Sulfur energy level diagram

Energy levels and transitions of neutral sulfur (S I): the 81 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 47 levels they connect, each line with its vacuum wavelength, frequency and, for 74 of them, the reduced dipole matrix element derived from the NIST transition rate. Measured lifetimes, transition rates, hyperfine constants and isotope shifts from the literature are included, each with its citation.

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 sulfur

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).

³³S 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 sulfur

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.

Listed S 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.

S energy levels

S⁺ ionisation limit 83559.17 cm⁻¹ = 10.36002 eV (119.676 nm)

Sources

• Beideck, Schectman, Federman, Ellis, Astrophys. J. 428, 393 (1994), beam-foil spectroscop…
• Beideck, Schectman, Federman, Ellis, Astrophys. J. 428, 393 (1994), beam-foil spectroscop…
• Beideck, Schectman, Federman, Ellis, Astrophys. J. 428, 393 (1994), beam-foil spectroscop…
• Beideck, Schectman, Federman, Ellis, Astrophys. J. 428, 393 (1994), beam-foil spectroscop…
• Berzinsh, Luo Caiyan, Zerne, Svanberg, Biemont, Phys. Rev. A 55, 1836 (1997), time-resolv…
• Biemont, Garnir, Federman, Li, Svanberg, Astrophys. J. 502, 1010 (1998), Table 1 (entries…
• Biemont, Garnir, Federman, Li, Svanberg, Astrophys. J. 502, 1010 (1998), Table 1 (entries…
• Biemont, Garnir, Federman, Li, Svanberg, Astrophys. J. 502, 1010 (1998), Table 2, column …
• Carette & Godefroid, J. Phys. B 44, 105001 (2011), arXiv:1101.5645, MCHF/CI with relativi…
• Delalic, Erman, Kallne, Phys. Scr. 42, 540 (1990), high-frequency deflection technique; v…
• Kurucz, R. L., Can. J. Phys. 89, 417 (2011); semi-empirical line list gf1600.pos of 2011-…
• Lai, Salumbides, Ubachs, J. Phys. B 53, 175002 (2020), arXiv:2006.11322, Doppler-free two…
• NIST ASD
• NIST ASD S I lines table (tp_ref T8595,T7942c84), local cache data/nist/S_I_lines_from1nm…
• NIST ASD S I lines table (tp_ref T8595,T7942c84), local cache data/nist/S_I_lines_from1nm…
• NIST ASD level energies
• Savage & Lawrence, Astrophys. J. 146, 940 (1966), phase-shift method, Table 1 (3p4 1D - 4…
• Savage & Lawrence, Astrophys. J. 146, 940 (1966), phase-shift method, Table 1: line 1687.…
• Savage & Lawrence, Astrophys. J. 146, 940 (1966), phase-shift method, Table 1; lifetime o…
• Zatsarinny & Bartschat, J. Phys. B 39, 2861 (2006), B-spline R-matrix calculation; level-…
• Zerne, Luo Caiyan, Berzinsh, Svanberg, Phys. Scr. 56, 459 (1997), two-photon UV excitatio…
• Zerne, Luo Caiyan, Berzinsh, Svanberg, Phys. Scr. 56, 459 (1997), two-photon UV excitatio…
• relativistic Hartree-Fock, Biemont, Garnir, Federman, Li, Svanberg, Astrophys. J. 502, 10…

Level energies are the NIST ASD values (data/nist/S_I_levels.tsv). Uncertainties copied from Biemont et al. 1998 Table 1 are 2 sigma ('b represents a 2 sigma uncertainty'); Beideck et al. 1994 uncertainties are 1 sigma as printed in the original (Biemont et al. list them doubled). Lifetimes attributed to Berzinsh et al. 1997, Delalic et al. 1990, Bridges & Wiese, Smith 1978, Mueller 1968, Federman & Cardelli 1995 are second-hand (method 'compilation'). The Federman & Cardelli 'lifetimes' are inferred from interstellar absorption f-values, not laboratory lifetimes. Savage & Lawrence values are multiplet lifetimes attached to each fine-structure level. A-values of the 3P - ns 3S°, nd 3D° lines from Biemont et al. are semi-empirical (measured lifetime x calculated branching ratio); they are close to what NIST ASD already lists. 'f_abs' (absorption oscillator strength) is a non-schema field; type 'two-photon' is used for the Doppler-free two-photon lines (frequency = total energy of both photons). 32S and 34S have I = 0; 33S has I = 3/2. Lifetimes of 1D2 and 1S0 are derived from calculated A-values (theory).

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-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