Vanadium energy level diagram

Energy levels and transitions of neutral vanadium (V I): the 90 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 75 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 vanadium

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).

⁵¹V hyperfine structure (I = 7/2)

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

Closed and nearly closed transitions of vanadium

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 V 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.

V energy levels

V⁺ ionisation limit 54411.67 cm⁻¹ = 6.74619 eV (183.784 nm)

Sources

• Den Hartog, Lawler, Wood, ApJS 215, 7 (2014) (TR-LIF on slow atomic beam), as tabulated b…
• Eustice, Cassella, Stamper-Kurn, Phys. Rev. A 102, 053327 (2020) (arXiv:2008.06147)
• Holmes, Pickering, Ruffoni, Blackwell-Whitehead, Nilsson, Engstrom, Hartman, Lundberg, Be…
• Lawler, Wood, Den Hartog, Feigenson, Sneden, Cowan, ApJS 215, 20 (2014), Table 3 (FTS/ech…
• Lawler, Wood, Den Hartog, Feigenson, Sneden, Cowan, ApJS 215, 20 (2014), Table 4 (least-s…
• NIST ASD
• NIST ASD level energies
• Wang, Jiang, Quinet, Palmeri, Zhang, Shang, Tian, Dai, ApJS 211, 31 (2014), Table 2 (this…
• Whaling et al., A&A 153, 109 (1985), as tabulated by Wang, Jiang, Quinet, Palmeri, Zhang,…
• Whaling, Hannaford, Lowe, Biemont, Grevesse, A&A 153, 109 (1985), as tabulated by Holmes,…
• Xu et al., JOSA B 23, 2597 (2006), as tabulated by Wang, Jiang, Quinet, Palmeri, Zhang, S…

Lifetimes: where several LIF measurements exist the entry is the one with the smallest relative uncertainty; the others are under lifetime.alternatives. Values labelled Den Hartog 2014, Whaling 1985, Doerr 1985, Rudolph & Helbig 1982, Xu 2006 are second-hand (read in the comparison tables of Holmes et al. 2016 and Wang et al. 2014, VizieR copies). Transition probabilities are Lawler et al. 2014 Table 3 (VizieR), for every line whose upper level is drawn on the site plus the z4I°15/2 cooling level; NIST ASD V I A-values (its reference T9399) appear to be the same data set, so these mainly add the printed uncertainties. Holmes et al. 2016 report that Lawler et al. underestimate log(gf) near 9000+-100 A and suggest a correction of +0.18(3) dex there. Hyperfine A are for 51V (I = 7/2), printed in mK, MHz derived by unit conversion. rme_J_ea0 values are derived from A_s. Level energies in the sources (Thorne et al. 2011) coincide with the NIST values. "drawn_on_site" marks what data/v/levels.csv / transitions.csv contain.

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