Europium energy level diagram

Energy levels and transitions of neutral europium (Eu I): the 90 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 68 levels they connect, each line with its vacuum wavelength, frequency and, for 90 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.

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 europium

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).

¹⁵³Eu hyperfine structure (I = 5/2)

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

Closed and nearly closed transitions of europium

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 Eu 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.

Eu energy levels

Eu⁺ ionisation limit 45734.74 cm⁻¹ = 5.67039 eV (218.652 nm)

Sources

• Den Hartog, Wickliffe, Lawler, Astrophys. J. Suppl. Ser. 141, 255 (2002)
• Fechner, Rinkleff, Steudel, Z. Phys. D 6, 31 (1987), linewidth as quoted by Inoue, Miyaza…
• Miyazawa, Inoue, Matsui, Takanashi, Kozuma, Phys. Rev. A 103, 053122 (2021)
• Miyazawa, Inoue, Nishida, Hosoya, Kozuma, Opt. Commun. 392, 171 (2017)
• Miyazawa, Inoue, Nishida, Hosoya, Kozuma, Opt. Commun. 392, 171 (2017). Note: derived: me…
• NIST ASD
• NIST ASD Eu I lines table (local copy data/nist/Eu_I_lines_from1nm.tsv)
• NIST ASD level energies
• Sandars, Woodgate, Proc. R. Soc. Lond. A 257, 269 (1960)

Lifetimes (85 levels, Table 1) and transition probabilities (140 lines, Table 4) were parsed from the text layer of the publisher PDF of Den Hartog et al. 2002 retrieved through the Internet Archive (iopscience.iop.org itself is bot-blocked); the +- signs are lost in the text layer but value/uncertainty pairs are unambiguous, and the count of parsed rows (85, 140) matches the numbers stated in the abstract. Den Hartog level energies are those of Martin, Zalubas, Hagan (1978) and coincide with the NIST energies used as identifiers. NIST ASD already carries the Den Hartog A values (same numbers); they are repeated here with their uncertainties. rme_J_ea0 entries are derived from the measured A with the SCHEMA convention. Hyperfine constants follow E = A K/2 + B [3K(K+1)/4 - I(I+1)J(J+1)] / [2I(2I-1)J(2J-1)]; both ground-state A values are negative. Extra fields beyond SCHEMA.md: top-level ionization_limit, laser_cooling_scheme, conflicts; level fields lifetime_other, hyperfine_note, decay_to_metastable, trap_loss, magnetic_moment_muB; transition fields linewidth_MHz / linewidth_kHz, saturation_intensity_*, doppler_limit_uK, leak_to_metastable. Entries whose note says LOWER BOUND / UPPER BOUND / derived are not direct measurements of the stated quantity. The line the brief calls "1148 nm" is the y8P9/2 -> a10D7/2 leak / repumper.

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