[en] A design study of a cold neutron irradiator (CNI) for materials characterization using prompt gamma-ray neutron activation analysis (PGNAA) is presented. Using ²⁵²Cf neutron sources in a block of moderator, a portion of which is maintained at a cryogenic temperature, the CNI employs cold neutrons instead of thermal neutrons to enhance the neutron capture reaction rate in a sample. Capture gamma rays are detected in an HPGe photon detector. Optimization of the CNI with respect to elemental sensitivity (counts per mg) is the primary goal of this design study. Monte Carlo simulation of radiation transport, by means of the MCNP code and the ENDF/B cross-section libraries, is used to model the CNI. A combination of solid methane at 22 K, room-temperature polyethylene, and room-temperature beryllium has been chosen for the neutron delivery subsystem of the CNI. Using four 250-microgram ²⁵²Cf neutron sources, with a total neutron emission rate of 2.3 x 10⁹ neutrons/s, a thermal-equivalent neutron flux of 1.7 x 10⁷ neutrons/cm²-s in an internally located cylindrical sample space of diameter 6.5 cm and height 6.0 cm is predicted by MCNP calculations. A cylindrical port with an integral annular collimator composed of bismuth, lead, polyethylene, and lithium carbonate, is located between the sample and the detector. Calculations have been performed of gamma-ray and neutron transport in the port and integral collimator with the objective of optimizing the statistical precision with which one can measure elemental masses in the sample while also limiting the fast neutron flux incident upon the HPGe detector to a reasonable level. The statistical precision with which one can measure elemental masses can be enhanced by a factor of between 2.3 and 5.3 (depending on the origin of the background gamma rays) compared with a neutron irradiator identical to the CNI except for the replacement of the cryogenic solid methane by room-temperature polyethylene. The projected performance of the CNI in the measurement of elemental concentrations is presented. In an illustrative calculation, it is projected that 5 ppm of boron in a silicon dioxide sample can be measured by PGNAA to within a statistical precision of ±20% in 30 minutes