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A better controlled route is selective solvent extraction in acid, followed by selective stripping, rather than precipitating everything near overlapping hydrolysis thresholds. Oxidize Ce(III) to Ce(IV) in a controlled acidic nitrate medium, extract its nitrate complexes into an organic donor phase, and separate the phases. Then reduce the extracted Ce(IV) to Ce(III) and back-extract it into an aqueous phase. Trivalent rare earths are less strongly extracted under suitable conditions.

This still needs a thorium separation: tributyl phosphate can coextract Th(IV). One demonstrated strategy deliberately coextracts Ce(IV) and Th(IV), then uses reducing peroxide solution to strip Ce as Ce(III), followed by a separate thorium strip. The appropriate controls are distribution measurements for each ion at the chosen acid concentration, a cerium oxidation-state check, and a complete mass balance over extraction and stripping. Selectivity comes from combining oxidation state and complexation, not from assuming that one extraction removes every contaminant.^[ref]

Conceptual scope: the safe account below describes the functions of spent nuclear fuel management and the chemical basis of partitioning. It does not supply an ordered fissile-separation flowsheet, reagents, process conditions or purification instructions. In particular, the requested operational eight-step separation scheme is outside this answer's scope.

Eight useful functional objectives are: receiving and identifying the spent nuclear fuel; managing residual decay heat; providing radioactive material confinement and radiation shielding; establishing the chemical and radiological inventory; partitioning reusable constituents from waste at a conceptual level; maintaining accountable control of recovered materials; conditioning solid and liquid wastes; and retaining or treating radioactive effluents. These are management and containment functions, not a claim that the question specifies one universal eight-stage plant design. Several occur throughout a facility's operation rather than sequentially.

The chemical principle of uranium/plutonium partitioning is that an element's oxidation state and complexation affect its chemical speciation, solubility and relative affinity for immiscible phases. solvent extraction can therefore separate elements whose chemistry differs, even though it does not distinguish uranium isotopes by this chemical selectivity. A recovery operation must account for the accompanying fission products, contaminated process materials and secondary wastes; the recovered material is only one output. radioactive material confinement, remote handling and nuclear material accountancy remain necessary because chemical partitioning redistributes both radioactive and fissile inventories.

The distinction is between partitioning reusable fuel constituents from fission-product waste, and subsequently partitioning uranium from plutonium. In the first operation, chemical selectivity transfers selected actinides into a different stream while most fission products remain in the waste stream. In the second, differences in chemical speciation allow the two recovered elements to follow different streams. Neither operation separates uranium isotopes: uranium enrichment and chemical element separation are different tasks.

At a conceptual level, solvent extraction exploits unequal affinities of dissolved species for immiscible liquid phases. complexation changes those affinities, while a change in oxidation state can change an element's preferred phase without changing its identity. This explains why a stream bearing actinides can first be separated from much of its accompanying waste, and why uranium and plutonium need not subsequently remain together. Dissolved and undissolved residues, contaminated solvents and off-gases remain waste-management obligations; a recovery percentage alone is not a complete material balance.

Equipment must provide phase contact and phase disengagement within shielded, confined systems. Remotely maintained contactors and settlers are equipment categories serving those functions; sealed transfer systems, shielded cells and monitored off-gas handling limit contamination and exposure. Cooling manages residual decay heat, and nuclear material accountancy follows inventories and losses. criticality control in radioactive waste is essential because solvent extraction can redistribute fissile constituents. Scoped limitation: this answer gives the chemical principles and equipment functions; operational fissile-separation recipes, reagent sequences, contactor design details and process conditions are intentionally not supplied.

A neutral oxygen-donor extractant, $\mathrm{OP}(\mathrm{OBu}{)}_3$, often abbreviated TBP. It can solvate metal nitrate species in solvent extraction. Selectivity depends on acidity, metal oxidation state, diluent and subsequent stripping conditions.