The reactor comprises a vessel (3) containing the core of the reactor (4) and arranged with its axis vertical in a vessel well (2). The cooling and protection device (11) rests on the bottom of the vessel well. It consists of a metal floor (11) which covers the bottom of the vessel well (5) and in which are made channels (20) for cooling by circulation of a cooling fluid. The cooling fluid supply is connected to the cooling channels (20).