In certain atomic physics experiments performed in conjunction with underground nuclear-weapon testing, it is desired that radiation energy converter plates be irradiated so as to reemit a maximum amount of radiation. The plates, composed of thin layers of materials of differing atomic number, are to be designed by choosing the material atomic number for each layer so that the plate, in toto, produces minimum photoelectron kinetic energy. Minimum photoelectron kinetic energy implies maximum energy reradiated, in the context of the radiation energy spectral regime of interest. The optimum choice of layer atomic numbers involves the solution of a novel variational problem where the minimizing function, the atomic numbers, take on integer values only. A comparison is made between the optimally designed plate and the corresponding homogeneous plate in terms of photoelectron kinetic energy produced. The homogeneous plate produces more than two orders of magnitude more photoelectric kinetic energy than does the optimally designed plate.