Thulium-169 energy level diagram

Energy levels and transitions of neutral ¹⁶⁹Tm (Tm I, nuclear spin I = 1/2): the 73 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 72 levels they connect, each line with its vacuum wavelength, frequency and, for 71 of them, the reduced dipole matrix element. Level energies come from NIST and refer to the natural isotope mixture; transition rates are 68 NIST, 3 measured, 1 theory. Hyperfine constants and measured frequencies are those of this isotope.

Hover a line or a level to isolate it, click to keep it selected. Scroll to zoom, drag to move.

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

Key transitions of ¹⁶⁹Tm

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).

¹⁶⁹Tm hyperfine structure (I = 1/2)

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

Closed and nearly closed transitions of ¹⁶⁹Tm

A transition is closed when its upper level can decay only to the level it was excited from, so the atom keeps scattering photons. “closed”: among the levels NIST lists, no other level below the upper level has the opposite parity and |ΔJ| ≤ 1, so no other electric-dipole decay exists. Otherwise the leak is the sum of the branching ratios of the other decay lines of the upper level (or 1 − branching ratio where that of the line itself has been measured), and the number of photons is 1 / leak. “≥” and “≤”: at least one possible decay path has no listed rate, so the leak is a lower limit. These numbers are derived from the branching ratios, lifetimes and rates of this page, not measured as such; the tag names the weakest of the inputs, * marks theory and ≈ a model or semi-empirical calculation. Listed: lines that start on the ground level or on a metastable level and leak at most 10 %, unless more than three possible decay paths have no listed rate. Fine-structure levels only: hyperfine and Zeeman dark states and forbidden decays without a listed rate are not considered. Select a line in the diagram for the full list of its leak channels.

Listed ¹⁶⁹Tm 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.

¹⁶⁹Tm energy levels

Tm⁺ ionisation limit 49880.57 cm⁻¹ = 6.18440 eV (200.479 nm)

Sources

• Anderson, Den Hartog, Lawler, J. Opt. Soc. Am. B 13, 2382 (1996), Table 1
• Anderson, Den Hartog, Lawler, J. Opt. Soc. Am. B 13, 2382 (1996), Table 2
• Fedorov, Vishnyakova, Kalganova, Sukachev, Golovizin, Tregubov, Khabarova, Akimov, Kolach…
• Giglberger, Penselin, Z. Phys. 199, 244 (1967) (abstract)
• Golovizin, Fedorova, Tregubov, Sukachev, Khabarova, Sorokin, Kolachevsky, Nat. Commun. 10…
• Kolachevsky, Akimov, Tolstikhina, Chebakov, Sokolov, Rodionov, Kanorski, Sorokin, Appl. P…
• Kolachevsky, Akimov, Tolstikhina, Chebakov, Sokolov, Rodionov, Kanorski, Sorokin, Appl. P…
• Mishin, Tregubov, Golovizin, Kolachevsky, arXiv:2406.20002 (2024)
• NIST ASD
• NIST ASD level energies
• Sukachev, Fedorov, Tolstikhina, Tregubov, Kalganova, Vishnyakova, Golovizin, Kolachevsky,…

169Tm has I=1/2: every level is a hyperfine doublet F=J+-1/2 with splitting A(J+1/2), no B. Signed splittings follow Kolachevsky et al. 2007 (negative = larger F lower). The Anderson et al. 1996 lifetime tables (68 even + 126 odd levels) were read from the publisher abstract page, whose HTML embeds the tables, through an automated page reader (direct download is captcha-blocked), not from the PDF; every row was matched to a NIST level by energy (0.02 cm^-1) and J, and all lifetimes were checked to be <= 1/sum(A) from the NIST lines file within 15%; rows used on the site were read twice. No per-level uncertainty is printed in those tables (so no unc is given). Extra fields beyond SCHEMA.md: top-level ionization_limit; level fields lifetime_other, hfs_splitting_MHz; transition fields linewidth_MHz / linewidth_kHz / linewidth_Hz, leak_to_metastable, frequency_component_THz, magic_wavelength_nm, differential_frequency_MHz. frequency_THz of the clock line is the hyperfine centre of gravity derived from the measured F=4->F=3 component. rme_J_ea0 values are derived from the A coefficient of the same entry (schema convention). Entries flagged LOWER BOUND / UPPER BOUND / LOWER LIMIT in their note are bounds. g_J without a literature source is copied from the NIST levels file.

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
• 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