Narrow Results

The binding energies per-nucleon for 1654 nuclei, whose mass numbers range from 16 to 263 and charge numbers range from 8 to 106, are calculated by the relativistic mean field theory, with finite nucleon size effect being taken into account. The calculated energy surface goes through the middle of experimental points, and the root mean square deviation for the binding energies per-nucleon is 0.08163 MeV. The numerical results may be well simulated by a droplet model type mass formula. The droplet model is therefore put on the relativistic mean field theoretical foundations.

We analyze the relation between the symmetry energy coefficient $a_{\mathrm{\text{sym}}}(A)$ of finite nuclei with mass number $A$ in the semi-empirical mass formula. The nuclear matter symmetry energy $E_{\mathrm{\text{sym}}}({\rho }_A)$ at reference density ${\rho }_A$ in the subsaturation density region can be determined by the symmetry energy $E_{\mathrm{\text{sym}}}({\rho }_0)$ and its density slope $L$ at the saturation density ${\rho }_0$. From this relation, the neutron skin thickness ‘$S$’ in finite nuclei with droplet model are correlated to the various symmetry energy parameters. A prominent role of the bulk symmetry energy $E_{\mathrm{\text{sym}}}({\rho }_0)$ to the so-called surface stiffness coefficient $Q$ is observed in deriving the size of the neutron skin. Two types of neutron skins are distinguished: the “surface” and the “bulk”. The linear dependence of the neutron skin thickness for different stable nuclei ($40\le A\le 238$) on the slope $L$ of the symmetry energy as well as on the relative neutron excess $I=\frac{N-Z}{A}$ is observed. Though the value of the surface width is found to be limited within 0.1fm, its contribution should not be neglected to measure neutron skin thickness.