Silicon energy level diagram

Energy levels and transitions of neutral silicon (Si I): the 79 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 44 levels they connect, each line with its vacuum wavelength, frequency and, for 79 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 silicon

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).

²⁹Si 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 silicon

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 Si 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.

Si energy levels

Si⁺ ionisation limit 65747.76 cm⁻¹ = 8.15168 eV (152.096 nm)

Sources

• Brown, Zink, Evenson, Astrophys. J. 423, L151 (1994), far-infrared laser magnetic resonan…
• Brown, Zink, Evenson, Astrophys. J. 423, L151 (1994), far-infrared laser magnetic resonan…
• Brown, Zink, Evenson, Astrophys. J. 423, L151 (1994), far-infrared laser magnetic resonan…
• Den Hartog, Lawler, Sneden, Roederer, Cowan, Astrophys. J. Suppl. Ser. 265, 42 (2023), ar…
• Lee & Fairbank, Phys. Rev. A 82, 042515 (2010), arXiv:1009.4961, laser-induced fluorescen…
• Lee & Fairbank, Phys. Rev. A 82, 042515 (2010), arXiv:1009.4961, laser-induced fluorescen…
• NIST ASD
• NIST ASD Si I lines table (tp_ref c22,T4209), local cache data/nist/Si_I_lines_from1nm.ts…
• NIST ASD Si I lines table, forbidden lines 1587.6, 1607.3, 1645.9 nm (tp_ref c22,T4209), …
• NIST ASD level energies
• O'Brian & Lawler, Phys. Rev. A 44, 7134 (1991), time-resolved laser-induced fluorescence …
• Pehlivan Rhodin, Hartman, Nilsson, Joensson, Astron. Astrophys. 682, A184 (2024), MCDHF/R…

Level energies are the NIST ASD values (data/nist/Si_I_levels.tsv). Lifetimes of O'Brian & Lawler are quoted at second hand (method 'compilation'). Den Hartog et al. 2023 A-values = their measured branching fractions / O'Brian & Lawler lifetimes, so they are not independent of the lifetimes; the 'branching' field is the measured branching fraction of that decay channel. rme_J_ea0 values are derived from A as described in each note. Isotope shifts are nu(heavier) - nu(28Si) as printed (positive = heavier isotope at higher frequency for the 221.7 nm line). 29Si has I = 1/2 (no quadrupole constant); the 29Si frequency of the 3P1-3P2 interval is the hyperfine-free fine-structure interval. The g_J values of 3P1 and 3P2 are fitted from laser magnetic resonance and carry systematic errors larger than the printed 1-sigma. Lifetimes of 3P1, 3P2, 1D2, 1S0 are derived from calculated A-values (theory), not measured. Additional measured data not transcribed here: Pehlivan Rhodin et al. 2024 Table B.3 (CDS tableb3.dat) gives 17 semi-experimental log(gf) for near-infrared 4s-4p and 3s3p3 3D°-4p lines (measured branching fractions x calculated lifetimes); Smith et al. 1987 give branching fractions / f-values for 108 lines (already the basis of NIST ASD).

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