Decay dynamics of helium-cluster dinuclear systems in the spontaneous fission of $^{252}$Cf

The decay dynamics of helium-cluster dinuclear systems (DNS) in the spontaneous fission of $^{252}$Cf have been systematically investigated within the framework of the TNS and DNS model, with particular focus on the catalytic role of external Coulomb fields from foil materials. The analysis demonstrates a pronounced and monotonic decrease in decay barrier heights as DNS systems approach foil nuclei, with the effect exhibiting clear dependence on both the atomic number of the foil material and the specific composition of the DNS. Calculations of half-lives using the WKB approximation confirm the dramatic consequences of this barrier modification. These results provide a quantitative theoretical foundation for understanding the experimentally observed catalysis of foil materials on the decay of fissile fragments.