properties of @roberge1991. Their extinction calculated for the wavelength range appropriate to CO is adopted here for , that is with $\gamma_\mathrm{dust} = 3.53$. Further calculations were made by @van_dishoeck2006 assuming larger dust grains ($>1\mu$m in size) as identified in protoplanetary discs [@li2003a; @jonkheid2006]. For this case $\gamma_\mathrm{dust}=0.6$.

[cc]{} ![image](shielding_functions_self_shielding_14N15N_14N2) & ![image](shielding_functions_14N15N_shielding_by_14N2)\

Detailed shielding functions for were given in @li2013 and the associated on-line material. Here, new calculations are made for $\mathrm{{}^{14}N{}^{15}N}$ using Eq. (\[eq:def shielding function\]), with some representative results plotted in Fig. \[fig:shielding functions\], and full details available from the Leiden photodissociation database.[^1] The data in Fig. \[fig:shielding functions\] assume that the lines of shielding H and H$_2$ are Doppler broadened by $b=1$ and $3\,\mathrm{km\,s^{-1}}$, respectively. The N$_2$ lines are assigned thermal Doppler widths according to their excitation temperatures but are also naturally broadened by the predissociation process, in some cases by a few .

Unsurprisingly, the similarity of the two isotopologues leads to very similar shielding functions. There is some difference evident in Fig. \[fig:shielding functions\] with respect to shielding by atomic hydrogen. That is, the shielding of $\mathrm{{}^{14}N{}^{15}N}$ by a $N(\mathrm{H})=10^{20}\,\mathrm{cm}^{-2}$ column is somewhat more effective than for . This is the result of a nearer 