Tungsten energy level diagram

Energy levels and transitions of neutral tungsten (W I): the 90 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 69 levels they connect, each line with its vacuum wavelength, frequency and, for 90 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 tungsten

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).

¹⁸³W 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 tungsten

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 W 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.

W energy levels

W⁺ ionisation limit 63427.70 cm⁻¹ = 7.86403 eV (157.660 nm)

Sources

• Büttgenbach, Dicke, Träber, Phys. Rev. A 19, 1383 (1979), as quoted in Table 1 of Lee, Ch…
• Den Hartog, Duquette, Lawler, J. Opt. Soc. Am. B 4, 48 (1987), Table 2
• Lee, Chen, Leanhardt, arXiv:1212.5718 (2012), Table 1
• NIST ASD
• NIST ASD level energies
• branching ratio / lifetime

Lifetimes, branching ratios and A values: Den Hartog, Duquette, Lawler 1987 (39 levels). The table was read through the publisher's HTML table view with a page reader, not from the PDF; each row was verified numerically (gA = (2J+1) BR / tau reproduces the printed gA within rounding for every entered line), J values and level energies are taken from the NIST file. A_s is gA/(2J+1) (derived). Rows printed as upper limits ('<', blended lines) were skipped, so the entered branching ratios of 25983.60 and 27488.11 do not sum to 1. NIST ASD already lists A values from the same paper (tp_ref T4976); what is new here is lifetimes, branching ratios and uncertainties. Isotope shifts are nu(heavier) - nu(lighter); 183W shifts are for the hyperfine centre of gravity. 183W has I = 1/2: only A constants exist. No laser-cooling transition is known for W.

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