Dysprosium-161 energy level diagram

Energy levels and transitions of neutral ¹⁶¹Dy (Dy I, nuclear spin I = 5/2): 39 levels and 55 lines below 2 µm, each with its vacuum wavelength, frequency and, for 54 of them, the reduced dipole matrix element. Level energies come from the NIST Atomic Spectra Database; transition rates are 26 NIST, 23 measured, 5 theory.

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

Key transitions of ¹⁶¹Dy

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).

¹⁶¹Dy hyperfine structure (I = 5/2)

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

Isotope shifts

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

Closed and nearly closed transitions of ¹⁶¹Dy

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.

All ¹⁶¹Dy 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.

¹⁶¹Dy energy levels

Dy⁺ ionisation limit 47901.76 cm⁻¹ = 5.93906 eV (208.761 nm)

Sources

• Curry, Den Hartog, Lawler, J. Opt. Soc. Am. B 14, 2788 (1997), Table 1
• Dzuba, Flambaum, Phys. Rev. A 81, 052515 (2010)
• Gustavsson, Lundberg, Nilsson, Svanberg, J. Opt. Soc. Am. 69, 984 (1979), Table II
• Leefer, Cingoz, Budker, Opt. Lett. 34, 2548 (2009)
• Li, Wyart, Dulieu, Nascimbene, Lepers, J. Phys. B 50 (2017), arXiv:1607.05628, Tables 3-4…
• Lu, Youn, Lev, Phys. Rev. A 83, 012510 (2011)
• NIST ASD
• NIST ASD level energies
• Ng et al., 'Two-dimensional shelving spectroscopy of ultraviolet ground state transitions…
• Petersen, Truemper, Windpassinger, Phys. Rev. A 101, 042502 (2020)
• Petersen, Truemper, Windpassinger, Phys. Rev. A 101, 042502 (2020). Note: LOWER LIMIT (ta…
• Petersen, Truemper, Windpassinger, Phys. Rev. A 101, 042502 (2020). Note: UPPER LIMIT, = …
• Schmitt, Henn, Billy, Kadau, Maier, Griesmaier, Pfau, Opt. Lett. 38, 637 (2013)
• T. Maier, PhD thesis, Univ. Stuttgart (2015), Tab. 2.2
• White, Bulstrode, Forest, Honeyball, Evans, Butt, J. Phys. B 58, 035001 (2025)
• branching ratio / lifetime

Isotope shifts are nu(first)-nu(second) as in the schema; where a source tabulated nu(A)-nu(164) the sign was flipped and this is stated in the entry note. Keys other than 164-x (e.g. 162-164 for Petersen et al., 163-162 for White et al.) are kept as printed. Extra fields beyond SCHEMA.md are used where the schema had no slot: top-level ionization_limit; level fields lifetime_other, hyperfine_other, level_energy_measured; transition fields linewidth_MHz / linewidth_kHz, wavenumber_cm, reduced_dipole_au (|<f||D||i>| in atomic units, theory), leak_to_metastable, isotope_shift_other, frequency_other, polarizability_ratio_1064nm, note. Entries flagged LOWER LIMIT / UPPER LIMIT / LOWER BOUND in their note are bounds, not central values. g_J values are copied from the NIST levels file (Lande column). Hyperfine A, B follow the usual convention E = A K/2 + B [3K(K+1)/4 - I(I+1)J(J+1)] / [2I(2I-1)J(2J-1)], K = F(F+1)-I(I+1)-J(J+1); 161Dy has negative A (inverted structure). The Curry 1997 and Gustavsson 1979 lifetime tables were read from the publisher HTML pages through an automated page reader (direct download is captcha-blocked), not from a PDF; the Curry values were spot-checked against 1/sum(A) from the NIST lines file for 15194.83, 15972.35, 16693.87, 16733.20, 23832.06, 23877.74 and 24708.97 cm-1 and agree. Curry uncertainties are the blanket +-5% (+-10% or +-8% where flagged). Rows of Curry Table 1 above 28200 cm-1 were not transcribed, and levels the reader may have skipped a

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-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