Isotopic and isotonic evolution of the symmetry energy and skins of mirror nuclei

The knowledge of the neutron skin is important for nuclear physics and astrophysics, but its experimental determination faces many challenges. We calculate the neutron skin of a nucleus by using the possibility to relate it with the difference between the proton radii of the corresponding mirror nuclei as an alternative way. The calculations are based on the Hartree-Fock- Bogoliubov method by using the cylindrical transformed deformed harmonic oscillator basis. Predictions for proton skins are also made for several mirror pairs in the middle mass range. The correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated for Ni isotopic chain with mass number A = 48 − 60 and the respective mirror nuclei. These quantities are calculated within the coherent density fluctuation model using Brueckner and Skyrme energy-density functionals for isospin asymmetric nuclear matter with two Skyrme-type effective interactions, SkM* and SLy4. Results are also presented for the symmetry energy as a function of A for a family of mirror pairs from selected chains of nuclei with Z = 20, N = 14, and N = 50. The evolution curves show a similar behavior crossing at the double-magic nucleus in each chain and a smooth growing deviation when N 6= Z starts. Comparison of our results for the radii and skins with those from the calculations based on high-precision chiral forces is made. (author)