Very dilute Fe-Cu systems, model alloys of nuclear reactor pressure vessel (RPV) steels, irradiated by fast neutrons, are studied by positron annihilation experiments and simple calculations. The ultrafine Cu precipitates, which are never formed by thermal aging in the dilute alloys, are observed clearly and are strongly suggested to be responsible for irradiation-induced embrittlement of RPV steels. The formation and recovery process of the precipitates are revealed: (i) irradiation-induced Cu-vacancy complexes aggregate into microvoids; (ii) around $400\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ the dissociation of vacancies from the microvoids leads to the formation of the Cu precipitates of about 1 nm in size; and (iii) the Cu precipitates anneal out at about $650\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}.$