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 $A\gtrsim4$. 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 $N_p \neq N_n$, 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.