Tin energy level diagram

Energy levels and transitions of neutral tin (Sn I): the 51 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 29 levels they connect, each line with its vacuum wavelength, frequency and, for 51 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 tin

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).

¹¹⁹Sn hyperfine structure (I = 1/2)

Measured A, B constants; sources in the data file.

Isotope shifts

Shift = ν(first isotope) − ν(second isotope).

Closed and nearly closed transitions of tin

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 Sn 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, this site's own Cowan-code calculation with the parameters fitted to the NIST energies (HFR fit; inputs and fit report in the repository folder cowan/; used only where nothing else gives a rate; strong lines typically within a factor 2, weak lines worse), or a model calculation.

Sn energy levels

Sn⁺ ionisation limit 59232.69 cm⁻¹ = 7.34392 eV (168.826 nm)

Sources

• Childs, Goodman, Phys. Rev. 137, A35 (1965) (atomic-beam magnetic resonance; values read …
• Childs, Phys. Rev. A 4, 439 (1971) (atomic-beam magnetic resonance; values read in the ab…
• Holmgren, Svanberg, Phys. Scr. 5, 135 (1972) (Hanle / zero-field level crossing on an ato…
• NIST ASD
• NIST ASD level energies
• Yordanov et al., Commun. Phys. 3, 107 (2020) "Structural trends in atomic nuclei from las…
• Zhang, Feng, Xu, Dai, Palmeri, Quinet, Biémont, J. Phys. B 43, 205005 (2010), Table 1 (ti…
• Zhang, Xu, Zhang, You, Ma, Han, Li, Sun, Jiang, Enzonga Yoca, Quinet, Biémont, Dai, Phys.…
• Zheng, Wang, Verma, Wang, Langin, DeMille, "Simulated Laser Cooling and Magneto-Optical T…

Isotope shifts are nu(first) - nu(second), kept relative to the reference isotope each source used (112Sn for Baird 1983 and the CRIS lines, 124Sn for the COLLAPS lines). For Gustafsson et al. "unc" is statistical and "unc_syst" systematic; only the stable isotopes 112-124 were transcribed (the table continues from 104Sn to 134Sn). 115Sn, 117Sn, 119Sn have I = 1/2, so there are no B constants; all A values are negative for 5p6s 3P°1 and 5p2 3P2/1D2 and positive for 5p2 3P1 (negative nuclear moments). Lifetime entries: Zhang et al. 2010 (time-resolved LIF, 38 odd levels 43682-56839 cm-1) for 5p5d, 5pns (n>=7), 5pnd; Holmgren & Svanberg 1972 (Hanle) for the three 5p6s levels - their paper was read only as the abstract on the Lund University portal; Zhang et al. 2008 for 5p7p (two-step excitation), which also gives Zeeman quantum-beat g_J factors. Older and conflicting values are under lifetime.alternatives. Zhang et al. print energies from Moore / Brown et al.; they were matched to the NIST energies by J and nearest energy (differences up to 0.6 cm-1 for the 5p7p levels, below 0.06 cm-1 otherwise). Ground-term (5p2) metastable lifetimes and linewidths are THEORY (Biémont et al. 1995 rates as tabulated by Zheng et al. 2026) and flagged as such. Extra fields beyond SCHEMA.md: ionization_limit, lifetime.alternatives, hyperfine.<A>.alternatives, isotope_shift_other, linewidth_Hz / linewidth_MHz, unc_syst, note. Level-wise comparison with NIST: the NIST Sn I A values are all from th

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