A nuclear reactor core comprising fissile material is surrounded by a core former. The core former comprises one or more single-piece annular rings wherein each single-piece annular ring comprises neutron-reflecting material. In some embodiments the core former comprises a stack of two or more such single-piece annular rings. In some embodiments the stack of single-piece annular rings is self-supporting. In some embodiments the stack of single-piece annular rings does not include welds or fasteners securing adjacent single-piece annular rings together. A core basket may contain the nuclear reactor core and the core former, and in some embodiments an annular gap is defined between the core former and the core basket. In some embodiments the core former does not include welds and does not include fasteners.