It was shown that light nuclei such as ${}^4\mathrm{He}, {}^8\mathrm{Be}$, and ${}^{12}\mathrm{C}$ can be well described by RMF models, which enables a unified description for nuclei with baryon numbers $A\gtrsim 4$. In this work, I propose a hybrid treatment for investigating the clustering phenomenon in nuclear medium, where clusters ranging from light nuclei (e.g., ${}^3\mathrm{H}, {}^3\mathrm{He}$, and ${}^4\mathrm{He}$) to heavy ones (e.g., ${}^{12}\mathrm{C}, {}^{16}\mathrm{O}, {}^{40}\mathrm{Ca}, {}^{48}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$) can be treated in a unified manner. In particular, assuming a spherical Wigner-Seitz cell, the clusters are fixed by solving the Dirac equations imposing the Dirichlet-Neumann boundary condition, while the nuclear medium are treated with Thomas-Fermi approximation and take constant densities. In the presence of nuclear medium, the clusters eventually become unbound as density increases, while the root-mean-square charge radii increase. For clusters with different proton and neutron numbers $N_p\ne N_n$, their binding energies vary with the proton fraction of nuclear medium, which are less significant for clusters with $N_p=N_n$. The uncertainties of density functionals on the clustering phenomenon are investigated as well, adopting 8 different functionals. Based on the obtained results, an analytical formula describing the binding energies of in-medium clusters is then obtained. The results presented in this work should be useful to understand the clustering phenomenon in both heavy-ion collisions and neutron stars.

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• Nuclear astrophysics
• Nuclear binding
• Nuclear many-body theory