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

Motivated by the newly observed ${}^{39}\mathrm{Na}$ in experiments, systematic calculations of global nuclear binding energies with seven Skyrme forces are performed. We demonstrate the strong correlation between the two-neutron separation energies of ${}^{39}\mathrm{Na}$ and the total number of bound nuclei of the whole nuclear landscape. Furthermore, with calculated nuclear masses, we perform astrophysical rapid neutron capture process ($r$-process) simulations by using the nuclear reaction code talys and the nuclear reaction network code skynet. $r$-process abundances from ejecta of neutron star mergers (NSM) and core-collapse supernova are compared. Prominent covariance correlations between nuclear landscape boundaries and $r$-process abundances in the NSM scenario before the third peak are shown. We also see that statistical correlations disappear where shell effects dominated. This study highlights the need for further experimental studies of drip-line nuclei around ${}^{39}\mathrm{Na}$ for better constraints on nuclear landscape boundaries and the $r$-process in extremely neutron-rich environments.

Figure 1

Calculated neutron pairing gaps ${\mathrm{\Delta }}_{\mathrm{LN}}$ and two-neutron separation energies $S_{2n}$ of Sn isotopes towards to the neutron drip line with different pairing interactions. The experimental $S_{2n}$ values are taken from Ref. [45].

Figure 2

Calculated $S_{2n}$ of ${}^{39}\mathrm{Na}$ with seven Skyrme forces and the corresponding total number of bound nuclei from $Z=8$ to 120. The shadow shows the standard deviation $\sigma$ as the uncertainty.

Figure 3

The calculated nuclear landscape boundaries with seven Skyrme forces (see text). The black squares denote stable nuclei and the green (gray) squares denote nuclei with experimental masses [45].

Figure 4

Calculated $r$-process final abundances as a function of nuclear mass $A$ with seven Skyrme forces (see text for calculation details). The $r$-process abundances of the NSM scenario (a) and the CCSN scenario (b) are displayed. The solar $r$-process abundances in black dots are also shown for comparison.

Figure 5

Similar to Fig. 4 but for $r$-process abundance before freeze-out. For the NSM scenario (a) and the CCSN scenario (b), the abundances are obtained at 1.2 and 0.72 s, respectively.

Figure 6

Calculated correlation matrix between the $r$-process abundance and the relative number of bound isotopes, according to Eq. (3). The correlation between the logarithm of abundances $log\left[Y\right(A\left)\right]$ in terms of mass number $A$ ($x$ axis) and the relative value of $N_b(Z$)/$Z$ in terms of proton number $Z$ ($y$ axis) are calculated, where $N_b(Z$) is the number of bound isotopes for each $Z$. The results for NSM final abundance (a), NSM freeze-out abundance (b), CCSN final abundance (c), and CCSN freeze-out abundance (d) are shown.