@gredel1987 and @gredel1989. This model includes the effects of cascading from sufficiently high-energy states into $B\,{}^1\Sigma_u^+$ and competing predissociative decay. ]{}

[ The final result of the H$_2$ emission model is a spectrum, $P(\lambda)$, describing the number of photons generated per unit spectral density per H$_2$ ionisation event. A plot of $P(\lambda)$ is shown in Fig. \[fig:cross sections\] and demonstrates a large number of narrow emission lines which actually occupy very little of the wavelength interval shown. The widths of these lines are Doppler limited and assigned full-width half-maxima of 0.005Å, which is appropriate for a typical dark-cloud non-thermal Doppler broadening of $b=1\,\mathrm{km\,s^{-1}}$. This is comparable to the widths of N$_2$ absorption lines, also shown in Fig. \[fig:cross sections\], so model spectra of both species are treated at similarly high resolution. Spectra are shown in Fig. \[fig:cross sections\] assuming limiting high- and low-temperature ratios for the ortho:para H$_2$ populations, $o\!-\!\mathrm{H}_2\!:\!p\!-\!\mathrm{H}_2=3:1$ and $0:1$, respectively. The difference is quite apparent and is significant in the following calculations of N$_2$ photodissociation. Despite the 170K energy separation of $o\!-\!\mathrm{H}_2$ and $p\!-\!\mathrm{H}_2$ ground-state levels it is not evident that their low-temperature equilibrium populations are always attained in real molecular clouds [@tielens2013]. Thus, we choose to 