Gadolinium energy level diagram

Energy levels and transitions of neutral gadolinium (Gd I): the 60 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 53 levels they connect, each line with its vacuum wavelength, frequency and, for 22 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 gadolinium

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).

¹⁵⁷Gd hyperfine structure (I = 3/2)

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

Isotope shifts

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

Listed Gd 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.

Gd energy levels

Gd⁺ ionisation limit 49601.45 cm⁻¹ = 6.14980 eV (201.607 nm)

Sources

• Adhikari, Battles, Simien, OSA Continuum 2, 1548 (2019), Table 1
• Childs, Phys. Rev. A 39, 4956 (1989) (atomic-beam laser-rf double resonance; quoted in Pe…
• Den Hartog, Bilty, Lawler, J. Phys. B 44, 055001 (2011), Table 1 (pp. 3-5; time-resolved …
• Lawler, Bilty, Den Hartog, J. Phys. B 44, 095001 (2011), Table 6 (printed portion, p. 7)
• NIST ASD
• NIST ASD level energies
• Rotter, Carson, Robben, Haynam, Johnson, Isselhardt, Appl. Phys. B 132, 100 (2026), Table…
• Unsworth, J. Phys. B 2, 122 (1969), Table 1 (p. 124; atomic-beam magnetic resonance, weak…
• Wang, Jiang, Jiang, Shang, Tian, Dai, J. Phys. B 46, 045003 (2013), Table 1 (p. 3; time-r…

Stable isotopes: 155Gd and 157Gd have I = 3/2 (both nuclear moments negative: mu = -0.2591 and -0.3398 nuclear magnetons in the IAEA table); the others have I = 0. Hyperfine convention: E = A K/2 + B [3K(K+1) - 4I(I+1)J(J+1)] / [8I(2I-1)J(2J-1)], K = F(F+1)-J(J+1)-I(I+1) (as printed by Adhikari et al.). Ground-term 9D°J (J = 2-6) hyperfine constants of 155Gd and 157Gd are from Unsworth 1969, Table 1 (scanned PDF pdf/Gd_Unsworth_1969.pdf, numbers checked against the page image, signs as printed); the unsigned LLNL modeling constants for 9D°2 are kept as alternatives and agree in magnitude. The LLNL constants for the 17380.827 level and the 575.19 nm line are modeling inputs printed without signs or uncertainties; treat them as indicative. Lifetimes: all 136 levels of Den Hartog, Bilty, Lawler 2011, Table 1 (pdf/Gd_DenHartog_2011.pdf; parsed from the PDF text, all matched to NIST energy and J within 0.002 cm-1); one common stated uncertainty of ±5 % (unc = 5 % of the value). Directly read values of Xu, Jiang, Svanberg 2003 (pdf/Gd_Xu_2003.pdf, 25 levels) and Wang et al. 2013 (pdf/Gd_Wang_2013.pdf, 27 levels; checked against the page image) are stored as "alternatives" where Den Hartog has the level, and as the entry for 13 levels that only they measured (30394.64, 35794.634, 36191.722, 36394.507 from Xu; 31327.52, 32226.746, 32272.125, 32549.565, 37090.08, 37284.744, 37425.155, 37809.508, 38434.97 from Wang). Values of Marek & Stahnke 1980, Miyabe 1997 and Gorshkov 1983 are sec

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