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Motivated by the newly observed $^{39}$Na in experiments, systematiccalculations of global nuclear binding energies with seven Skyrme forces areperformed. We demonstrate the strong correlation between the two-neutronseparation energies ($S_{2n}$) of $^{39}$Na and the total number of boundnuclei of the whole nuclear landscape. Furthermore, with calculated nuclearmasses, we perform astrophysical rapid-neutron capture process ($r$-process)simulations by using nuclear reaction code TALYS and nuclear reaction networkcode SkyNet. $r$-process abundances from ejecta of neutron star mergers andcore-collapse supernova are compared. Prominent covariance correlations betweennuclear landscape boundaries and neutron-rich $r$-process abundances before thethird peak are shown. This study highlights the needs for further experimentalstudies of drip-line nuclei around $^{39}$Na for better constraints on nuclearlandscape boundaries and $r$-process.

Correlations between nuclear landscape boundaries and neutron-rich r-process abundances