Barium-137 energy level diagram

Energy levels and transitions of neutral ¹³⁷Ba (Ba I, nuclear spin I = 3/2): 44 levels and 89 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 80 NIST, 8 measured, 1 theory. Neutral barium is also the starting point for loading Ba⁺ ion traps by photoionisation.

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Download: diagram (PDF) diagram (SVG) transitions (CSV) levels (CSV) source code

Key transitions of ¹³⁷Ba

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).

¹³⁷Ba 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 ¹³⁷Ba

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 ¹³⁷Ba 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, a semi-empirical calculation (Kurucz line list, used only where no measurement or NIST value exists; typically within a factor 2), or a model calculation.

¹³⁷Ba energy levels

Ba⁺ ionisation limit 42034.91 cm⁻¹ = 5.21166 eV (237.897 nm)

Sources

• Bizzarri & Huber, Phys. Rev. A 42, 5422 (1990), as tabulated in De, Dammalapati, Jungmann…
• Brink, Glassman, Gupta, Opt. Commun. 33, 17 (1980), Hanle effect (abstract). CONFLICT: th…
• Brust & Gallagher, Phys. Rev. A 52, 2120 (1995), as tabulated in S. De, PhD thesis 'Laser…
• De, Dammalapati, Jungmann, Willmann, Phys. Rev. A 79, 041402(R) (2009) [arXiv:0807.4100],…
• Dzuba & Flambaum, J. Phys. B 40, 227 (2007) [arXiv:physics/0610119], Table 1
• Dzuba & Ginges, Phys. Rev. A 73, 032503 (2006) [arXiv:physics/0511199], Table V
• Dzuba & Ginges, Phys. Rev. A 73, 032503 (2006) [arXiv:physics/0511199], Table V (E2 decay…
• G. zu Putlitz, Ann. Phys. 11, 248 (1963), optical double resonance; F-level shifts from c…
• Grundevik, Gustavsson, Olsson, Olsson, Z. Phys. A 312, 1 (1983), as quoted in Choi, Lee, …
• Gustavsson, Olsson, Rosen, Z. Phys. A 290, 231 (1979), atomic-beam magnetic resonance (ab…
• Migdalek & Baylis, Phys. Rev. A 42, 6897 (1990), as quoted in Dammalapati, De, Jungmann, …
• NIST ASD
• NIST ASD level energies
• Niggli & Huber (1987), as tabulated in De, Dammalapati, Jungmann, Willmann, Phys. Rev. A …
• Niggli & Huber, Phys. Rev. A 35, 2908 (1987), as tabulated (with experimental error) in S…
• Niggli & Huber, Phys. Rev. A 35, 2908 (1987), as tabulated (with experimental error) in S…
• Niggli & Huber, Phys. Rev. A 35, 2908 (1987), as tabulated in De, Dammalapati, Jungmann, …
• Schmelling, Phys. Rev. A 9, 1097 (1974) (abstract)
• Scielzo et al., Phys. Rev. A 73, 010501(R) (2006) (abstract)
• experimental value quoted in Dzuba & Ginges, Phys. Rev. A 73, 032503 (2006) [arXiv:physic…
• van Wijngaarden & Li, Can. J. Phys. 73, 484 (1995) (abstract)

Isotope shifts are nu(first) - nu(second); several sources print nu(138) - nu(A), signs were converted (138Ba lies lowest in frequency on 553.7, 791 and 413 nm). Level energies/wavelengths are NIST vacuum values; papers label the lines 553.7, 791.3 (vac) / 791.1 (air), 413.3, 659.7, 667.7, 1107.8, 1130.6, 1500.4 nm. method='compilation' means the number was read in a later paper/thesis table that names the original experiment (given in source); 'derived': true marks values computed here from printed numbers (3P1 A/B from F-level shifts; 791 nm frequency from an iodine offset). All lifetimes with method 'theory' are CI+MBPT calculations printed without uncertainty; lifetimes credited to Niggli & Huber 1987 are obtained from emission branching fractions combined with published lifetimes/absorption data (per their abstract), as tabulated in De's thesis. A_s values for lines NIST already lists (553.7, 1107.9, 1130.6, 791.4, 413.4, 659.7, 667.7 nm) are repeated only because the source gives an uncertainty or a newer measurement. Hyperfine sign convention: E_F = A*K/2 + B*[3K(K+1)/4 - I(I+1)J(J+1)]/[2I(2I-1)J(2J-1)], K = F(F+1)-I(I+1)-J(J+1). Extra keys beyond SCHEMA.md: 'ionization', 'conflicts', 'derived', 'note', 'F_shifts_from_centroid_MHz', 'hyperfine_component_shifts_MHz', 'photons_before_leak', 'abundance_unc', 'url_spin'.

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-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