Atomic energy level diagrams

Protactinium energy level diagram

Energy levels and transitions of neutral protactinium (Pa I): 64 levels and 64 classified lines below 2 µm taken from the cited literature, each line with its vacuum wavelength and frequency. The NIST Atomic Spectra Database lists only the ground level and the ionisation limit of protactinium, so the level energies on this page are those of the literature sources named below.

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Protactinium energy level diagram with transition wavelengths and dipole matrix elements

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Listed Pa transitions below 2 µm

Lower levelUpper levelλ vacuum (nm)λ air (nm)ν (THz)Type|⟨J‖er‖J′⟩| (ea₀)A (s⁻¹)Branching (%)Source of matrix element / A
4K13/2(32234)°11/2350.5968350.4965855.0919E1––––
4I°9/2(30658)11/2357.1578357.0559839.3837E1––––
4K11/2(27989)°9/2357.2840357.1820839.0873E1––––
4I9/2(28316)°9/2363.7561363.6524824.1580E1––––
4K11/2(26999)°9/2370.3796370.2743809.4194E1––––
4K11/2(26640)°9/2375.3728375.2661798.6526E1––––
4K11/2(25810)°11/2387.4455387.3357773.7669E1––––
4I9/2(26252)°11/2393.2952393.1839762.2582E1––––
4K11/2(25107)°13/2398.2955398.1829752.6885E1––––
4K11/2(25104)°11/2398.3357398.2230752.6126E1––––
4I9/2(25104)°11/2411.8779411.7617727.8673E1––––
4K11/2(22536)°13/2443.7372443.6127675.6081E1––––
4K11/2(21601)°13/2462.9483462.8187647.5723E1––––
4K11/2(20740)°13/2482.1691482.0344621.7579E1––––
4I9/2(21389)°11/2486.2852486.1494616.4952E1––––
2H9/2(19887)°9/2603.7446603.5775496.5551E1––––
2H9/2(19546)°11/2616.4259616.2554486.3398E1––––
4K11/2(16082)°13/2621.8059621.6339482.1319E1––––
4K11/26K°9/2636.0360635.8602471.3451E1 (intercombination)––––
4K11/26L°13/2638.1002637.9238469.8204E1 (intercombination)––––
4H7/2(18493)°7/2644.0751643.8971465.4620E1––––
4H7/2(17684)°7/2679.4630679.2755441.2197E1––––
4K11/26L°11/2694.7624694.5708431.5036E1 (intercombination)––––
2H9/2(17684)°7/2696.3703696.1783430.5072E1––––
(4121)11/2(18418)°9/2699.4660699.2732428.6019E1––––
4H11/2(23509)°9/2707.8208707.6257423.5429E1––––
4G7/2(18793)°7/2710.2901710.0943422.0705E1––––
4I9/2(14877)°9/2711.6865711.4904421.2423E1––––
4K13/2(17652)°11/2717.3542717.1565417.9141E1––––
2H9/26K°11/2722.9129722.7137414.7007E1 (intercombination)––––
2H9/2(16984)°9/2732.0805731.8788409.5075E1––––
4I9/26L°11/2737.0286736.8256406.7583E1 (intercombination)––––
2H9/2(16704)°9/2747.3962747.1904401.1159E1––––
2H9/2(16666)°7/2749.5224749.3160399.9780E1––––
4K15/2(20740)°13/2756.0342755.8261396.5329E1––––
2H9/2(16464)°9/2761.0286760.8192393.9306E1––––
4K13/2(16820)°11/2762.8903762.6803392.9693E1––––
4K15/2(20606)°13/2763.7278763.5176392.5383E1––––
(4121)11/26K°11/2767.1456766.9345390.7895E1––––
4K11/24I°9/2768.1312767.9198390.2881E1––––
4G5/2(14519)°5/2775.1319774.9186386.7631E1––––
(4121)11/2(16820)°11/2787.5120787.2953380.6831E1––––
(4121)11/2(16704)°9/2794.7739794.5553377.2047E1––––
4K13/24I°11/2804.1559803.9348372.8039E1––––
(4121)11/2(16464)°9/2810.2073809.9846370.0194E1––––
4I9/24I°9/2820.1296819.9042365.5428E1––––
4I9/2(12911)°7/2827.4142827.1868362.3245E1––––
4K13/26L°13/2836.1277835.8980358.5486E1 (intercombination)––––
6L11/2(18945)°9/2837.1896836.9596358.0938E1––––
6L13/2(20350)°11/2844.3382844.1063355.0620E1––––
4H7/2(14683)°5/2853.4990853.2646351.2511E1––––
6L11/2(18662)°9/2857.5292857.2937349.6003E1––––
(4576)11/24I°11/2864.2280863.9907346.8904E1––––
4H7/2(14519)°5/2865.5892865.3514346.3450E1––––
4K11/24,1/2°9/2873.7665873.5266343.1036E1––––
4I13/2(16820)°11/21059.72901059.4387282.8954E1––––
4H7/24,1/2°7/21092.63111092.3319274.3766E1––––
(8082)5/2(16666)°7/21164.99541164.6765257.3336E1––––
4H7/24,1/2°9/21179.49911179.1764254.1693E1––––
6I7/26I°7/21228.23571227.8997244.0838E1––––
6I7/26K°9/21323.77481323.4128226.4679E1––––
6L11/26L°11/21352.60891352.2391221.6402E1––––
4H7/24,1/2°7/21434.86741434.4753208.9339E1––––
4G5/24,1/2°7/21848.36391847.8593162.1934E1––––

Reduced dipole matrix elements follow the convention A = ω³|d|²/(3πε₀ħc³(2J′+1)), with J′ the upper level. Tags show where a number comes from: measured, NIST compilation, high-accuracy theory, or a model calculation.

Pa energy levels

LevelEnergy (cm⁻¹)JParityLifetimegJHyperfine A (MHz)Hyperfine B (MHz)Lifetime sourceHyperfine source
4K11/20.00011/2evenstable–––––
4I9/2825.4159/2even–0.805––––
4G5/21618.3255/2even–0.73––––
4I°9/22659.4059/2odd–0.8––––
4H7/22966.5307/2even–0.75––––
2H9/23323.8609/2even–0.89––––
4K13/23711.62513/2even–0.975––––
(4121)11/24121.45011/2even–0.985––––
(4576)11/24576.00511/2even–1––––
4G7/24713.8707/2even–0.97––––
4H7/25149.4657/2even–0.725––––
4G5/26708.5605/2even–0.7––––
6L11/27000.29011/2even––––––
4I13/27383.29513/2even–1.085––––
4K15/27512.69515/2even–1.09––––
(8082)5/28081.9655/2even––––––
6I7/28168.2257/2even––––––
6L13/28506.45513/2even–0.88––––
4H11/29380.64011/2even––––––
4,1/2°9/211444.7059/2odd–0.88––––
4,1/2°7/212118.7507/2odd–0.935––––
(12911)°7/212911.2607/2odd–1.055––––
4I°9/213018.6109/2odd–0.81––––
6L°11/214393.41011/2odd–0.675––––
(14519)°5/214519.3555/2odd–0.94––––
(14683)°5/214683.0055/2odd–0.895––––
(14877)°9/214876.5459/2odd–0.9––––
6L°13/215671.52013/2odd––––––
6K°9/215722.3809/2odd––––––
(16082)°13/216082.19013/2odd––––––
4I°11/216147.02511/2odd–1.01––––
6I°7/216309.9857/2odd––––––
(16464)°9/216463.9709/2odd–0.89––––
(16666)°7/216665.6907/2odd–0.865––––
(16704)°9/216703.6459/2odd–0.875––––
(16820)°11/216819.67011/2odd–1.01––––
(16984)°9/216983.5609/2odd–1.015––––
6K°11/217156.78511/2odd–0.905––––
(17652)°11/217651.74011/2odd–1.04––––
(17684)°7/217684.0357/2odd–0.865––––
(18418)°9/218418.0709/2odd–1.09––––
(18493)°7/218492.6707/2odd–0.79––––
(18662)°9/218661.7009/2odd––––––
(18793)°7/218792.6257/2odd–0.92––––
(18945)°9/218945.0159/2odd–1.035––––
(19546)°11/219546.41011/2odd–1.015––––
(19887)°9/219887.1559/2odd–1––––
(20350)°11/220350.05011/2odd–1.04––––
(20606)°13/220606.36513/2odd–1.075––––
(20740)°13/220739.61013/2odd–1.035––––
(21389)°11/221389.48011/2odd–1.04––––
(21601)°13/221600.68513/2odd––––––
(22536)°13/222535.86013/2odd–1.055––––
(23509)°9/223508.5109/2odd–1.045––––
(25104)°11/225104.45511/2odd–0.99––––
(25107)°13/225106.98513/2odd–0.98––––
(25810)°11/225810.08511/2odd–1.065––––
(26252)°11/226251.61011/2odd–0.975––––
(26640)°9/226640.1859/2odd–1.055––––
(26999)°9/226999.3259/2odd––––––
(27989)°9/227988.9409/2odd–1.075––––
(28316)°9/228316.3659/2odd–1.005––––
(30658)11/230658.23011/2even–1.125––––
(32234)°11/232234.42011/2odd––––––

Pa⁺ ionisation limit 47500.00 cm⁻¹ = 5.88925 eV (210.526 nm)

Sources

All Pa I levels and line classifications come from the archived online version (2002/2003 captures) of the Blaise & Wyart actinide tables (Laboratoire Aime Cotton); energies refer to 231Pa (hyperfine centre of gravity). NIST ASD lists only the ground level 5f2.6d.7s2 4K11/2 and an estimated limit. Configurations are stored without the parent terms (the full printed string is in each level note). The classification in the wavelength table uses truncated level energies; each line was matched to the level tables with J and with the observed wavenumber (air wavelength converted with the Edlen formula; the residual is in each line note). 'relative_intensity' is the coarse photographic/emission intensity printed there (3000 or 10000) and only ranks lines. Lines with upper levels slightly above 30000 cm^-1 (30658.23 and 32234.42 cm^-1) are kept because they belong to the selected strong lines.

Atoms with measured data

All elements: periodic table