Within the framework of Lanzhou quantum molecular dynamics transport model, the cluster dynamics and double differential cross sections in the spallation reactions have been systematically investigated. The cluster yields are contributed from the preequilibrium emission in the cascade collisions and from the statistical decay via the hot fragments, in which the surface coalescence and GEMINI statistical decay are used for the cluster production. The spallation reactions of proton, deuteron, triton, ${}^3\mathrm{He}$, and $\alpha$ on ${}^{208}\mathrm{Pb}, {}^{209}\mathrm{Bi}$, and ${}^{232}\mathrm{Th}$ are systematically investigated. It is demonstrated that the energetic clusters are mainly contributed from the preequilibrium emission, in particular, at the kinetic energies above 30 MeV. The more bound nucleus is available for the production in the spallation reactions, i.e., the larger yields for $\alpha$ in comparison with ${}^3\mathrm{He}$. The kinetic energy tail of cluster production is enhanced with increasing beam energy. The low-energy clusters are mainly produced from the decay of hot fragments and correlated with the energy deposition of incident nuclides. The experimental double differential cross sections are well reproduced within the combined approach.

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• H & He induced nuclear reactions
• Nuclear fragmentation