Radium energy level diagram

Energy levels and transitions of neutral radium (Ra I): the 22 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 18 levels they connect, each line with its vacuum wavelength, frequency and, for 22 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 radium

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).

²²³Ra hyperfine structure (I = 3/2)

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

Isotope shifts

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

Closed and nearly closed transitions of radium

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 Ra 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, or a model calculation.

Ra energy levels

Ra⁺ ionisation limit 42573.36 cm⁻¹ = 5.27842 eV (234.889 nm)

Sources

• Bieron, Indelicato, Jonsson, Eur. Phys. J. Special Topics 144, 75 (2007) [arXiv:physics/0…
• Booth, Rabga, Ready, Bailey, Bishof, Dietrich, Greene, Mueller, O'Connor, Singh, Spectroc…
• Booth, Rabga, Ready, Bailey, Bishof, Dietrich, Greene, Mueller, O'Connor, Singh, Spectroc…
• Dzuba & Flambaum, J. Phys. B 40, 227 (2007) [arXiv:physics/0610119]; Table 3 (CI + MBPT)
• Dzuba & Ginges, Phys. Rev. A 73, 032503 (2006) [arXiv:physics/0511199], Table VI (CI + ma…
• Guest, Scielzo, Ahmad, Bailey, Greene, Holt, Lu, O'Connor, Potterveld, Phys. Rev. Lett. 9…
• Guest, Scielzo, Ahmad, Bailey, Greene, Holt, Lu, O'Connor, Potterveld, Phys. Rev. Lett. 9…
• Guest, Scielzo, Ahmad, Bailey, Greene, Holt, Lu, O'Connor, Potterveld, Phys. Rev. Lett. 9…
• NIST ASD
• NIST ASD level energies
• Santra, Dammalapati, Groot, Jungmann, Willmann, Phys. Rev. A 90, 040501(R) (2014) [arXiv:…
• Scielzo, Guest, Schulte, Ahmad, Bailey, Bowers, Holt, Lu, O'Connor, Potterveld, Phys. Rev…
• Trimble, Sulai, Ahmad, Bailey, Graner, Greene, Holt, Korsch, Lu, Mueller, O'Connor, Phys.…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), Ra I tables…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), Ra I tables…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), Ra I tables…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), Ra I tables…
• UDel Portal for High-Precision Atomic Data and Computation (Safronova group), Ra I tables…
• Wendt, Ahmad, Klempt, Neugart, Otten, Stroke, Z. Phys. D 4, 227 (1987) (collinear laser s…
• Wendt, Ahmad, Klempt, Neugart, Otten, Stroke, Z. Phys. D 4, 227 (1987) (collinear laser s…
• Wendt, Ahmad, Klempt, Neugart, Otten, Stroke, Z. Phys. D 4, 227 (1987) (collinear laser s…
• experimental rate 2.37(12)[6] s^-1 attributed to Scielzo et al. 2006 in Table 1 of Bieron…

Level energies are the NIST ASD values (226Ra; NIST adopts Santra et al. for 1P1 and Guest/Scielzo et al. for 3P1). rme_J_ea0 is |<J||D||J'>| in e a0 in the symmetric convention of the Safronova papers / UDel portal, A = 2.02613e18 |d|^2 / ((2J'+1) lambda^3[Angstrom]), J' = upper level; Dzuba & Flambaum (their Eq. 12) and Dzuba & Ginges use the same convention, so no conversion was needed. The UDel portal does carry neutral Ra (element key "Ra1": 48 matrix elements, 24 rates, lifetimes; data service https://atom.ece.udel.edu/graphql behind https://www1.udel.edu/atom/); all its Ra I numbers are theory except the 3P1 lifetime, which it attributes to Scielzo et al. It also carries Ra+ (key "Ra2"), not used here. Isotope shifts are nu(first) - nu(second); the ISOLDE tables are referenced to 214Ra, and for odd isotopes refer to hyperfine centres of gravity. Hyperfine A, B signs as printed in the compilation. frequency_THz entries are for 226Ra (I = 0, no hyperfine structure); frequency_THz_225 entries are centres of gravity derived here from the measured hyperfine component and A, and the measured components themselves are under hyperfine_component_frequency_THz. Extra fields beyond the schema: ionization_energy, linewidth_MHz and measured_energy_cm on levels, oscillator_strength, hyperfine_component_frequency_THz, wavenumber_cm inside frequency entries, half_life / mu / Q in isotopes (abundance_percent is null: no stable isotope). Radium has no stable isotope; 226Ra (1600 y) and

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