Sodium-23 energy level diagram

Energy levels and transitions of neutral ²³Na (Na I, nuclear spin I = 3/2): 36 levels and 106 lines below 2 µm, each with its vacuum wavelength, frequency and, for 88 of them, the reduced dipole matrix element. Level energies come from the NIST Atomic Spectra Database; transition rates are 102 NIST, 2 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 ²³Na

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.

²³Na 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 ²³Na

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 ²³Na 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.

²³Na energy levels

Na⁺ ionisation limit 41449.45 cm⁻¹ = 5.13908 eV = 1242.623 THz (241.258 nm)

Sources

• ARC (sum of calculated rates, 0 K)
• ARC model potential
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; 'Recom…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; 'Recom…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; 'Recom…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; 'Recom…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; 'Recom…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; from A…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; origin…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; origin…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; origin…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; origin…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; origin…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; weight…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; weight…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; weight…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table II; weight…
• Burghardt, Hoffmann, Meisel, Z. Phys. D 8, 109 (1988), abstract as given by OSTI ETDEWEB:…
• Kandela, Appl. Opt. 23, 2152 (1984), abstract (stepwise laser excitation of a fast beam; …
• Kandela, Appl. Opt. 23, 2152 (1984), abstract (stepwise laser excitation of a fast beam; …
• NIST ASD
• NIST ASD A = 1.01e+07 s^-1
• NIST ASD A = 1.08e+06 s^-1
• NIST ASD A = 1.14e+06 s^-1
• NIST ASD A = 1.17e+06 s^-1
• NIST ASD A = 1.18e+06 s^-1
• NIST ASD A = 1.21e+07 s^-1
• NIST ASD A = 1.23e+06 s^-1
• NIST ASD A = 1.25e+05 s^-1
• NIST ASD A = 1.29e+06 s^-1
• NIST ASD A = 1.31e+07 s^-1
• NIST ASD A = 1.49e+05 s^-1
• NIST ASD A = 1.59e+03 s^-1
• NIST ASD A = 1.76e+05 s^-1
• NIST ASD A = 1.76e+07 s^-1
• NIST ASD A = 1.81e+05 s^-1
• NIST ASD A = 1.84e+05 s^-1
• NIST ASD A = 1.93e+03 s^-1
• NIST ASD A = 177 s^-1
• NIST ASD A = 2.02e+06 s^-1
• NIST ASD A = 2.08e+06 s^-1
• NIST ASD A = 2.18e+06 s^-1
• NIST ASD A = 2.21e+05 s^-1
• NIST ASD A = 2.25e+05 s^-1
• NIST ASD A = 2.27e+06 s^-1
• NIST ASD A = 2.44e+05 s^-1
• NIST ASD A = 2.49e+06 s^-1
• NIST ASD A = 2.5e+06 s^-1
• NIST ASD A = 2.61e+06 s^-1
• NIST ASD A = 2.73e+06 s^-1
• NIST ASD A = 2.75e+06 s^-1
• NIST ASD A = 2.97e+05 s^-1
• NIST ASD A = 281 s^-1
• NIST ASD A = 3.13e+05 s^-1
• NIST ASD A = 3.5e+05 s^-1
• NIST ASD A = 3.76e+05 s^-1
• NIST ASD A = 31.2 s^-1
• NIST ASD A = 354 s^-1
• NIST ASD A = 4.09e+06 s^-1
• NIST ASD A = 4.29e+07 s^-1
• NIST ASD A = 4.33e+04 s^-1
• NIST ASD A = 4.35e+04 s^-1
• NIST ASD A = 4.38e+06 s^-1
• NIST ASD A = 4.46e+04 s^-1
• NIST ASD A = 4.4e+04 s^-1
• NIST ASD A = 4.7e+03 s^-1
• NIST ASD A = 4.88e+06 s^-1
• NIST ASD A = 4.98e+06 s^-1
• NIST ASD A = 5.14e+07 s^-1
• NIST ASD A = 5.31e+05 s^-1
• NIST ASD A = 5.38e+05 s^-1
• NIST ASD A = 5.3e+04 s^-1
• NIST ASD A = 5.42e+04 s^-1
• NIST ASD A = 5.65e+03 s^-1
• NIST ASD A = 5.85e+05 s^-1
• NIST ASD A = 5.92e+05 s^-1
• NIST ASD A = 522 s^-1
• NIST ASD A = 6.19e+05 s^-1
• NIST ASD A = 6.29e+05 s^-1
• NIST ASD A = 604 s^-1
• NIST ASD A = 67.2 s^-1
• NIST ASD A = 7.24e+05 s^-1
• NIST ASD A = 7.32e+05 s^-1
• NIST ASD A = 7.5e+05 s^-1
• NIST ASD A = 7.96e+04 s^-1
• NIST ASD A = 748 s^-1
• NIST ASD A = 8.13e+04 s^-1
• NIST ASD A = 8.45e+04 s^-1
• NIST ASD A = 8.53e+04 s^-1
• NIST ASD A = 8.57e+06 s^-1
• NIST ASD A = 8.65e+04 s^-1
• NIST ASD A = 8.8e+06 s^-1
• NIST ASD A = 9.35e+05 s^-1
• NIST ASD A = 9.72e+04 s^-1
• NIST ASD A = 9.91e+04 s^-1
• NIST ASD level energies
• Steck, Sodium D Line Data (steck.us/alkalidata), Table 3 (computed there from the vacuum …
• Steck, Sodium D Line Data (steck.us/alkalidata), Table 3: weighted mean of Volz et al. 19…
• Steck, Sodium D Line Data (steck.us/alkalidata), Table 4 (computed there from the vacuum …
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group; data service…
• Volz, Majerus, Liebel, Schmitt, Schmoranzer, Phys. Rev. Lett. 76, 2862 (1996), abstract (…

Atoms with measured data

• Lithium-632 levels, 85 lines
• Lithium-732 levels, 85 lines
• Beryllium-917 levels, 26 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