Calcium-43 energy level diagram

Energy levels and transitions of neutral ⁴³Ca (Ca I, nuclear spin I = 7/2): 35 levels and 61 lines below 2 µm, each with its vacuum wavelength, frequency and, for 59 of them, the reduced dipole matrix element. Level energies come from the NIST Atomic Spectra Database; transition rates are 53 NIST, 5 measured, 2 semi-empirical. Neutral calcium is also the starting point for loading Ca⁺ ion traps by photoionisation.

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Download: diagram (PDF) diagram (SVG) transitions (CSV) levels (CSV) source code

Key transitions of ⁴³Ca

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).

⁴³Ca hyperfine structure (I = 7/2)

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

Isotope shifts

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

Closed and nearly closed transitions of ⁴³Ca

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.

All ⁴³Ca 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.

⁴³Ca energy levels

Ca⁺ ionisation limit 49305.92 cm⁻¹ = 6.11315 eV (202.815 nm)

Sources

• '118 minutes' as quoted in Mills, Puri, Yu, Derevianko, Schneider, Hudson, Phys. Rev. A 9…
• Arnold, Bergmann, Bopp, Dorsch, Kowalski, Stehlin, Traeger, zu Putlitz, Hyperfine Interac…
• Aydin, Ertmer, Johann, Z. Phys. A 306, 1 (1982) (atomic-beam magnetic resonance); values …
• Degenhardt, Stoehr, Lisdat, Wilpers, Schnatz, Lipphardt, Nazarova, Pottie, Sterr, Helmcke…
• Drozdowski, Kwela, Walkiewicz, Z. Phys. D 27, 321 (1993) (time of flight); as quoted in D…
• Grundevik, Gustavsson, Lindgren, Olsson, Robertsson, Rosen, Svanberg, Phys. Rev. Lett. 42…
• Havey, Balling, Wright, J. Opt. Soc. Am. 67, 488 (1977); as tabulated in Den Hartog, Lawl…
• Hunter, Watson, Weiss, Zajonc, Phys. Rev. A 31, 2268 (1985) (Hanle effect); as tabulated …
• Kurucz, R. L., Can. J. Phys. 89, 417 (2011); semi-empirical line list gf2000.pos of 2013-…
• Mortensen, Lindballe, Jensen, Staanum, Voigt, Drewsen, Phys. Rev. A 69, 042502 (2004), ar…
• NIST ASD
• NIST ASD level energies
• Noertershaeuser, Trautmann, Wendt, Bushaw, Spectrochim. Acta B 53, 709 (1998); values as …
• Vogt, Grain, Nazarova et al., Eur. Phys. J. D 44, 73 (2007) (photoassociation spectroscop…
• compiled in Table I of Bucay, Helal, Raizen, 'Surface ionization of metastable calcium at…
• compiled in Table I of Bucay, Helal, Raizen, 'Surface ionization of metastable calcium at…
• compiled in Table I of Bucay, Helal, Raizen, 'Surface ionization of metastable calcium at…
• rate quoted without uncertainty in Hansen, Mohr, Hemmerich, Phys. Rev. A 67, 021401(R) (2…
• this-work TR-LIF measurement (UW Madison, +-5%) in Den Hartog, Lawler, Sneden, Cowan, Roe…

Isotope shifts are nu(A) - nu(40), in MHz; for 43Ca they refer to the hyperfine centre of gravity. Frequencies refer to 40Ca. Hyperfine A, B follow the usual convention (43Ca has a negative nuclear moment, mu = -1.317643 mu_N, I = 7/2). Extra (non-schema) fields used: linewidth_Hz / linewidth_kHz / linewidth_MHz (natural linewidth, FWHM, as printed), wavelength_vac_nm, zeeman, note, alternatives (other measurements of the same quantity), top-level ionization and photoionization blocks. Lifetimes marked 'compilation' are the experimental values collected in Table 1 of Den Hartog et al. 2021 (laser-based methods only), which was read from a rendered image of the arXiv PDF because its text layer drops digits. The NIST Ca I levels file has no Lande-g column; the two measured g_J values given here are the only ones found. The 1D2 -> 3P1,2 rates (300 and 96 s^-1) and the 1D2 total lifetime are poorly known: experiment 1.5(4) ms versus theory 1.71 ms, while 300 + 96 + 40 s^-1 would give 2.3 ms.

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
• 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