Rhodium energy level diagram

Energy levels and transitions of neutral rhodium (Rh I): the 48 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 26 levels they connect, each line with its vacuum wavelength, frequency and, for 48 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

Strongest transitions of rhodium

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).

Closed and nearly closed transitions of rhodium

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 Rh 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.

Rh energy levels

Rh⁺ ionisation limit 60160.10 cm⁻¹ = 7.45890 eV (166.223 nm)

Sources

• Kwiatkowski, Zimmermann, Biémont, Grevesse, Astron. Astrophys. 112, 337 (1982), Table 3 (…
• Malcheva, Engström, Lundberg, Nilsson, Hartman, Blagoev, Palmeri, Quinet, MNRAS 450, 223 …
• NIST ASD
• NIST ASD level energies
• Salih, Duquette, Lawler, Phys. Rev. A 27, 1193 (1983), value as quoted in Table 2 of Malc…

Rh has a single stable isotope, 103Rh (I=1/2), so there are no isotope shifts and no electric-quadrupole B constants. All lifetimes are time-resolved laser-induced-fluorescence values. Entry choice per level: Malcheva et al. 2015 where they measured the level (17 levels); otherwise Kwiatkowski et al. 1982 (original scan opened, 13 levels); otherwise Salih et al. 1983 as quoted by Malcheva et al. (method "compilation"). Remaining measurements and the HFR+CPOL theory value are under lifetime.alternatives. Kwiatkowski et al. print level energies rounded to 1 cm-1; they were matched to the NIST energies by designation. Malcheva et al. state uncertainties "include the statistical uncertainties as well as the variation of the results between the repeated measurements"; Kwiatkowski et al. error limits are statistical deviations plus time-calibration uncertainty. Malcheva et al. write that four levels were measured in all three experiments, but their Table 2 shows three such levels (31101.75, 33867.04, 36787.48 cm-1); 35333.85 cm-1 has only Salih + Malcheva. The transitions list is empty on purpose: nothing measured beyond what NIST ASD already holds was found. Levels above 36000 cm-1 are included although not drawn on the site.

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