The neutron skin of nuclei is an important fundamental property, but its accurate measurement faces many challenges. Inspired by charge symmetry of nuclear forces, the neutron skin of a neutron-rich nucleus is related to the difference between the charge radii of the corresponding mirror nuclei. We investigate this relation within the framework of the Hartree-Fock-Bogoliubov method with Skyrme interactions. Predictions for proton skins are also made for several mirror pairs in the middle mass range. For the first time the correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated simultaneously for nuclei and their corresponding mirror partners. As an example, the Ni isotopic chain with mass number $A=48-60$ is considered. 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 $N=Z$ nucleus in each chain and a smooth growing deviation when $N\ne Z$ starts. Comparison of our results for the radii and skins with those from the calculations based on high-precision chiral forces is made.

原子核的中子皮是一个重要的基本特性，但其精确测量面临许多挑战。受核力的电荷对称性的启发，富中子核的中子皮与相应镜像核的电荷半径之间的差异有关。我们在与Skyrme相互作用的Hartree-Fock-Bogoliubov方法的框架内研究了这种关系。还针对中等质量范围内的几副镜对做出了质子皮的预测。首次同时研究了原子核及其对应的镜像伙伴的中子皮厚度与与核对称能量的密度依赖性有关的特性之间的相关性。例如，质量数为Ni的同位素链$\mathrm{一种}=48-60$被认为。这些数量是在相干密度波动模型中使用Brueckner和Skyrme能量密度泛函计算的，具有两个Skyrme型有效相互作用的同位旋非对称核物质SkM *和SLy4。还给出了来自所选原子核链的一系列镜像对的对称能量与A的函数关系的结果。$ž=20$， $ñ=14$和 $ñ=50$。演化曲线显示出类似的行为交叉$ñ=ž$ 每个链中的原子核和当 $ñ\ne ž$开始。我们将半径和蒙皮的结果与基于高精度手性力的计算结果进行了比较。