Rubidium-87 energy level diagram

Energy levels and transitions of neutral ⁸⁷Rb (Rb I, nuclear spin I = 3/2): 36 levels and 94 lines below 2 µm, each with its vacuum wavelength, frequency and, for 92 of them, the reduced dipole matrix element. Level energies come from the NIST Atomic Spectra Database; transition rates are 77 theory, 11 NIST, 4 measured.

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 ⁸⁷Rb

λ and ν from NIST level energies (centre of gravity, no hyperfine structure); λ air uses standard air (Ciddor). Γ/2π: natural linewidth of the upper level, 1/(2πτ). Branch: share of the upper level's decays that takes this line.

Rydberg excitation wavelengths (vacuum, nm)

Rydberg term energies from pairinteraction, lower level from NIST. d₇₀ = |⟨J‖er‖J′⟩| to n = 70 in ea₀ (calculated). S → nP values come from a near-cancelling integral: treat them as an order of magnitude.

⁸⁷Rb hyperfine structure (I = 3/2)

A, B: magnetic-dipole and electric-quadrupole constants (measured; see data file for sources).

Closed and nearly closed transitions of ⁸⁷Rb

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 ⁸⁷Rb 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.

⁸⁷Rb energy levels

Rb⁺ ionisation limit 33690.81 cm⁻¹ = 4.17713 eV = 1010.025 THz (296.817 nm)

Sources

• ARC (sum of calculated rates, 0 K)
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table V; origina…
• Herold, Vaidya, Li, Rolston, Porto, Safronova, Phys. Rev. Lett. 109, 243003 (2012) (light…
• NIST ASD A = 1.37e+05 s^-1
• NIST ASD A = 2.01e+04 s^-1
• NIST ASD A = 2.89e+05 s^-1
• NIST ASD A = 2.95e+06 s^-1
• NIST ASD A = 3.38e+04 s^-1
• NIST ASD A = 3.71e+06 s^-1
• NIST ASD A = 3.84e+04 s^-1
• NIST ASD A = 3.96e+05 s^-1
• NIST ASD A = 6.3e+05 s^-1
• NIST ASD A = 6.4e+04 s^-1
• NIST ASD A = 8.91e+04 s^-1
• NIST ASD level energies
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011) (all-order theory), as listed in th…
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011), Table IV, column "Present" (relati…
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011), Table IV; original: Ekers, Glodz, …
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011), Table IV; original: Gomez, Aubin, …
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011), Table IV; original: Gomez, Baumer,…
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011), Table IV; original: Lundberg & Sva…
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011), Table IV; original: Marek & Munste…
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011), Table IV; original: experimental v…
• Safronova & Safronova, Phys. Rev. A 83, 052508 (2011), Table IV; original: van Wijngaarde…
• Sheng, Perez Galvan, Orozco, Phys. Rev. A 78, 062506 (2008)
• Steck, Rubidium 87 D Line Data, rev. 2.3.4 (8 Aug 2025), Table 3 (hyperfine centre of gra…
• Steck, Rubidium 87 D Line Data, rev. 2.3.4 (8 Aug 2025), Table 4 (hyperfine centre of gra…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), read 2026-1…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), read 2026-1…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), read 2026-1…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), read 2026-1…
• pairinteraction

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
• 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