Line positions

Selection rules and branches

For a 0u⁺ ← 0g⁺ transition only ΔJ = J′ − J″ = ±1 is allowed. The lines form an R branch (ΔJ = +1) and a P branch (ΔJ = −1); there is no Q branch. The hyperfine-free line positions are

\[ \nu_\text{R}(J'') = E_B(v', J''+1) - E_X(v'', J''),\qquad \nu_\text{P}(J'') = E_B(v', J''-1) - E_X(v'', J''). \tag{1} \]

A line is labelled R(J″) v′–v″ or P(J″) v′–v″; for example, R(56) 32–0 lies at 532 nm. The hyperfine-free position is the centre of gravity of the hyperfine components (see Hyperfine structure); it is not itself an observable line.

Figure 1. P and R lines of the 32–0 band near the band origin, plotted against J″ (Fortrat diagram). The rotational constant of the upper level, B′ ≈ 0.022 cm⁻¹, is smaller than that of the lower level, B″ ≈ 0.037 cm⁻¹, because the equilibrium distance of B is larger. The R branch therefore reaches a band head at J″ ≈ 1 and then turns towards lower wavenumber. R(56), the 532 nm reference line, lies 46 cm⁻¹ below the band origin.

Correction for the near-infrared bands

The bands v′ = 0 → v″ = 12–17 (755–815 nm) require a J′ dependence of the level B v′ = 0 that cannot be applied to the level without also changing bands for which no measurements exist. For these bands a correction of the same form as the level corrections is applied to the line positions directly, and only within the J″ range of the measurements at each v″. It reproduces the 108 frequency-comb and beat-note measurements in this region with a held-out rms deviation of 0.13 MHz.

Units

The model computes wavenumbers in vacuum. Frequencies are ν × 29 979.2458 MHz/cm⁻¹. Air wavelengths are computed with the Edlén (1966) dispersion formula for standard air.