Copper energy level diagram

Energy levels and transitions of neutral copper (Cu I): the 31 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 23 levels they connect, each line with its vacuum wavelength, frequency and, for 29 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 copper

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).

⁶³Cu 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 copper

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 Cu 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.

Cu energy levels

Cu⁺ ionisation limit 62317.46 cm⁻¹ = 7.72638 eV (160.469 nm)

Sources

• Ankush, Deo, J. Quant. Spectrosc. Radiat. Transfer 134, 21 (2014), as tabulated in Popov,…
• Bengtsson, Larsson, Svanberg, Wahlstrom, Phys. Rev. A 41, 233 (1990), abstract (pulsed le…
• Bergstrom, Peng, Persson, Z. Phys. D 13, 203 (1989), as tabulated in Popov, Sushkov, Zayt…
• Carlsson, Sturesson, Svanberg, Z. Phys. D 11, 287 (1989), abstract
• Carlsson, Sturesson, Svanberg, Z. Phys. D 11, 287 (1989), abstract (delayed-coincidence p…
• Carlsson, Sturesson, Svanberg, Z. Phys. D 11, 287 (1989), abstract (lifetime) combined wi…
• Cocolios et al., "Magnetic dipole moment of 57,59Cu measured by in-gas-cell laser spectro…
• Dzuba, Allehabi, Flambaum, Li, Schiller, Phys. Rev. A 103, 022822 (2021), Table I (CIPT; …
• Dzuba, Allehabi, Flambaum, Li, Schiller, Phys. Rev. A 103, 022822 (2021), Table I (CIPT; …
• Dzuba, Allehabi, Flambaum, Li, Schiller, Phys. Rev. A 103, 022822 (2021), Table II (E2, C…
• Dzuba, Allehabi, Flambaum, Li, Schiller, Phys. Rev. A 103, 022822 (2021), Table II (M1 on…
• Dzuba, Allehabi, Flambaum, Li, Schiller, Phys. Rev. A 103, 022822 (2021), Table IV (value…
• Kowalski, zu Putlitz, Z. Phys. 208, 459 (1968), abstract (optical double resonance on the…
• NIST ASD
• NIST ASD level energies
• R. L. Kurucz, hyperfine data file ab290063.dat (compilation; A, B in MHz, no uncertaintie…
• R. L. Kurucz, hyperfine data file ab290063.dat (compilation; A, B in MHz, no uncertaintie…
• R. L. Kurucz, hyperfine data file ab290063.dat (compilation; A, B in MHz, no uncertaintie…
• R. L. Kurucz, hyperfine data file ab290063.dat (compilation; A, B in MHz, no uncertaintie…
• Ting, Lew, Phys. Rev. 105, 581 (1957), abstract (hyperfine splitting 11733.83(1) Mc/s; th…
• Vingerhoets et al., Phys. Rev. C 82, 064311 (2010), Table II (collinear laser spectroscop…

Both stable isotopes have I = 3/2. Ground-state A is derived from the directly measured hyperfine splitting (Delta nu = 2A). The 3d9 4s4p 4P3/2 level (40114.01 cm^-1) is included because the 249.2 nm line carries the only isotope shift that could be sourced. A_s / rme_J_ea0 for the two resonance lines are derived from the Carlsson et al. 1989 lifetimes after subtracting the weak 2P-2D branches with NIST A values (notes say 'derived'); all other A_s entries are CIPT theory from Dzuba et al. 2021 for the E2/M1 lines NIST does not list; no theory is entered for the 2P-2D E1 lines because NIST has measured A values. rme convention: A = 2.02613e18 |d|^2 / (lambda_vac[Angstrom]^3 (2J'+1)), J' the upper level. The two copper-vapour-laser lines are 3d10 4p 2P3/2 -> 3d9 4s2 2D5/2 (510.6 nm) and 2P1/2 -> 2D3/2 (578.2 nm); the E2 clock lines are 2S1/2-2D5/2 at 892.6 nm and 2S1/2-2D3/2 at 755.0 nm. Extra keys beyond the schema: ionization_energy, g_J_ratio_to_Cs133, hyperfine_anomaly_percent, E2_amplitude_au, lifetime_alternatives. Second pass: hyperfine constants marked "Kurucz" are read from R. L. Kurucz's Cu I hyperfine input files (uncertainty-free, second-hand; entries whose reference code there is LLLcalc are calculations and carry method "theory"). Isotope shifts of the 510.6, 515.3 and 521.8 nm lines are second-hand from Popov et al. (arXiv:1907.02920) with the sign converted to nu(63) - nu(65). Added levels not drawn on the site: 4P5/2, 4F9/2 (metastable, atomic-beam hyperfine d

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