Uncertainty estimates

Each line position is given with a standard (1σ) uncertainty. The uncertainty is not derived from the covariance of a fit. It is estimated from the agreement of the model with measurements that were not used to determine the relevant parameters, and it depends on how the upper and lower levels of the line are determined (Table 1).

levels of the line	uncertainty	basis
both levels corrected by frequency-comb data, within 15 in J of the data	0.05–1 MHz	held-out rms of each level
NIR bands v′ = 0 → v″ = 12–17, within the measured J range	0.13 MHz	held-out rms of the band correction
B v′ = 7, 12, 13, 19, 27, 29 (no correction of their own) to X v″ ≤ 5	0.5–3 MHz	Gaussian-process interpolation from the corrected levels around them; held out a level at a time, 1.1 MHz rms over v′ = 3–35
X v″ = 18–25 within the J range of the Orsay atlas	15–50 MHz	held-out rms of each level
range of the 2008 fit, without level corrections	3–8 MHz	comparison with BIPM and comb data by region
B v′ = 44–50	15 MHz	comparison with Matsunaga (2024) and Yoshiki (2023)
X v″ = 26–75	150 MHz	the X potential fitted to the level constants of Martin et al. (1986), 55–73 MHz rms
X v″ = 76–89	400 MHz	the same, 174 MHz rms
X v″ > 89	2.1 THz	not physical: the X potential is fitted to v″ = 89 only (no B–X line in the list reaches these levels)
B v′ = 51–79 within the J range of the Orsay atlas Partie IV, including the quasi-bound levels above the asymptote	20–250 MHz	held-out rms of each level
B v′ > 50 otherwise	1 GHz	the refitted B potential alone, 150–350 MHz from the atlas levels, extrapolated

Table 1. Uncertainty of the hyperfine-free line position.

Figure 1. Uncertainty of the R(50) line of each band v′–v″. Below v″ = 17 and v′ = 43 the 2008 potentials and the level corrections give a few MHz or better; the ≤ 1 MHz rows are levels with direct frequency-comb measurements. At v″ = 18–25 the Orsay atlas determines the levels to 15–50 MHz where it observed them, and v″ = 48–54 are determined by emission measurements. Elsewhere the positions are extrapolations of the potentials.

The uncertainty of the hyperfine offsets is given on the Hyperfine structure page. Where the local near-infrared model of Knöckel, Bodermann & Tiemann (2004) applies, the command line and the line explorer indicate this.