The invention relates to a pressurised water nuclear reactor vessel, comprising: an outer casing which comprises at least one cylindrical shell and a dished bottom head, a core support plate, a vessel bottom head space being delimited between the support plate and the dished bottom head, the support plate being perforated with holes for circulation of the primary coolant which place the vessel bottom head space in communication with the core, a calming device which is arranged in the vessel bottom head space, wherein the calming device comprises at least one calming plate which is substantially perpendicular relative to the centre axis of the vessel and a plurality of calming holes, the calming holes being provided in the calming plate and being capable of calming the primary coolant by passing the fluid through the holes.