Carbon energy level diagram

Energy levels and transitions of neutral carbon (C I): the 80 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 59 levels they connect, each line with its vacuum wavelength, frequency and, for 79 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 carbon

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).

¹³C hyperfine structure (I = 1/2)

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

Isotope shifts

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

Closed and nearly closed transitions of carbon

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 C 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.

C energy levels

C⁺ ionisation limit 90820.35 cm⁻¹ = 11.26029 eV (110.107 nm)

Sources

• Kurucz, R. L., Can. J. Phys. 89, 417 (2011); semi-empirical line list gf0600.pos of 2015-…
• NIST ASD
• NIST ASD level energies
• T. R. O'Brian and J. E. Lawler, J. Quant. Spectrosc. Radiat. Transf. 57, 309 (1997) (lase…
• Wolber, Figger, Haberstroh, Penselin, Z. Phys. 236, 337 (1970); K. Haris and A. Kramida, …
• Wolber, Figger, Haberstroh, Penselin, Z. Phys. 236, 337 (1970); K. Haris and A. Kramida, …
• weighted mean of Lawrence and Savage (1966, phase shift), Bromander (1971, beam-foil), Ma…
• weighted mean of Lawrence and Savage (1966, phase shift), Pegg et al. (1970, beam-foil), …

Isotope shifts are nu(13C) - nu(12C) (and nu(14C) - nu(12C)); MHz values are unit conversions of shifts printed in cm^-1 or mK (1 cm^-1 = 29979.2458 MHz) and carry a 'derived' note, with the printed number kept in value_cm / value_mK. 12C has I = 0 (no hyperfine structure); 13C has I = 1/2, so only magnetic-dipole A constants exist. The 609 um / 370 um ground-term lines are outside the site's range; their frequencies are kept only under additional_isotope_data because they fix the 13C level positions. g_J values refer to 12C. Non-schema fields: J, lower_J/upper_J, alternatives, value_cm, value_mK, wavelength_air_A, top-level ionization_energy, additional_isotope_data, conflicts. Second pass (2026-10-01): A_s values from Goldbach & Nollez (1987) and Goldbach et al. (1989) were read from the scanned pages on NASA ADS (image checked by eye, not only the character recognition); they are wall-stabilised-arc emission measurements whose absolute scale rests on the mean measured lifetime of the 2s2p3 3D° term, blended lines were left out. Lifetimes of 3s 3P° and 2s2p3 3D° are term values copied to each J level. The ground-term M1 lines 3P0-3P1 and 3P1-3P2 now have schema entries (frequency_THz for 12C, frequency_THz_13 for the 13C hyperfine centre of gravity); the older additional_isotope_data block is kept unchanged. The two-photon entry carries the laser wavelength in wavelength_vac_nm. Owner's rule (2026-10-01): measurements older than 20 years do not replace NIST; the 1987/1989 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-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