Surface properties of neutron-rich exotic nuclei within relativistic mean field formalisms

In this theoretical study, we establish a correlation between the neutron skin thickness and the nuclear symmetry energy for the even-even isotopes of Fe, Ni, Zn, Ge, Se, and Kr within the framework of the axially deformed self-consistent relativistic mean field for the nonlinear $\mathrm{NL}{3}^{*}$ and density-dependent DD-ME1 interactions. The coherent density functional method is used to formulate the symmetry energy, the neutron pressure, and the curvature of finite nuclei as a function of the nuclear radius. We have performed broad studies for the mass dependence on the symmetry energy in terms of the neutron-proton asymmetry for mass $70\le A\le 96$. From this analysis, we found a notable signature of a shell closure at $N=50$ in the isotopic chains of Fe, Ni, Zn, Ge, Se, and Kr nuclei. The present study reveals a interrelationship between the characteristics of infinite nuclear matter and the neutron skin thickness of finite nuclei.

Figure 1

The two neutron separation energies $S_{2n}$ (upper panel) and the differential variation of the separation energy $d{S}_{2n}$ (lower panel) from the $\mathrm{NL}{3}^{*}$ and the DD-ME1 interactions are given for Fe, Ni, Zn, Ge, Se, and Kr isotopic chains. The experimental data [117] are given for comparison, wherever available. See text for details.

Figure 2

The microscopic relativistic mean field with nonlinear $\mathrm{NL}{3}^{*}$ and Dirac-Hartree-Bogoliubov with DD-ME1 total density distribution for ${}^{76}\mathrm{Fe}$ and ${}^{86}\mathrm{Kr}$ isotopes. See text for details.

Figure 3

The weight function ${\left|f\left(x\right)\right|}^2$ calculated for ${}^{76}\mathrm{Fe}$ and ${}^{86}\mathrm{Kr}$ isotopes by using the self-consistent $\mathrm{NL}{3}^{*}$ and DD-ME1 total density distributions of these nuclei. The arrows stand for the minimum and maximum values of the integration limit taken in the subsequent calculations. See text for details.

Figure 4

The symmetry energy $S_0$ for ${}^{70\text{–}86}\mathrm{Fe}$, ${}^{72\text{–}88}\mathrm{Ni}$, ${}^{74\text{–}90}\mathrm{Zn}$, ${}^{76\text{–}92}\mathrm{Ge}$, ${}^{78\text{–}94}\mathrm{Se}$, and ${}^{80\text{–}96}\mathrm{Kr}$ isotopes as a function of the neutron skin thickness $\mathrm{\Delta }R$ as calculated using the RMF $\mathrm{NL}{3}^{*}$ (solid line) and DD-ME1 (dashed line) interactions. The Skyrme-Hartree-Fock + BCS results for the LNS interaction [64, 67] (dotted line) are given for comparison, where available. See the text for details.

Figure 5

The symmetry energy $S_0$ and the quadrupole deformation ${\beta }_2$ for ${}^{70\text{–}86}\mathrm{Fe}$, ${}^{72\text{–}88}\mathrm{Ni}$, ${}^{74\text{–}90}\mathrm{Zn}$, ${}^{76\text{–}92}\mathrm{Ge}$, ${}^{78\text{–}94}\mathrm{Se}$, and ${}^{80\text{–}96}\mathrm{Kr}$ isotopes as a function of neutron number $N$ are given in the upper and lower panels, respectively. The calculated results from RMF $\mathrm{NL}{3}^{*}$ (solid line) and DD-ME1 (dashed line) interactions are compared with the Skyrme-Hartree-Fock + BCS results for the LNS interaction [64, 67] (dotted line) where available. See the text for details.

Figure 6

The neutron pressure $p_0$ and the curvature $K_0$ for ${}^{70\text{–}86}\mathrm{Fe}$, ${}^{72\text{–}88}\mathrm{Ni}$, ${}^{74\text{–}90}\mathrm{Zn}$, ${}^{76\text{–}92}\mathrm{Ge}$, ${}^{78\text{–}94}\mathrm{Se}$, and ${}^{80\text{–}96}\mathrm{Kr}$ isotopes as a function of neutron skin thickness $\mathrm{\Delta }R$ using the nonlinear $\mathrm{NL}{3}^{*}$ (solid line) and density-dependent DD-ME1 (dashed line) interactions are displayed in the upper and lower panels, respectively. The Skyrme-Hartree-Fock results for the LNS interaction [64, 67] (dotted line) are given for comparison, where available. See text for details.

Figure 7

The neutron pressure $P_0$ and the curvature $K_0$ for ${}^{70\text{–}86}\mathrm{Fe}$, ${}^{72\text{–}88}\mathrm{Ni}$, ${}^{74\text{–}90}\mathrm{Zn}$, ${}^{76\text{–}92}\mathrm{Ge}$, ${}^{78\text{–}94}\mathrm{Se}$, and ${}^{80\text{–}96}\mathrm{Kr}$ isotopes as a function of mass number for the nonlinear $\mathrm{NL}{3}^{*}$ and density-dependent DD-ME1 interactions are given in the upper and lower panels, respectively. The Skyrme-Hartree-Fock results for the LNS interaction [64, 67] (dotted line) are also given for comparison, where available. See the text for details.