Phosphorus energy level diagram

Energy levels and transitions of neutral phosphorus (P I): the 50 strongest classified lines below 2 µm from the NIST Atomic Spectra Database and the 23 levels they connect, each line with its vacuum wavelength, frequency and, for 42 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 phosphorus

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).

³¹P hyperfine structure (I = 1/2)

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

Closed and nearly closed transitions of phosphorus

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 P 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.

P energy levels

P⁺ ionisation limit 84580.83 cm⁻¹ = 10.48669 eV (118.230 nm)

Sources

• Berzinsh, Svanberg, Biemont, Astron. Astrophys. 326, 412 (1997), Table 1, relativistic Ha…
• Berzinsh, Svanberg, Biemont, Astron. Astrophys. 326, 412 (1997), Table 1: two-photon UV l…
• Lambert & Pipkin, Phys. Rev. 128, 198 (1962) (erratum 129, 2836 (1963) not opened): spin-…
• NIST ASD
• NIST ASD P I lines table (tp_ref T761, accuracy C-D), local cache data/nist/P_I_lines_fro…
• NIST ASD P I lines table (tp_ref T761, accuracy C-D), local cache data/nist/P_I_lines_fro…
• NIST ASD P I lines table (tp_ref T761, accuracy C-D), local cache data/nist/P_I_lines_fro…
• NIST ASD P I lines table (tp_ref T761, accuracy C-D), local cache data/nist/P_I_lines_fro…
• NIST ASD level energies
• Savage & Lawrence, Astrophys. J. 146, 940 (1966), phase-shift method with cascade correct…
• Savage & Lawrence, Astrophys. J. 146, 940 (1966), phase-shift method with cascade correct…
• Savage & Lawrence, Astrophys. J. 146, 940 (1966), phase-shift method with cascade correct…

Level energies are the NIST ASD values (data/nist/P_I_levels.tsv); Berzinsh et al. print slightly different energies (e.g. 66813.04 for 4p 2D°3/2, NIST 66813.271). Savage & Lawrence lifetimes are multiplet values and are attached to every fine-structure level of the upper term. Berzinsh error bars are two standard deviations. Their two-photon excitation wavelengths were 299-306 nm (from 3p3 4S°3/2), detection on the 178 nm (quartets) or 214 nm (doublet) cascade. The lifetimes of the metastable 2D° and 2P° levels are derived from calculated A-values (theory). Note for the site: for the forbidden lines NIST lists separate M1 and E2 A-values at the same wavelength (e.g. 533.39 nm: M1 1.08e-1, E2 3.3e-7 s^-1); both must be summed for the decay rate. 'multiplet_intensity_fraction' is a non-schema field holding the measured relative line intensities of Mazzoni & Ricci.

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