Within many-body systems governed by Skyrme density functional, we confirm that the correlations between neutron skin thickness $\mathrm{\Delta }{R}_{\mathrm{np}}$ (or charge radius difference of mirror nuclei,$\mathrm{\Delta }{R}_{\mathrm{mirr}}$) and the isospin asymmetry ($I=\frac{N-Z}{A}$) persistently emerge, demonstrating the parameter-independent nature of these correlations when using the Skyrme force. We further determine that the slopes of the linear $\mathrm{\Delta }{R}_{\mathrm{mirr}}\text{−}I$ or $\mathrm{\Delta }{R}_{\mathrm{np}}\text{−}I$ correlations (denoted as $C_{\mathrm{np}}$ and $C_{\mathrm{mirr}}$, respectively) are also correlated to the slope of the symmetry energy ($L$), which may offer a new approach to constrain $L$ while mitigating the influence of density irregularities in specific nuclei. The linear correlations of $C_{\mathrm{np}}\text{−}L$ and $C_{\mathrm{mirr}}\text{−}L$ are adopted to constrain $L$ to 12–44 MeV with $1\sigma$ confidence. Shape coexistence, or shape effect on charge radius, is considered to explain the experimental deviation of ${}^{18}\mathrm{O}/\mathrm{Ne}$ and some odd-$A\mathrm{\Delta }{R}_{\mathrm{mirr}}\text{'}\mathrm{s}$ from the $\mathrm{\Delta }{R}_{\mathrm{mirr}}\text{−}I$ linearity. Considering the deviation of ${}^{18}\mathrm{O}/\mathrm{Ne}\mathrm{\Delta }{R}_{\mathrm{mirr}}$ due to shape coexistence, the $1\sigma$ range for $L$ is further narrowed to 24–40 MeV, suggesting a soft equation of state for nuclear matter.

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• Neutron skin thickness
• Nuclear charge distribution
• Nuclear shapes and moments
• Symmetry energy
• Nuclear many-body theory