Potassium-40 energy level diagram

Energy levels and transitions of neutral ⁴⁰K (K I, nuclear spin I = 4): 34 levels and 84 lines below 2 µm, each with its vacuum wavelength, frequency and, for 80 of them, the reduced dipole matrix element. Level energies come from the NIST Atomic Spectra Database; transition rates are 77 NIST, 5 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 ⁴⁰K

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.

⁴⁰K hyperfine structure (I = 4)

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

Closed and nearly closed transitions of ⁴⁰K

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 ⁴⁰K 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.

⁴⁰K energy levels

K⁺ ionisation limit 35009.81 cm⁻¹ = 4.34066 eV = 1049.568 THz (285.634 nm)

Sources

• ARC (sum of calculated rates, 0 K)
• ARC model potential
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table III; 'Reco…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table III; from …
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table III; origi…
• Allegrini, Arimondo, Orozco, J. Phys. Chem. Ref. Data 51, 043102 (2022), Table III; origi…
• Falke, Sherstov, Tiemann, Lisdat, J. Chem. Phys. 125, 224303 (2006), abstract (from the l…
• Gallagher & Cooke, Phys. Rev. A 20, 670 (1979), abstract (time-resolved laser-induced flu…
• Glodz, Huzandrov, Safronova, Sydoryk, Szonert, Klavins, Phys. Rev. A 77, 022503 (2008), a…
• Glodz, Huzandrov, Safronova, Sydoryk, Szonert, Klavins, Phys. Rev. A 77, 022503 (2008), a…
• Mills, Behr, Courneyea, Pearson, Phys. Rev. A 72, 024501 (2005), abstract as given by OST…
• NIST ASD
• NIST ASD A = 1.04e+06 s^-1
• NIST ASD A = 1.07e+06 s^-1
• NIST ASD A = 1.12e+06 s^-1
• NIST ASD A = 1.14e+05 s^-1
• NIST ASD A = 1.15e+05 s^-1
• NIST ASD A = 1.15e+06 s^-1
• NIST ASD A = 1.19e+06 s^-1
• NIST ASD A = 1.22e+04 s^-1
• NIST ASD A = 1.24e+05 s^-1
• NIST ASD A = 1.27e+04 s^-1
• NIST ASD A = 1.2e+04 s^-1
• NIST ASD A = 1.31e+04 s^-1
• NIST ASD A = 1.31e+06 s^-1
• NIST ASD A = 1.37e+04 s^-1
• NIST ASD A = 1.37e+05 s^-1
• NIST ASD A = 1.45e+05 s^-1
• NIST ASD A = 1.46e+07 s^-1
• NIST ASD A = 1.58e+07 s^-1
• NIST ASD A = 1.62e+04 s^-1
• NIST ASD A = 1.65e+05 s^-1
• NIST ASD A = 1.67e+04 s^-1
• NIST ASD A = 1.6e+03 s^-1
• NIST ASD A = 1.78e+05 s^-1
• NIST ASD A = 1.91e+06 s^-1
• NIST ASD A = 1.99e+05 s^-1
• NIST ASD A = 1.9e+04 s^-1
• NIST ASD A = 2.17e+05 s^-1
• NIST ASD A = 2.29e+05 s^-1
• NIST ASD A = 2.2e+04 s^-1
• NIST ASD A = 2.35e+06 s^-1
• NIST ASD A = 2.4e+03 s^-1
• NIST ASD A = 2.5e+06 s^-1
• NIST ASD A = 2.7e+03 s^-1
• NIST ASD A = 2.86e+05 s^-1
• NIST ASD A = 2.97e+05 s^-1
• NIST ASD A = 260 s^-1
• NIST ASD A = 3.21e+06 s^-1
• NIST ASD A = 3.39e+05 s^-1
• NIST ASD A = 3.51e+05 s^-1
• NIST ASD A = 3.71e+05 s^-1
• NIST ASD A = 3.86e+05 s^-1
• NIST ASD A = 4.07e+05 s^-1
• NIST ASD A = 4.08e+05 s^-1
• NIST ASD A = 4.16e+05 s^-1
• NIST ASD A = 4.22e+05 s^-1
• NIST ASD A = 4.35e+05 s^-1
• NIST ASD A = 4.36e+05 s^-1
• NIST ASD A = 4.47e+05 s^-1
• NIST ASD A = 4.55e+04 s^-1
• NIST ASD A = 4.77e+04 s^-1
• NIST ASD A = 4.86e+05 s^-1
• NIST ASD A = 4.96e+06 s^-1
• NIST ASD A = 4e+04 s^-1
• NIST ASD A = 5.01e+04 s^-1
• NIST ASD A = 5.23e+04 s^-1
• NIST ASD A = 5.69e+05 s^-1
• NIST ASD A = 5.7e+04 s^-1
• NIST ASD A = 5.87e+05 s^-1
• NIST ASD A = 6.13e+04 s^-1
• NIST ASD A = 6.1e+06 s^-1
• NIST ASD A = 6.62e+05 s^-1
• NIST ASD A = 690 s^-1
• NIST ASD A = 7.01e+04 s^-1
• NIST ASD A = 7.24e+04 s^-1
• NIST ASD A = 7.8e+04 s^-1
• NIST ASD A = 7.95e+06 s^-1
• NIST ASD A = 8.06e+05 s^-1
• NIST ASD A = 8.1e+04 s^-1
• NIST ASD A = 8e+05 s^-1
• NIST ASD level energies
• Safronova, Safronova, Clark, 'Laser cooling and trapping of potassium at magic wavelength…
• Safronova, Safronova, Clark, 'Laser cooling and trapping of potassium at magic wavelength…
• Safronova, Safronova, Clark, 'Laser cooling and trapping of potassium at magic wavelength…
• Tiecke, Properties of Potassium, v1.03 (2019), Table 5 (hyperfine centre of gravity); ori…
• Tiecke, Properties of Potassium, v1.03 (2019), Table 6 (hyperfine centre of gravity); ori…
• 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…

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-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