  The dynamical structure factor of solid $^{15}$N$_{2}$ in the $\alpha$ phase
($T<35$K) is measured at the IN4 time-of-flight spectrometer at the Institut
Laue Langevin, and the potential performance of this substance as a UCN
converter is assessed. The cross-section to down-scatter neutrons to ultra-cold
neutron energies is determined as a function of incident energy, as well as the
up-scattering mean free path. The UCN production cross-section is found to be
approximately 20% of that of deuterium. However, UCN with energy 181 neV have
an up-scattering mean free path of 46 cm at $T=5.9$ K, which is $\sim20$ times
larger than deuterium. Therefore, a large volume $\alpha-^{15}$N$_{2}$ source
may produce an improved UCN density if sufficient isotopic purity can be
achieved.
