Nebulia

Nebulia, a veiled oracle in deep-navy robes, holds a ring of doubly ionised oxygen whose green light fills a planetary-nebula halo.

The Physics

The bright green nebular lines at 5006.84 Å and 4958.91 Å (air wavelengths) were long blamed on a hypothetical element, “nebulium”. In 1927 I. S. Bowen identified them as forbidden transitions of doubly ionised oxygen, O²⁺ (spectroscopic notation O III), from the metastable ¹D₂ level of the 2p² ground configuration down to the ³P₂ and ³P₁ levels. Because both levels share the same configuration and parity, an electric-dipole (E1) transition is forbidden; the lines go mainly by the much slower magnetic-dipole (M1) channel. In a lab gas, collisions empty ¹D₂ long before it can radiate. In a nebula they do not, because the density sits far below the level’s critical density.

n_crit = A_ul / q_ul

λ = hc / ΔE_ul

• n_crit: critical electron density, where collisional de-excitation equals radiative decay (m⁻³)
• A_ul: Einstein spontaneous-emission coefficient from upper level u to lower level l (s⁻¹)
• q_ul: collisional de-excitation rate coefficient (m³ s⁻¹)
• λ: emitted wavelength (m)
• h: Planck constant, 6.626 070 15 × 10⁻³⁴ J s (exact)
• c: speed of light in vacuum, 299 792 458 m s⁻¹ (exact)
• ΔE_ul: energy gap between the two levels (J)

Below n_crit nearly every excitation ends in a photon, so a weak transition can still be one of the brightest lines in the spectrum. William Huggins first saw these lines in 1864 in NGC 6543. Sources: I. S. Bowen, Nature 120, 473 (1927), doi:10.1038/120473a0; A. Fowler, Nature 120, 582 (1927); NIST Atomic Spectra Database (O III).

Honest caveat: “Forbidden” means strongly suppressed, not impossible. Quoted wavelengths are in air (500.68 nm); the vacuum value is slightly longer.

The glow is the approximate line colour: a pure spectral colour lies outside the sRGB range a print can show.

In character

I was called a new element for sixty years. I was oxygen all along, speaking only where the dark is quiet enough to hear me.

On the hoodie

Front: a three-level ladder emblem with a dashed green ¹D→³P arrow. Back: Nebulia in full pixel art with “FORBIDDEN. OBSERVED ANYWAY.” and “NEBULIUM WAS OXYGEN.” Gildan 18500 Heavy Blend hoodie, Black, S to 5XL.

Part of the Forbidden Transitions set with Coronix, Flipwarden, Viridael, Sanguora, Sulphra. Browse all physics hoodies, more astrophysics & cosmology designs, or the Deep Cuts.