Germanium energy level diagram

Energy levels and transitions of neutral germanium (Ge I): the 54 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 20 levels they connect, each line with its vacuum wavelength, frequency and, for 48 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 germanium

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).

⁷³Ge 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 germanium

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 Ge 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, this site's own Cowan-code calculation with the parameters fitted to the NIST energies (HFR fit; inputs and fit report in the repository folder cowan/; used only where nothing else gives a rate; strong lines typically within a factor 2, weak lines worse), or a model calculation.

Ge energy levels

Ge⁺ ionisation limit 63713.24 cm⁻¹ = 7.89943 eV (156.953 nm)

Sources

• Biemont, Lynga, Li, Svanberg, Garnir, Doidge, Mon. Not. R. Astron. Soc. 303, 721 (1999), …
• Childs and Goodman, Phys. Rev. 141, 15 (1966) (atomic-beam magnetic resonance; values rea…
• Childs and Goodman, Phys. Rev. 141, 15 (1966) (atomic-beam magnetic resonance; values rea…
• Kanellakopoulos et al., Phys. Rev. C 102, 054331 (2020), arXiv:2011.01659, Table I (colli…
• Li, Norin, Persson, Wahlstrom, Svanberg, Doidge, Biemont, Phys. Rev. A 60, 198 (1999), Ta…
• Li, Norin, Persson, Wahlstrom, Svanberg, Doidge, Biemont, Phys. Rev. A 60, 198 (1999), Ta…
• NIST ASD
• NIST ASD level energies
• R. H. Garstang, J. Res. Natl. Bur. Stand. 68A, 61 (1964), Table 16 (intermediate-coupling…
• R. H. Garstang, J. Res. Natl. Bur. Stand. 68A, 61 (1964), Table 16. Note: derived: 1/A of…
• R. H. Garstang, J. Res. Natl. Bur. Stand. 68A, 61 (1964), Table 16. Note: derived: 1/sum …
• R. H. Garstang, J. Res. Natl. Bur. Stand. 68A, 61 (1964), Table 16. Note: derived: 1/sum …
• R. H. Garstang, J. Res. Natl. Bur. Stand. 68A, 61 (1964), Table 16. Note: derived: 1/sum …
• branching ratio / lifetime

Level energies are the NIST ASD values (data/nist/Ge_I_levels.tsv); Li et al. and Biemont et al. quote the same levels rounded to 0.01 cm^-1. A_s of E1 lines = measured branching ratio x 1/(measured laser lifetime) as printed by the authors; rme_J_ea0 is derived from that A with the NIST energies (convention of SCHEMA.md, J' = upper level). 4p5s lifetimes and 4p2-4p5s A values come from Biemont et al. 1999 (read directly; Li et al. 1999 reprints them), 4p4d / 4p6s / 4p5d lifetimes and 4p2-4p4d A values from Li et al. 1999. Forbidden-line rates and the metastable lifetimes derived from them are 1964 intermediate-coupling THEORY (Garstang), not measurements. Isotope shifts are nu(first) - nu(second), centre of gravity, natural reference isotope 72Ge. Hyperfine constants refer to 73Ge (I = 9/2). Deverall, Meissner, Zissis, Phys. Rev. 95, 1463 (1954) (abstract) report no resolvable structure in eight Ge I lines and estimate the shift between consecutive even isotopes as smaller than 0.005 cm^-1 (bound).

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