Breit and QED effects. grasp2: includes Breit and QED effects. The quantity in brackets gives the standard error.

$\langle \text{\Delta}E(Z,N)\rangle $ | grasp1 | grasp2 | superstructure |
---|---|---|---|

$\langle \text{\Delta}E(3,2)\rangle $ | $-23.8\left(7\right)$ ${}^{a}$ | $-23.9\left(7\right)$ ${}^{a}$ | |

$\langle \text{\Delta}E(4,2)\rangle $ | $-23.0\left(8\right)$ ${}^{a}$ | $-22.5\left(8\right)$ ${}^{a}$ | |

$\langle \text{\Delta}E(5,2)\rangle $ | $-22.4\left(8\right)$ ${}^{a}$ | $-22.9\left(8\right)$ ${}^{a}$ | |

$\langle \text{\Delta}E(6,2)\rangle $ | $-21.9\left(8\right)$ ${}^{a}$ | $-22.6\left(8\right)$ ${}^{a}$ | |

$\langle \text{\Delta}E(7,2)\rangle $ | $-21.2\left(9\right)$ ${}^{b}$ | $-22.5\left(9\right)$ ${}^{b}$ | $+3.0\left(15\right)$ ^{e} |

$\langle \text{\Delta}E(8,2)\rangle $ | $-20.1\left(9\right)$ ${}^{c}$ | $-22.0\left(9\right)$ ${}^{c}$ | $+0.79\left(53\right)$ ${}^{f}$ |

$\langle \text{\Delta}E(9,2)\rangle $ | $-20.6\left(15\right)$ ${}^{b}$ | $-23.4\left(16\right)$ ${}^{b}$ | |

$\langle \text{\Delta}E(10,2)\rangle $ | $+1.5\left(17\right)$ ${}^{d}$ | $+5.0\left(20\right)$ ^{e}, $-3.5\left(17\right)$ ${}^{g}$ |

`zz_02`workbooks. In Table 5, we tabulate for these species the average differences between the spectroscopic level energies listed in the nist database (v5.1) and those obtained with grasp and superstructure; it must be noted that, for $(3-9,2)$, they have been calculated with and without the Breit and QED corrections. For $(3-9,2)$, the grasp average differences are approximately constant at $\langle \text{\Delta}E(3-9,2)\rangle \sim -22\times {10}^{3}$ cm${}^{-1}$, and the inclusion of the Breit and QED corrections does not lead to significant reductions. By contrast, for $(10,2)$ the grasp average difference is an order of magnitude smaller ($1.5\times {10}^{3}$ cm${}^{-1}$) and so are those obtained with superstructure for other ions, a level of agreement more compatible with that encountered in the calculation by [121]. It must also be appreciated that, for $(10,2)$, the superstructure energy differences are both positive and negative depending on authorship. In conclusion, the general outcome of this exercise seems to indicate that a variety of strategies for atomic model optimization have been employed—some more successful than others—and due to their relevance in the final data products, a great deal of pondering and effort must go into the atomic system representation.

**Figure 6.**Ratio of theoretical A-values for selected transitions relative to the standard [110,113]. (

**a**) $A{(2-10,2,2\phantom{\rule{0.166667em}{0ex}}{}^{1}{\mathrm{P}}^{\mathrm{o}},1\phantom{\rule{0.166667em}{0ex}}{}^{1}\mathrm{S})}_{\mathrm{E}1}$; (

**b**) $A{(2-10,2,2\phantom{\rule{0.166667em}{0ex}}{}^{3}\mathrm{S},1\phantom{\rule{0.166667em}{0ex}}{}^{1}\mathrm{S})}_{\mathrm{M}1}$ and (

**c**) $A{(2-10,2,3\phantom{\rule{0.166667em}{0ex}}{}^{1}\mathrm{D},1\phantom{\rule{0.166667em}{0ex}}{}^{1}\mathrm{S})}_{\mathrm{E}2}$. Filled circles: calculations with grasp for $(3-9,2)$ [122,123,124]. Star: calculation with grasp for $(10,2)$ [125]. Squares: calculation with autostructure, present work. Crosses: relativistic CI calculation [121]. Diamonds: A-values from the norad database computed with the R-matrix method [95,119,120]. Triangles: OP [129].

**Figure 7.**$A{(Z,2,n\phantom{\rule{0.166667em}{0ex}}{}^{1}{\mathrm{P}}^{\mathrm{o}},1\phantom{\rule{0.166667em}{0ex}}{}^{1}\mathrm{S})}_{\mathrm{E}1}$ as a function of n for (a) $Z=6$ and (b) $Z=10$. Circles: mcdf calculation with grasp for $Z=6$ [124]. Stars: mcdf calculation with grasp for $Z=10$ [125]. Squares: Breit–Pauli CI calculation with autostructure, present work. Crosses: relativistic CI calculation [121]. Triangles: OP [129].

**Table 6.**Experimental and theoretical lifetimes (s) for states in He i. Experiment: ${}^{a}$ [133]; ${}^{b}$ [134]; ${}^{c}$ [135]; ${}^{d}$ [136]; ${}^{e}$ [137]; ${}^{f}$ [138]; ${}^{g}$ [139]; ${}^{h}$ [140]. Theory: ${}^{i}$ [88]; ${}^{j}$ [118]. Note: the quantity in brackets gives the experimental error.

$\tau (2,2,i)$ | Experiment | Theory |
---|---|---|

$\tau (2,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $7.87\left(51\right)\mathrm{E}+03$ ${}^{a}$ | $7.862\mathrm{E}+03$ ${}^{i}$ |

$\tau (2,2,2{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}})$ | $5.60\left(14\right)\mathrm{E}-10$ ${}^{b}$ | $5.553\mathrm{E}-10$ ${}^{i}$, $5.560\mathrm{E}-10$ ${}^{j}$ |

$\tau (2,2,3{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $3.594\left(20\right)\mathrm{E}-08$ ${}^{c}$ | $3.590\mathrm{E}-08$ ${}^{i}$, $3.588\mathrm{E}-08$ ${}^{j}$ |

$\tau (2,2,3{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $5.63\left(20\right)\mathrm{E}-08$ ${}^{d}$ | $5.465\mathrm{E}-08$ ${}^{i}$, $5.463\mathrm{E}-08$ ${}^{j}$ |

$\tau (2,2,3{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}^{\mathrm{o}})$ | $1.05\left(10\right)\mathrm{E}-07$ ${}^{d}$, $9.64\left(82\right)\mathrm{E}-08$ ^{e} | $9.480\mathrm{E}-08$ ${}^{i}$, $9.475\mathrm{E}-08$ ${}^{j}$ |

$\tau (2,2,3{\phantom{\rule{0.166667em}{0ex}}}^{3}\mathrm{D})$ | $1.412\left(6\right)\mathrm{E}-08$ ${}^{c}$, $1.42\left(6\right)\mathrm{E}-08$ ${}^{f}$ | $1.414\mathrm{E}-08$ ${}^{i}$, $1.414\mathrm{E}-{08}^{j}$ |

$\tau (2,2,3{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{D}}_{2})$ | $1.53\left(3\right)\mathrm{E}-08$ ${}^{f}$ | $1.569\mathrm{E}-08$ ${}^{i}$, $1.569\mathrm{E}-08$ ${}^{j}$ |

$\tau (2,2,3{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}})$ | $1.71\left(4\right)\mathrm{E}-09$ ${}^{b}$ | $1.724\mathrm{E}-09$ ${}^{i}$, $1.725\mathrm{E}-09$ ${}^{j}$ |

$\tau (2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $8.87\left(30\right)\mathrm{E}-08$ ${}^{d}$ | $8.800\mathrm{E}-08$ ${}^{i}$, $8.801\mathrm{E}-08$ ${}^{j}$ |

$\tau (2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}^{\mathrm{o}})$ | $1.64\left(7\right)\mathrm{E}-07$ ${}^{d}$ | $1.385\mathrm{E}-07$ ${}^{i}$, $1.385\mathrm{E}-07$ ${}^{j}$ |

$\tau (2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{D}}_{2})$ | $3.1\left(3\right)\mathrm{E}-08$ ${}^{g}$ | $3.707\mathrm{E}-08$ ${}^{i}$, $3.706\mathrm{E}-08$ ${}^{j}$ |

$\tau (2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{F}}_{3}^{\mathrm{o}})$ | $7.4\left(2\right)\mathrm{E}-08$ ${}^{h}$ | $7.229\mathrm{E}-08$ ${}^{i}$ |

$\tau (2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}})$ | $4.01\left(8\right)\mathrm{E}-09$ ${}^{b}$, $4.3\left(2\right)\mathrm{E}-09$ ${}^{g}$ | $3.964\mathrm{E}-09$ ${}^{i}$, $3.967\mathrm{E}-09$ ${}^{j}$ |

$\tau (2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $1.49\left(5\right)\mathrm{E}-07$ ${}^{d}$ | $1.465\mathrm{E}-07$ ${}^{i}$, $1.466\mathrm{E}-07$ ${}^{j}$ |

$\tau (2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}^{\mathrm{o}})$ | $2.45\left(15\right)\mathrm{E}-07$ ${}^{d}$ | $2.193\mathrm{E}-07$ ${}^{i}$, $2.193\mathrm{E}-07$ ${}^{j}$ |

$\tau (2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{D}}_{2})$ | $5.4\left(5\right)\mathrm{E}-08$ ${}^{g}$ | $7.180\mathrm{E}-08$ ${}^{i}$, $7.205\mathrm{E}-08$ ${}^{j}$ |

$\tau (2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{F}}_{3}^{\mathrm{o}})$ | $1.33\left(5\right)\mathrm{E}-07$ ${}^{h}$ | $1.398\mathrm{E}-07$ ${}^{i}$ |

$\tau (2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}})$ | $7.68\left(15\right)\mathrm{E}-09$ ${}^{b}$ | $7.625\mathrm{E}-09$ ${}^{i}$, $7.631\mathrm{E}-09$ ${}^{j}$ |

**Table 7.**Experimental and theoretical lifetimes (s) for states in He-like ions. ${}^{a}$ [141]; ${}^{b}$ [132]; ${}^{c}$ [142]; ${}^{d}$ [143]; ${}^{e}$ [144]; ${}^{f}$ [145]; ${}^{g}$ [146]; ${}^{h}$ [147]; ${}^{i}$ [148]. Theory: ${}^{j}$ [88]; ${}^{k}$ [149]; ${}^{l}$ [150]; ${}^{m}$ [121]; ${}^{n}$ [105]. Note: the quantity in brackets gives the experimental error.

$\tau (Z,2,i)$ | Experiment | Theory |
---|---|---|

$\tau (3,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $5.22\left(50\right)\mathrm{E}+01$ ${}^{a}$ | $4.904\mathrm{E}+01$ ${}^{j}$ |

$\tau (4,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $1.80\left(5\right)\mathrm{E}+00$ ${}^{b}$ | $1.780\mathrm{E}+00$ ${}^{k}$ |

$\tau (4,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}^{\mathrm{o}})$ | $2.91\left(2\right)\mathrm{E}-08$ ${}^{c}$ | $2.934\mathrm{E}-08$ ${}^{k}$ |

$\tau (6,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $2.059\left(5\right)\mathrm{E}-02$ ${}^{d}$ | $2.059\mathrm{E}-02$ ${}^{l}$, $2.052\mathrm{E}-02$ ${}^{m}$ |

$\tau (6,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}})$ | $1.13\left(5\right)\mathrm{E}-08$ ^{e} | $1.185\mathrm{E}-08$ ${}^{l}$, $1.195\mathrm{E}-08$ ${}^{m}$ |

$\tau (6,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}^{\mathrm{o}})$ | $1.67\left(6\right)\mathrm{E}-08$ ^{e} | $1.763\mathrm{E}-08$ ${}^{l}$, $1.747\mathrm{E}-08$ ${}^{m}$ |

$\tau (7,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $3.94\left(5\right)\mathrm{E}-03$ ${}^{f}$ | $3.922\mathrm{E}-03$ ${}^{l}$, $3.932\mathrm{E}-03$ ${}^{m}$ |

$\tau (7,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}})$ | $4.9\left(3\right)\mathrm{E}-09$ ^{e} | $4.931\mathrm{E}-09$ ${}^{m}$ |

$\tau (7,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}^{\mathrm{o}})$ | $1.49\left(7\right)\mathrm{E}-08$ ^{e} | $1.463\mathrm{E}-08$ ${}^{l}$, $1.444\mathrm{E}-08$ ${}^{m}$ |

$\tau (8,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $9.56\left(5\right)\mathrm{E}-04$ ${}^{g}$ | $9.615\mathrm{E}-04$ ${}^{l}$, $9.551\mathrm{E}-04$ ${}^{m}$ |

$\tau (8,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}})$ | $1.52\left(8\right)\mathrm{E}-09$ ${}^{h}$ | $1.625\mathrm{E}-09$ ${}^{m}$ |

$\tau (8,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}^{\mathrm{o}})$ | $1.210\left(20\right)\mathrm{E}-08$ ${}^{h}$ | $1.240\mathrm{E}-08$ ${}^{l}$, $1.216\mathrm{E}-08$ ${}^{m}$ |

$\tau (9,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $2.76\left(2\right)\mathrm{E}-04$ ${}^{f}$ | $2.772\mathrm{E}-04$ ${}^{n}$ |

$\tau (9,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}})$ | $5.31\left(20\right)\mathrm{E}-10$ ${}^{h}$ | |

$\tau (9,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}^{\mathrm{o}})$ | $1.044\left(15\right)\mathrm{E}-08$ ${}^{h}$ | |

$\tau (10,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1})$ | $9.17\left(4\right)\mathrm{E}-05$ ${}^{i}$ | $9.141\mathrm{E}-05$ ${}^{m}$, $9.200\mathrm{E}-05$ ${}^{n}$ |

**Table 8.**Experimental and theoretical transition rates (s${}^{-1}$) for He-like ions. ${}^{a}$ [151]; ${}^{b}$ [152]; ${}^{c}$ [153]; ${}^{d}$ [154]; ${}^{e}$ [144]; ${}^{f}$ [147]. Theory: ${}^{g}$ [88]; ${}^{h}$ [118]; ${}^{i}$ [107]; ${}^{j}$ [121]. Note: the quantity in brackets gives the experimental error.

$A(Z,2,k,i)$ | Experiment | Theory |
---|---|---|

$A(2,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $1.77\left(8\right)\mathrm{E}+{02}^{a}$ | $1.764\mathrm{E}+{02}^{g}$, $1.731\mathrm{E}+{02}^{h}$ |

$A(2,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $3.24\left(16\right)\mathrm{E}-{01}^{b}$ | $3.270\mathrm{E}-{01}^{g}$ |

$A(2,2,2{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $1.758\left(50\right)\mathrm{E}+{09}^{c}$, $1.82\left(5\right)\mathrm{E}+{09}^{d}$ | $1.799\mathrm{E}+{09}^{g}$, $1.797\mathrm{E}+{09}^{h}$ |

$A(2,2,3{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $5.68\left(18\right)\mathrm{E}+{08}^{c}$, $5.71\left(5\right)\mathrm{E}+{08}^{d}$ | $5.663\mathrm{E}+{08}^{g}$, $5.660\mathrm{E}+{08}^{h}$ |

$A(2,2,4{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $2.47\left(6\right)\mathrm{E}+{08}^{d}$ | $2.436\mathrm{E}+{08}^{g}$, $2.434\mathrm{E}+{08}^{h}$ |

$A(2,2,5{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $1.27\left(3\right)\mathrm{E}+{08}^{d}$ | $1.258\mathrm{E}+{08}^{g}$, $1.257\mathrm{E}+{08}^{h}$ |

$A(6,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $2.90\left(16\right)\mathrm{E}+{07}^{e}$ | $2.825\mathrm{E}+{07}^{i}$, $2.701\mathrm{E}+{07}^{j}$ |

$A(7,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $1.38\left(11\right)\mathrm{E}+{08}^{e}$ | $1.394\mathrm{E}+{08}^{i}$, $1.348\mathrm{E}+{08}^{j}$ |

$A(8,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $5.80\left(35\right)\mathrm{E}+{08}^{f}$ | $5.499\mathrm{E}+{08}^{i}$, $5.357\mathrm{E}+{08}^{j}$ |

$A(9,2,2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}^{\mathrm{o}},1{\phantom{\rule{0.166667em}{0ex}}}^{1}{\mathrm{S}}_{0})$ | $1.78\left(7\right)\mathrm{E}+{09}^{f}$ | $1.834\mathrm{E}+{09}^{i}$ |

## 6. Conclusions and Recommendations

`S`n to

`R`n where n is just an integer assignment.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Mendoza, C.; Boswell, J.S.; Ajoku, D.C.; Bautista, M.A. AtomPy: An Open Atomic Data Curation Environment for Astrophysical Applications. *Atoms* **2014**, *2*, 123-156.
https://doi.org/10.3390/atoms2020123

**AMA Style**

Mendoza C, Boswell JS, Ajoku DC, Bautista MA. AtomPy: An Open Atomic Data Curation Environment for Astrophysical Applications. *Atoms*. 2014; 2(2):123-156.
https://doi.org/10.3390/atoms2020123

**Chicago/Turabian Style**

Mendoza, Claudio, Josiah S. Boswell, David C. Ajoku, and Manuel A. Bautista. 2014. "AtomPy: An Open Atomic Data Curation Environment for Astrophysical Applications" *Atoms* 2, no. 2: 123-156.
https://doi.org/10.3390/atoms2020123