Rare gas diffusion is usually determined following homogeneous labelling of the solid using a nuclear reaction and reactor irradiation or ion bombardment with vertical incidence of the beam. Frequently, however, these methods cannot be used as either no suitable nuclear reaction exists in the substance to be studied, an ion accelerator is not available, or the substance is only available in the form of powder. In these cases, recoil processes can be used to introduce the gas into the solid: following adsorption of a thin layer of 226Ra on the solid, the daughter product 222Rn is recoiled into the sample with an energy of about 85 keV. Alternatively, the fission rare gases Kr and Xe can be introduced into any solid with a recoil energy of about 80 MeV by reactor irradiating the solid in contact with a uranium bearing matrix. The present paper presents the mathematical solutions of the diffusion equation needed for evaluating gas release curves from such samples for the two most important geometrical shapes of a slab (infinite plane sheet) and for powdered samples (assuming spherical shape of the particles). Some experimental data are shown to demonstrate agreement between theory and experiment.