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The shell corrections and shell gaps in nuclei are systematically studiedwith the latest Weizs\"acker-Skyrme (WS4) mass model. We find that most ofasymmetric nuclei with (sub)-shell closures locate along the shell stabilityline (SSL), $N=1.37Z+13.5$, which might be due to a strong correlation betweenneutrons and protons near Fermi surface. The double magicity of nuclei$^{46}$Si and $^{78}$Ni is predicted according to the corresponding shell gaps,shell corrections and nuclear deformations. The unmeasured super-heavy nuclei$^{296}$118 and $^{298}$120, with relatively large shell gaps and shellcorrections, also locate along the SSL, whereas the traditional magic nucleus$^{298}$Fl evidently deviates from the line. The $\alpha$-decay energies ofsuper-heavy nuclei with $Z=113-126$ are simultaneously investigated by usingthe WS4 model together with the radial basis function corrections. Forsuper-heavy nuclei with large shell corrections, the smallest $\alpha$-decayenergy for elements $Z=116$, 117 and 118 in their isotope chains locates at$N=178$ rather than $184$.

Correlations between neutrons and protons near Fermi surface and $Q_{\alpha}$ of super-heavy nuclei