Titanium energy level diagram

Energy levels and transitions of neutral titanium (Ti I): the 88 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 74 levels they connect, each line with its vacuum wavelength, frequency and, for 88 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 titanium

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).

⁴⁷Ti hyperfine structure (I = 5/2)

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

Isotope shifts

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

Closed and nearly closed transitions of titanium

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 Ti 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.

Ti energy levels

Ti⁺ ionisation limit 55072.50 cm⁻¹ = 6.82812 eV (181.579 nm)

Sources

• Channappa & Pendlebury 1965 / Aydin et al. 1990, as tabulated in Schrott, Eustice, Sadegh…
• Duim, Eustice, Schrott, Sawaoka, Stamper-Kurn, "Narrow-line magneto-optical trap of titan…
• Eustice, Filin, Schrott, Porsev, Cheung, Novoa, Stamper-Kurn, Safronova, Phys. Rev. A 107…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013)
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• Lawler, Guzman, Wood, Sneden, Cowan, Astrophys. J. Suppl. Ser. 205, 11 (2013). Note: deri…
• NIST ASD
• NIST ASD Ti I lines table (local copy data/nist/Ti_I_lines_from1nm.tsv)
• NIST ASD level energies
• Schrott, Eustice, Sadeghpour, Duim, Sawaoka, Filin, Safronova, Stamper-Kurn, "Hyperfine s…

Transition probabilities are from the machine-readable Table 3 of Lawler et al. 2013 (948 lines), restricted to lines the site draws plus all lines from y5G, y5D4; level energies there (Saloman 2012) equal the NIST energies. NIST ASD already carries A values for most of these lines (often from the same group). rme_J_ea0 is derived from A with the SCHEMA convention. Level lifetimes marked "derived" are 1/sum(A) over the Lawler branches (see note in each entry); only z5G6 has a direct cold-atom lifetime measurement. Isotope shifts are nu(A) - nu(48) as printed in the sources; fermion shifts refer to the hyperfine centre of gravity. Hyperfine A, B follow E = A K/2 + B [3K(K+1) - 4J(J+1)I(I+1)] / [8I(2I-1)J(2J-1)] (Eq. 6 of Schrott et al.); all A are negative. Extra fields beyond SCHEMA.md: top-level ionization_limit, laser_cooling_scheme, conflicts; level fields hyperfine_other, lifetime_other, decay_rates_theory, magnetic_moment_muB; transition fields linewidth_MHz / linewidth_kHz, A_s_other, saturation_intensity_*, doppler_limit_uK, leak_to_metastable, king_plot. Entries whose note says UPPER BOUND / LOWER BOUND / derived / theory are not direct measurements.

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