Beryllium-9 energy level diagram

Energy levels and transitions of neutral ⁹Be (Be I, nuclear spin I = 3/2): 17 levels and 26 lines below 2 µm, each with its vacuum wavelength, frequency and, for 22 of them, the reduced dipole matrix element. Level energies come from the NIST Atomic Spectra Database; transition rates are 26 NIST. Neutral beryllium is also the starting point for loading Be⁺ ion traps by photoionisation.

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 ⁹Be

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).

⁹Be hyperfine structure (I = 3/2)

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

Isotope shifts

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

Closed and nearly closed transitions of ⁹Be

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 ⁹Be 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, a semi-empirical calculation (Kurucz line list, used only where no measurement or NIST value exists; typically within a factor 2), or a model calculation.

⁹Be energy levels

Be⁺ ionisation limit 75192.64 cm⁻¹ = 9.32270 eV (132.992 nm)

Sources

• Ahrendsen, Karani, Williams, Phys. Rev. A 110, 032818 (2024) (abstract); saturated absorp…
• Ahrendsen, Karani, Williams, Phys. Rev. A 110, 032818 (2024) (abstract); saturated absorp…
• Ahrendsen, Karani, Williams, Phys. Rev. A 110, 032818 (2024) (abstract); saturated absorp…
• Blachman & Lurio, Phys. Rev. 153, 164 (1967), atomic-beam magnetic resonance; corrected (…
• Bromander, Phys. Scr. 4, 61 (1971), beam-foil (re-analysis of the Stockholm decay curves)…
• Kerkhoff, Schmidt, Zimmermann, Phys. Lett. A 80, 11 (1980) (abstract): selective pulsed d…
• Kerkhoff, Schmidt, Zimmermann, Phys. Lett. A 80, 11 (1980) (abstract): selective pulsed d…
• NIST ASD
• NIST ASD level energies
• Schnabel & Kock, Phys. Rev. A 61, 062506 (2000) (abstract): nonlinear time-resolved laser…
• Wu, Tian, Si, Wang, Jonsson, Gaigalas, Godefroid, Amarsi, Chen, 'Atomic data benchmarked …
• Wu, Tian, Si, Wang, Jonsson, Gaigalas, Godefroid, Amarsi, Chen, 'Atomic data benchmarked …
• Wu, Tian, Si, Wang, Jonsson, Gaigalas, Godefroid, Amarsi, Chen, 'Atomic data benchmarked …
• Wu, Tian, Si, Wang, Jonsson, Gaigalas, Godefroid, Amarsi, Chen, 'Atomic data benchmarked …
• Wu, Tian, Si, Wang, Jonsson, Gaigalas, Godefroid, Amarsi, Chen, 'Atomic data benchmarked …

All energies identifying levels are copied from data/nist/Be_I_levels.tsv. 9Be is the only stable isotope (I = 3/2). Hyperfine sign convention: A and B of 2s2p 3P1,2 are the Blachman-Lurio constants AFTER second/third-order corrections for hyperfine mixing among the 3P_J levels (A negative because the 9Be nuclear moment is negative). First-order constants fitted directly to the same intervals (A1 = -140.1564, B1 = -3.2363, A2 = -124.6165, B2 = 0.7800 MHz; Puchalski et al. 2021) are a different definition - do not mix. The abstract of arXiv:2411.13013 quotes the old B(3P2) as 1.427(9) MHz while its Table VI and arXiv:2603.11098 give 1.429(8) MHz; the table value is used. Fine structure of 2s2p 3P: Blachman & Lurio (abstract) deduced W(3P2)-W(3P1) = 71.86(24) GHz and W(3P1)-W(3P0) = 19.41(19) GHz from the magnetic-field dependence of the hyperfine structure (not a direct measurement); Puchalski et al. 2021 calculate 71.379 and 19.498 GHz and suspect the experimental 3P2-3P1 value is inaccurate; the NIST level differences are 2.335 and 0.615 cm^-1. Lifetimes taken from Table IV of arXiv:2603.11098 are marked 'compilation' with the original paper named; for multiplets the measurement is a term value and is repeated on each J level. Where several measurements exist the laser (cascade-free) result is the main value and beam-foil results are in 'alternatives'; for 2p2 3P, 2s3d 1D and 2s4d 1D the main value is Bromander 1971 (a re-analysis of the Bergstrom 1969 Stockholm decay curves

Atoms with measured data

• Lithium-632 levels, 85 lines
• Lithium-732 levels, 85 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