Abstract: This invention relates to a method and apparatus for the generation of isotopes, and in particular radioisotopes, from a target material which is not normally a solid and which, when bombarded by selected high energy particles, produces the selected isotope. A surface is provided which is preferably of a thermally-conductive material, which surface is cooled to a temperature below the freezing temperature of the target material. A thin layer of target material is then frozen on the surface and the target material is bombarded with the high energy particles. The beam of high energy particles is preferably at an angle to the surface such that the particles pass through a thickness of the target material greater than the thickness of the layer before reaching the surface. When the desired quantity of isotope has been produced from the target material, the target material, which has now been altered nuclearly to contain the selected isotope, is removed from the surface.