An apparatus comprising: a pressurized water reactor including: a cylindrical pressure vessel with its cylinder axis oriented vertically, a nuclear reactor core disposed in the cylindrical pressure vessel, a separator plate disposed in the cylindrical pressure vessel that separates the pressure vessel to define an integral pressurizer containing a pressurizer volume disposed above the separator plate and a reactor vessel portion defining a reactor volume disposed below the separator plate and containing the nuclear reactor core, wherein the separator plate restricts but does not completely cut off fluid communication between the pressurizer volume and the reactor volume, a reactor coolant pump including (i) an impeller disposed inside the pressure vessel in the reactor volume, (ii) a pump motor disposed outside of the pressure vessel, and (iii) a drive shaft operatively connecting the pump motor with the impeller, wherein no portion of the reactor coolant pump is disposed in the pressurizer volume, and the drive shaft passes through an opening in the pressure vessel that is at least large enough to pass the impeller wherein (i) the reactor coolant pump further comprises a pump diffuser containing the impeller and (ii) the opening in the pressure vessel through which the drive shaft passes is too small for the pump diffuser to pass through, and further comprising a manway disposed at or below the pump diffuser that is large enough for the pump diffuser to pass through. a pressurized water reactor including: a cylindrical pressure vessel with its cylinder axis oriented vertically, a nuclear reactor core disposed in the cylindrical pressure vessel, a separator plate disposed in the cylindrical pressure vessel that separates the pressure vessel to define an integral pressurizer containing a pressurizer volume disposed above the separator plate and a reactor vessel portion defining a reactor volume disposed below the separator plate and containing the nuclear reactor core, wherein the separator plate restricts but does not completely cut off fluid communication between the pressurizer volume and the reactor volume, a reactor coolant pump including (i) an impeller disposed inside the pressure vessel in the reactor volume, (ii) a pump motor disposed outside of the pressure vessel, and (iii) a drive shaft operatively connecting the pump motor with the impeller, wherein no portion of the reactor coolant pump is disposed in the pressurizer volume, and the drive shaft passes through an opening in the pressure vessel that is at least large enough to pass the impeller wherein (i) the reactor coolant pump further comprises a pump diffuser containing the impeller and (ii) the opening in the pressure vessel through which the drive shaft passes is too small for the pump diffuser to pass through, and further comprising a manway disposed at or below the pump diffuser that is large enough for the pump diffuser to pass through. a cylindrical pressure vessel with its cylinder axis oriented vertically, a nuclear reactor core disposed in the cylindrical pressure vessel, a separator plate disposed in the cylindrical pressure vessel that separates the pressure vessel to define an integral pressurizer containing a pressurizer volume disposed above the separator plate and a reactor vessel portion defining a reactor volume disposed below the separator plate and containing the nuclear reactor core, wherein the separator plate restricts but does not completely cut off fluid communication between the pressurizer volume and the reactor volume, a reactor coolant pump including (i) an impeller disposed inside the pressure vessel in the reactor volume, (ii) a pump motor disposed outside of the pressure vessel, and (iii) a drive shaft operatively connecting the pump motor with the impeller, wherein no portion of the reactor coolant pump is disposed in the pressurizer volume, and the drive shaft passes through an opening in the pressure vessel that is at least large enough to pass the impeller wherein (i) the reactor coolant pump further comprises a pump diffuser containing the impeller and (ii) the opening in the pressure vessel through which the drive shaft passes is too small for the pump diffuser to pass through, and further comprising a manway disposed at or below the pump diffuser that is large enough for the pump diffuser to pass through.