  We report measurements of the optical gap in a GdN film at temperatures from
300 to 6K, covering both the paramagnetic and ferromagnetic phases. The gap is
1.31eV in the paramagnetic phase and red-shifts to 0.9eV in the spin-split
bands below the Curie temperature. The paramagnetic gap is larger than was
suggested by very early experiments, and has permitted us to refine a
(LSDA+U)-computed band structure. The band structure was computed in the full
translation symmetry of the ferromagnetic ground state, assigning the
paramagnetic-state gap as the average of the majority- and minority-spin gaps
in the ferromagnetic state. That procedure has been further tested by a band
structure in a 32-atom supercell with randomly-oriented spins. After fitting
only the paramagnetic gap the refined band structure then reproduces our
measured gaps in both phases by direct transitions at the X point.
