Symmetry energy of deformed neutron-rich nuclei

The symmetry energy, the neutron pressure, and the asymmetric compressibility of deformed neutron-rich even-even nuclei are calculated for the examples of Kr and Sm isotopes within the coherent density fluctuation model using the symmetry energy as a function of density within the Brueckner energy-density functional. The correlation between the thickness of the neutron skin and the characteristics related to the density dependence of the nuclear symmetry energy is investigated for isotopic chains of these nuclei in the framework of the self-consistent Skyrme-Hartree-Fock plus BCS method. Results for an extended chain of Pb isotopes are also presented. A remarkable difference is found in the trend followed by the different isotopic chains: the studied correlations reveal a smoother behavior in the Pb case than in the other cases. We also notice that the neutron skin thickness obtained for ${}^{208}$Pb with the SLy4 force is found to be in a good agreement with recent data.

Figure 1

Proton (a) and neutron (b) rms radii differences relative to ${}^{86}$Kr for oblate and prolate nuclear shapes. (c) Theoretical (with the SLy4 Skyrme force) and experimental isotope shifts $\delta \langle r_c^2\rangle$ of Kr isotopes relative to ${}^{86}$Kr. The results for oblate and prolate shape for $A=82,84$ isotopes are indistinguishable.

Figure 2

HF + BCS neutron skin thicknesses $\Delta R$ for Kr isotopes as a function of the symmetry energy $s$ and the pressure $p_0$ calculated with SLy4, SGII, Sk3, and LNS forces and for oblate and prolate shapes. The results for oblate and prolate shape for $A=82,84$ isotopes are indistinguishable.

Figure 3

The symmetry energies $s$ for Kr isotopes ($A=82$–120) calculated with SLy4, SGII, Sk3, and LNS forces.

Figure 4

The quadrupole parameter $\beta$ as a function of the mass number $A$ for the even-even Kr isotopes ($A=82$–120) in the case of the SLy4 force.

Figure 5

HF + BCS neutron skin thicknesses $\Delta R$ for Sm isotopes as a function of the symmetry energy $s$ (a), pressure $p_0$ (b), and asymmetric compressibility $\Delta K$ (c) calculated with the SLy4 force.

Figure 6

HF + BCS neutron skin thicknesses $\Delta R$ for Sm isotopes as a function of the symmetry energy $s$ (a) and the pressure $p_0$ (b) calculated with SGII, Sk3, and LNS forces.

Figure 7

HF + BCS neutron skin thicknesses $\Delta R$ for Pb isotopes as a function of the symmetry energy $s$ (a), pressure $p_0$ (b), and asymmetric compressibility $\Delta K$ (c) calculated with SLy4, SGII, Sk3, and LNS forces.

Figure 8

The weight function ${\left|f\left(x\right)\right|}^2$ calculated for three Ni ($A=76,78,80$) isotopes (a), three Sn ($A=130,132,134$) isotopes (b), and three Pb ($A=206,208,210$) isotopes (c) by using the HF + BCS total densities for these nuclei and with the SLy4 force.

Figure 9

The weight function ${\left|f\left(x\right)\right|}^2$ and the HF + BCS total density ${\rho }_0\left(R\right)$ of ${}^{208}$Pb calculated with the SLy4 force.

Figure 10

HF + BCS total densities in the surface region for five Ni ($A=74$–82) isotopes (a), five Sn ($A=128$–136) isotopes (b), and five Pb ($A=204$–212) isotopes (c) around double-magic ${}^{78}$Ni, ${}^{132}$Sn, and ${}^{208}$Pb nuclei, respectively, calculated with the SLy4 force.