Abstract: Process and apparatus for cooling the wall of the vessel of a fast neutron reactor comprising a main vessel which surrounds a second vessel containing the core and separating a volume of liquid metal contained in the main vessel into two regions called the hot collector and the cold collector respectively. The liquid metal drawn into the cold collector and passed through the core to the hot collector is circulated by means of pumps distributed around the core. A baffle and a counter-baffle are arranged concentrically to the main vessel wall and respectively define a first and second annular space issuing into the cold collector. The first annular space is traversed by a tapped flow of cooling liquid metal circulating from bottom to top in the first space in contact with the main vessel wall up to an upper constant level adjacent to the edge of the baffle.