Mercury-199 energy level diagram

Energy levels and transitions of neutral ¹⁹⁹Hg (Hg I, nuclear spin I = 1/2): the 47 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 27 levels they connect, each line with its vacuum wavelength, frequency and, for 46 of them, the reduced dipole matrix element. Level energies come from NIST and refer to the natural isotope mixture; transition rates are 43 NIST, 3 measured, 1 HFR fit (this site). Hyperfine constants and measured frequencies are those of this isotope.

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 ¹⁹⁹Hg

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).

Isotope shifts

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

Closed and nearly closed transitions of ¹⁹⁹Hg

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 ¹⁹⁹Hg 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.

¹⁹⁹Hg energy levels

Hg⁺ ionisation limit 84184.15 cm⁻¹ = 10.43750 eV (118.787 nm)

Sources

• Gravina, Clivati, Castrillo, Fasci, Chishti, Galzerano, Levi, Gianfrani, 'Measurement of …
• Margolis et al., 'The CIPM list Recommended values of standard frequencies: 2021 update',…
• Mosburg & Wilke, 'Some new transition probabilities for mercury I', J. Quant. Spectrosc. …
• Mosburg & Wilke, 'Some new transition probabilities for mercury I', J. Quant. Spectrosc. …
• NIST ASD
• NIST ASD level energies
• Porsev, Safronova, Safronova, 'A theoretical study of the g-factor and lifetime of the 6s…
• Porsev, Safronova, Safronova, 'A theoretical study of the g-factor and lifetime of the 6s…
• This site: Cowan-code HFR calculation of Hg I with the parameters fitted to the NIST ener…

Conventions. (1) Isotope-shift keys 'a-b' mean nu(a) - nu(b); the 253.7 nm and 313 nm shifts are relative to 198Hg as printed. 199Hg / 201Hg shifts of the 253.7 nm line are hyperfine centres of gravity corrected by Schelfhout & McFerran for the second-order hyperfine interaction. (2) Clock frequencies exceed double precision: use value_Hz_str / unc_Hz. frequency_THz_<A> carries further isotopes. (3) Fields beyond SCHEMA.md: natural_linewidth_*, hyperfine_component_frequencies, frequency_ratios, magic_frequency_MHz, g_factor_<A>Hg (g of the J=0 clock state, x1 not x1e3), top-level 'rydberg' (ionization limit) and 'conflicts'. (4) A_s, linewidth and rme_J_ea0 of the 253.7 nm line are derived here from the measured lifetime (schema convention, single decay channel). (5) Only the 201Hg magnetic hyperfine constants could be sourced; the 199Hg values are missing (see not_found).

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-20127 levels, 47 lines
• Mercury-20227 levels, 47 lines

All elements: periodic table