Astatine energy level diagram

Energy levels and transitions of neutral astatine (At I): the 2 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 3 levels they connect, each line with its vacuum wavelength, frequency and, for 0 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 astatine

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).

²⁰⁵At hyperfine structure (I = 9/2)

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

Isotope shifts

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

Closed and nearly closed transitions of astatine

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 At 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.

At energy levels

At⁺ ionisation limit 75150.80 cm⁻¹ = 9.31751 eV (133.066 nm)

Sources

• Cubiss et al., Phys. Rev. C 97, 054327 (2018), Sec. III B 2: ratios A(4P3/2)/A(ground) = …
• Cubiss, Barzakh, Seliverstov, Andreyev, et al., Phys. Rev. C 97, 054327 (2018), Table I (…
• NIST ASD level energies

Astatine has no stable or long-lived isotope (longest 210At, 8.1 h); every optical number comes from in-source laser resonance ionization at ISOLDE or TRIUMF, Doppler-limited (a few GHz linewidth). Isotope shifts are nu(A) - nu(205). Hyperfine keys ending in m, m1, m2 are nuclear isomers. The A and B constants listed for the 46233.6 cm^-1 level were obtained from fits of the 795 nm line with the upper/lower A ratio fixed. The electron affinity of astatine was measured as 2.41578(7) eV (Leimbach et al., Nat. Commun. (2020), doi:10.1038/s41467-020-17599-2, arXiv:2002.11418) - a property of the negative ion, recorded here only for reference. Calculated isotope-shift constants for the 795 nm line: F = -11.47(57) GHz/fm^2 (multiconfiguration Dirac-Hartree-Fock, quoted in Barzakh et al. 2019).

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