  The E1 contribution to the capture reaction
$^7\mathrm{Li}(n,\gamma)^8\mathrm{Li}$ is calculated at low energies. We employ
a coupled-channel formalism to account for the $^7\mathrm{Li}^\star$ excited
core contribution. We develop a halo effective field theory power counting
where capture in the spin $S=2$ channel is enhanced over the $S=1$ channel. A
next-to-leading order calculation is presented where the excited core
contribution is shown to affect only the overall normalization of the cross
section. The momentum dependence of the capture cross section, as a
consequence, is the same in a theory with or without the excited
$^7\mathrm{Li}^\star$ degree of freedom at this order of the calculation. The
kinematical signature of the $^7\mathrm{Li}^\star$ core is negligible at
momenta below 1 MeV and significant only beyond the $3^+$ resonance energy,
though still compatible with a next-to-next-to-leading order correction. We
compare our formalism with a previous halo effective field theory calculation
[Zhang, Nollett, and Phillips, Phys. Rev. C 89, 024613 (2014)] that also
treated the $^7\mathrm{Li}^\star$ core as an explicit degree of freedom. Our
formal expressions and analysis disagree with this earlier work in several
aspects.
