Molybdenum energy level diagram

Energy levels and transitions of neutral molybdenum (Mo I): the 90 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 82 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 molybdenum

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).

⁹⁵Mo 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 molybdenum

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 Mo 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.

Mo energy levels

Mo⁺ ionisation limit 57204.30 cm⁻¹ = 7.09243 eV (174.812 nm)

Sources

• Buettgenbach, Herschel, Meisel, Schroedl, Witte, Childs, Z. Phys. 266, 271 (1974) (abstra…
• Duquette, Salih, Lawler, Phys. Lett. A 83, 214 (1981) (abstract, as indexed by OSTI/ETDEW…
• Jiang, Wang, Shang, Tian, Yin, Jiang, Pei, Dai, J. Opt. Soc. Am. B 30, 489 (2013), Table 2
• Jiang, Wang, Shang, Tian, Yin, Jiang, Pei, Dai, J. Opt. Soc. Am. B 30, 489 (2013), Table 3
• Kurucz, R. L., Can. J. Phys. 89, 417 (2011); semi-empirical line list gf4200.pos of 2017-…
• Kwiatkowski, Micali, Werner, Zimmermann, Phys. Lett. A 85, 273 (1981) (abstract, as index…
• NIST ASD
• NIST ASD level energies
• Paladugu, Pilgram, Eckel, Norrgard, "Chirped magneto-optical trap of molybdenum", arXiv:2…
• Whaling, Hannaford, Lowe, Biemont, Grevesse, JQSRT 32, 69 (1984), as quoted in Paladugu, …

Lifetimes from Kwiatkowski 1981 and Duquette 1981 were read from the abstracts of the original papers (the abstracts list the numbers); the papers themselves are paywalled. Hyperfine constants of the ground state are the directly measured (uncorrected) ABMR values in MHz, B converted from kHz. Isotope shifts are nu(first) - nu(second). Frequencies are for 98Mo (boson, no hyperfine structure). The 15 lifetime entries above 39000 cm^-1 are J >= 5 levels that the site does not draw yet; the Whaling-Chevako-Lawler numbers were read from an OCR text layer of the scanned paper and checked by eye for the obvious OCR slips (e.g. "t4.0" = 14.0). Second pass: no new numerical entries could be sourced for Mo; see not_found for what was tried. Third pass: 13 new level lifetimes (44951.5-47184.5 cm^-1; none of these levels is drawn by the site at present, but they are the only TR-LIF lifetimes openly readable), one more lifetime for x5D3 (40488.28), and 129 transition rates with branching fractions were taken from Jiang et al. 2013 (Tables 2 and 3). Table 3 prints g_k*A_ki in units of 10^7 s^-1; A_s here is that number divided by g_k = 2J_upper+1 and is marked 'derived' in the note; its uncertainty is the printed one divided by g_k. Check done: lifetime x sum(A) = 0.995-1.000 for all 13 upper levels (the paper normalises the branching fractions to 1). Level energies in Jiang's tables are rounded to 0.01 cm^-1 and were matched to the NIST levels by energy and J.

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