Caesium-133 energy level diagram

Energy levels and transitions of neutral ¹³³Cs (Cs I, nuclear spin I = 7/2): 31 levels and 79 lines below 2 µm, each with its vacuum wavelength, frequency and, for 75 of them, the reduced dipole matrix element. Level energies come from the NIST Atomic Spectra Database; transition rates are 60 theory, 9 measured, 7 NIST.

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 ¹³³Cs

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 ARC quantum defects + NIST ionisation limit, 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.

¹³³Cs hyperfine structure (I = 7/2)

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

Closed and nearly closed transitions of ¹³³Cs

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 ¹³³Cs 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.

¹³³Cs energy levels

Cs⁺ ionisation limit 31406.47 cm⁻¹ = 3.89391 eV = 941.542 THz (318.406 nm)

Sources

• ARC model potential
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table VII; origi…
• Damitz, Toh, Putney, Tanner, Elliott, Phys. Rev. A 99, 062510 (2019)
• NIST ASD
• NIST ASD A = 1.43e+05 s^-1
• NIST ASD A = 2.2e+04 s^-1
• NIST ASD A = 3.9e+05 s^-1
• NIST ASD A = 6.3e+03 s^-1
• NIST ASD A = 6.3e+04 s^-1
• NIST ASD A = 9e+04 s^-1
• NIST ASD level energies
• Patterson, Sell, Ehrenreich, Gearba, Brooke, Scoville, Knize, Phys. Rev. A 91, 012506 (20…
• Pucher, Schneeweiss, Rauschenbeutel, Dareau, Phys. Rev. A 101, 042510 (2020)
• Safronova, Safronova, Clark, Phys. Rev. A 94, 012505 (2016), Table II, column "Recomm." (…
• Safronova, Safronova, Clark, Phys. Rev. A 94, 012505 (2016), Table II; original: DiBerard…
• Safronova, Safronova, Clark, Phys. Rev. A 94, 012505 (2016), Table II; original: Marek & …
• Safronova, Safronova, Clark, Phys. Rev. A 94, 012505 (2016), Table II; original: Marek & …
• Safronova, Safronova, Clark, Phys. Rev. A 94, 012505 (2016), Table II; original: Marek, J…
• Safronova, Safronova, Clark, Phys. Rev. A 94, 012505 (2016), Table II; original: Marek, P…
• Safronova, Safronova, Clark, Phys. Rev. A 94, 012505 (2016), Table II; original: Neil & A…
• Safronova, Safronova, Clark, Phys. Rev. A 94, 012505 (2016), Table II; original: Sieradza…
• Steck, Cesium D Line Data, rev. 2.3.4 (8 Aug 2025), Table 3 (hyperfine centre of gravity;…
• Steck, Cesium D Line Data, rev. 2.3.4 (8 Aug 2025), Table 4 (hyperfine centre of gravity;…
• Steck, Cesium D Line Data, rev. 2.3.4 (8 Aug 2025), Table 5 (exact: follows from the SI d…
• Toh, Chalus, Burgess, Damitz, Imany, Leaird, Weiner, Tanner, Elliott, Phys. Rev. A 100, 0…
• Toh, Chalus, Burgess, Damitz, Imany, Leaird, Weiner, Tanner, Elliott, Phys. Rev. A 100, 0…
• Toh, Chalus, Burgess, Damitz, Imany, Leaird, Weiner, Tanner, Elliott, Phys. Rev. A 100, 0…
• Toh, Damitz, Glotzbach, Quirk, Stevenson, Choi, Safronova, Elliott, Phys. Rev. A 99, 0325…
• Toh, Jaramillo-Villegas, Glotzbach, Quirk, Stevenson, Choi, Weiner, Elliott, Phys. Rev. A…
• 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…

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
• 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