Unified treatment for in-medium light and heavy clusters with RMF models

Abstract

It was shown that light nuclei such as ${}^4$He, ${}^8$Be, and ${}^{12}$C can be well described by RMF models, which enables a unified description for nuclei with baryon numbers $A\gtrsim 4$. In this work, we propose a hybrid treatment for investigating the clustering phenomenon in nuclear medium, where clusters ranging from light nuclei (e.g., ${}^3$H, ${}^3$He, and ${}^4$He) to heavy ones (e.g., ${}^{12}$C, ${}^{16}$O, ${}^{40}$Ca, ${}^{48}$Ca, and ${}^{208}$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 varies 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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