Volume and surface contributions to the nuclear symmetry energy within the coherent density fluctuation model

The volume and surface components of the nuclear symmetry energy (NSE) and their ratio are calculated within the coherent density fluctuation model (CDFM). The estimations use the results of the model for the NSE in finite nuclei based on the Brueckner energy-density functional for nuclear matter. In addition, we present results for the NSE and its volume and surface contributions obtained by using the Skyrme energy-density functional. The CDFM weight function is obtained using the proton and neutron densities from the self-consistent HF+BCS method with Skyrme interactions. We present and discuss the values of the volume and surface contributions to the NSE and their ratio obtained for the Ni, Sn, and Pb isotopic chains, studying their isotopic sensitivity. The results are compared with estimations of other approaches which have used available experimental data on binding energies, neutron-skin thicknesses, excitation energies to isobaric analog states (IAS), and also with results of other theoretical methods.

Figure 1

The ratio $\kappa =a_A^V/a_A^S$ as a function of $A$ for the isotopic chain of Ni. The SLy4 (solid line), SGII (dashed line), and Sk3 (dotted line) forces have been used in the HF+BCS calculations of the densities in the case of Brueckner EDF.

Figure 2

The same as in Fig. 1 but for the isotopic chain of Sn.

Figure 3

The same as in Fig. 1 but for the isotopic chain of Pb.

Figure 4

The values of $a_A^V$ (a) and $a_A^S$ (b) as functions of $A$ for the isotopic chain of Ni. The SLy4 (solid line), SGII (dashed line), and Sk3 (dotted line) forces have been used in the HF+BCS calculations of the densities in the case of Brueckner EDF.

Figure 5

The same as in Fig. 4 but for the isotopic chain of Sn.

Figure 6

The same as in Fig. 4 but for the isotopic chain of Pb.

Figure 7

The ratio $\kappa =a_A^V/a_A^S$ as a function of $A$ for the isotopic chain of Ni in the case of Skyrme EDF with use of SLy4, SGII, and Sk3 forces.

Figure 8

The same as in Fig. 7 but for the isotopic chain of Sn.

Figure 9

The same as in Fig. 7 but for the isotopic chain of Pb.

Figure 10

The values of $a_A^V$ (a) and $a_A^S$ (b) as functions of $A$ for the isotopic chain of Ni in the case of Skyrme EDF with use of SLy4, SGII, and Sk3 forces.

Figure 11

The same as in Fig. 10 but for the isotopic chain of Sn.

Figure 12

The same as in Fig. 10 but for the isotopic chain of Pb.