Thorium energy level diagram

Energy levels and transitions of neutral thorium (Th I): the 71 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 67 levels they connect, each line with its vacuum wavelength, frequency and, for 3 of them, the reduced dipole matrix element derived from the NIST transition rate. Measured lifetimes, transition rates, hyperfine constants and isotope shifts from the literature are included, each with its citation.

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Download: diagram (PDF) diagram (SVG) transitions (CSV) levels (CSV) source code

Key transitions of thorium

λ, ν from NIST level energies unless a measured frequency for this isotope is available. A: measured value or NIST. Γ/2π: natural linewidth of the upper level, 1/(2πτ).

²²⁹Th hyperfine structure (I = 5/2)

Measured A, B constants; sources in the data file.

Isotope shifts

Shift = ν(first isotope) − ν(second isotope).

Listed Th transitions below 2 µm

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.

Th energy levels

Th⁺ ionisation limit 50867.00 cm⁻¹ = 6.30670 eV (196.591 nm)

Sources

• NIST ASD level energies
• Sonnenschein, Raeder, Hakimi, Moore, Wendt, J. Phys. B 45, 165005 (2012) (high-resolution…
• value printed in Fig. 2 of Raeder, Sonnenschein, Gottwald, Moore, Reponen, Rothe, Trautma…
• value printed in Fig. 2 of Raeder, Sonnenschein, Gottwald, Moore, Reponen, Rothe, Trautma…

Natural thorium is 232Th (I = 0, no hyperfine structure); 229Th (I = 5/2) is the nuclear-clock isotope. Isotope shifts are nu(A) - nu(232); Raeder et al. give level shifts in cm^-1, converted here with 1 cm^-1 = 29979.2458 MHz. The pulsed-laser level energies of Raeder et al. for 232Th are much less precise than NIST and are listed only so that the 228-230Th values can be compared on the same scale. The intermediate levels re-measured by Li et al. 2025 (38807.60(6), 39096.36(15), 38366.56(15) cm^-1) agree with NIST and were not entered. The 2025 Leuven paper also determined the Th+ ionization potential, 12.300(9) eV. Second pass (2026-10-02): 229Th hyperfine A and B of the ground level and of the odd levels at 26096.98, 26113.27 and 38278.88 cm^-1 added second-hand (method 'compilation'); where the printed uncertainty is asymmetric the larger side is stored and the printed form is in the note.

Atoms with measured data

• Lithium-632 levels, 85 lines
• Lithium-732 levels, 85 lines
• Beryllium-917 levels, 26 lines
• Sodium-2336 levels, 106 lines
• Magnesium-2418 levels, 61 lines
• Magnesium-2518 levels, 61 lines
• Potassium-3934 levels, 84 lines
• Potassium-4034 levels, 84 lines
• Potassium-4134 levels, 84 lines
• Calcium-4035 levels, 61 lines
• Calcium-4335 levels, 61 lines
• Chromium-5256 levels, 87 lines
• Chromium-5356 levels, 87 lines
• Rubidium-8536 levels, 94 lines
• Rubidium-8736 levels, 94 lines
• Strontium-8440 levels, 70 lines
• Strontium-8640 levels, 70 lines
• Strontium-8740 levels, 70 lines
• Strontium-8840 levels, 70 lines
• Cadmium-11115 levels, 21 lines
• Cadmium-11315 levels, 21 lines
• Cadmium-11415 levels, 21 lines
• Caesium-13331 levels, 79 lines
• Barium-13744 levels, 89 lines
• Barium-13844 levels, 89 lines
• Dysprosium-16139 levels, 55 lines
• Dysprosium-16239 levels, 55 lines
• Dysprosium-16339 levels, 55 lines
• Dysprosium-16439 levels, 55 lines
• Erbium-16673 levels, 90 lines
• Erbium-16773 levels, 90 lines
• Erbium-16873 levels, 90 lines
• Thulium-16972 levels, 73 lines
• Ytterbium-17118 levels, 26 lines
• Ytterbium-17318 levels, 26 lines
• Ytterbium-17418 levels, 26 lines
• Mercury-19927 levels, 47 lines
• Mercury-20127 levels, 47 lines
• Mercury-20227 levels, 47 lines

All elements: periodic table