photodissociation rates of and $\mathrm{{}^{14}N{}^{15}N}$ calculated from Eq. (\[eq:kpd\]) are given in Tab. \[tab:kpd0\] assuming several different radiation fields. In all cases the difference between and $\mathrm{{}^{14}N{}^{15}N}$ rates is below 5%, and the calculated dependences on the N$_2$ ground state excitation temperature and the form of the incident field (a Draine ISRF, or blackbody radiation) are similar to those calculated by @li2013 for .

For N$_2$ embedded in an externally irradiated cloud or disc, the intervening gaseous and granular material acts as a shield [and leads to a reduced photodissociation rate, $k<k_0$.]{} The precise nature of shielding by H, H$_2$, , and $\mathrm{{}^{14}N{}^{15}N}$ is influenced by the wavelength dependence of their absorption cross sections, but is more usefully applied as a wavelength-integrated ratio of shielded and unshielded dissociation rates. That is, the shielding function given by $$\begin{aligned}
  \notag
  \theta &= \frac{k}{k_0} \\
  \label{eq:def shielding function}
  &= \frac{
    \int I(\lambda)
    \exp\left[-\sum_\mathrm{X} N_\mathrm{X}\sigma^\mathrm{abs}_\mathrm{X}(\lambda)\right]
    \exp\left( -\gamma_\mathrm{dust} A_V \right)
    \sigma^\mathrm{pd}(\lambda)\,d\lambda}
  {\int I(\lambda)\sigma^\mathrm{pd}(\lambda)\,d\lambda}.\end{aligned}$$ Here, $\sigma_\mathrm{X}^\mathrm{abs}(\lambda)$, is the absorption cross section of shielding species X and $N_\mathrm{X}$ its shielding column density.

[rcc]{}\
\
$T_\mathrm{ex}$(K) & & $\mathrm{{}^{14}N{}^{15}N}$\
\
10 & $1.64\times 10^{-10}$ & $1.68\times 10^{-10}$\
20 & $1.65\times 10^{-10}$ & $1.70\times 10^{-10}$\
30 & $1.66\times 10^{-10}$ 