Indium energy level diagram

Energy levels and transitions of neutral indium (In I): the 30 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 21 levels they connect, each line with its vacuum wavelength, frequency and, for 30 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 indium

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).

¹¹⁵In hyperfine structure (I = 9/2)

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

Isotope shifts

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

Closed and nearly closed transitions of indium

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 In 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.

In energy levels

In⁺ ionisation limit 46670.11 cm⁻¹ = 5.78636 eV (214.270 nm)

Sources

• Augenbraun, Carter, Rupasinghe, Majumder, Phys. Rev. A 94, 022515 (2016) (arXiv:1607.0179…
• Garcia Ruiz et al., Phys. Rev. X 8, 041005 (2018), Table I, literature column, attributed…
• Garcia Ruiz et al., Phys. Rev. X 8, 041005 (2018), Table I, literature column; original: …
• Garcia Ruiz et al., Phys. Rev. X 8, 041005 (2018), Table I, literature column; original: …
• Garcia Ruiz et al., Phys. Rev. X 8, 041005 (2018), Table I, literature; original: George,…
• Garcia Ruiz et al., Phys. Rev. X 8, 041005 (2018), Table I, this work
• Gunawardena, Cao, Hess, Majumder, Phys. Rev. A 80, 032519 (2009) (abstract): a = 79.33(7)…
• NIST ASD
• NIST ASD level energies
• Norton, Gallagher, Phys. Rev. A 3, 915 (1971) (abstract; Hanle effect)
• Safronova, Safronova, Kozlov, Phys. Rev. A 76, 022501 (2007), Table II (all-order SD)
• Safronova, Safronova, Kozlov, Phys. Rev. A 76, 022501 (2007), Table VI (55.0 +- 4) and Sa…
• Safronova, Safronova, Kozlov, Phys. Rev. A 76, 022501 (2007), Table VI; original: Anderse…
• Safronova, Safronova, Kozlov, Phys. Rev. A 76, 022501 (2007), Table VI; original: Jonsson…
• Safronova, Safronova, Kozlov, Phys. Rev. A 76, 022501 (2007), Table VI; original: Zaki Ew…
• Safronova, Safronova, Kozlov, Phys. Rev. A 76, 022501 (2007), Table VI; original: Zaki Ew…
• Sahoo, Das, Phys. Rev. A 84, 012501 (2011) (arXiv:1102.2496), Table III, column Expt; ori…
• Sahoo, Das, Phys. Rev. A 84, 012501 (2011) (arXiv:1102.2496), Table III, recommended valu…
• Vernon et al., arXiv:2005.06051 (2020), "Laser spectroscopy of indium Rydberg atom bunche…

Both stable isotopes have I = 9/2 (115In is very weakly radioactive, 95.71%). Hyperfine entries from Garcia Ruiz et al. 2018 carry statistical (A_unc) and systematic (A_unc_sys) uncertainties separately. level_isotope_shift_MHz is the shift of the level itself (113In minus 115In centroid, relative to the ionization limit) as tabulated by Sahoo et al. 2019 / Vernon et al. 2020. Transition isotope shifts keep the printed convention: keys "115-113" mean nu(115)-nu(113). rme_J_ea0 values are theory unless noted: "CC" = linearized coupled-cluster (Safronova, Safronova, Porsev 2013), sqrt(S) values derived from the all-order SD line strengths of Safronova, Safronova, Kozlov 2007 (same convention as the schema: A = 2.02613e18 S/((2J'+1) lambda^3)). The 6s-6p matrix elements and 6p lifetimes marked derived come from the measured 410 nm Stark shift (Ranjit et al. 2013) plus theory. Extra fields beyond SCHEMA.md: level_isotope_shift_MHz, natural_linewidth_MHz, stark_shift_kHz_per_kVcm2, C_MHz (magnetic octupole), *_unc_sys, ionization_energy, mu_N. The UDel portal has no neutral In entry (only In+).

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