Positioning the neutron drip line and the r-process paths in the nuclear landscape

Exploring nucleon drip lines and astrophysical rapid neutron capture process (r-process) paths in the nuclear landscape is extremely challenging in nuclear physics and astrophysics. While various models predict a similar proton drip line, their predictions for the neutron drip line and the r-process paths involving heavy neutron-rich nuclei exhibit a significant variation which hampers our accurate understanding of the r-process nucleosynthesis mechanism. By using microscopic density functional theory with a representative set of nonrelativistic and relativistic interactions, we demonstrate for the first time that this variation is mainly due to the uncertainty of nuclear matter symmetry energy $E_{\mathrm{sym}}\left({\rho }_{\mathrm{sc}}\right)$ at the subsaturation cross density ${\rho }_{\mathrm{sc}}=0.11/0.16\times {\rho }_0$ $({\rho }_0$ is saturation density), which reflects the symmetry energy of heavy nuclei. By using the recent accurate constraint on $E_{\mathrm{sym}}\left({\rho }_{\mathrm{sc}}\right)$ from the binding-energy difference of heavy-isotope pairs, we obtain quite precise predictions for the location of the neutron drip line, the r-process paths, and the number of bound nuclei in the nuclear landscape. Our results have important implications on extrapolating the properties of unknown neutron-rich rare isotopes from the data on known nuclei.

Figure 1

The calculated $N_{\mathrm{drip}}$ for $Z=68$ and $Z_{\mathrm{drip}}$ for $N=126$ versus $E_{\mathrm{sym}}\left({\rho }_{\mathrm{sc}}\right)$ and $L\left({\rho }_{\mathrm{sc}}\right)$. Solid squares are the results from SHFB calculations with MSL1 by varying individually $E_{\mathrm{sym}}\left({\rho }_{\mathrm{sc}}\right)$ and $L\left({\rho }_{\mathrm{sc}}\right)$. The results from the other 42 nonrelativistic and relativistic interaction are also included. The band in panel (a) indicates $E_{\mathrm{sym}}\left({\rho }_{\mathrm{sc}}\right)=26.65\pm 0.2$ MeV [41]. See text for details.

Figure 2

The calculated $N_{\mathrm{drip}}$ for $Z=68$ versus $E_{\mathrm{sym}}\left({\rho }_0\right)$ and $L\left({\rho }_0\right)$ from 43 nonrelativistic and relativistic interactions. See text for details.

Figure 3

The landscape of bound even-even nuclei as obtained from DFT calculations with four Skyrme interactions (KDE, SLy4, MSL1, $\mathrm{MSL}{1}^{*})$ and one relativistic interaction (DD-ME1). The prediction from the Weizsacker–Skyrme mass formula with WS4 [15] is also included for comparison. The gray band denotes the uncertainty of two-neutron drip line from the benchmark calculations in Refs. [22, 23, 24, 25]. The red band shows the r-process path of $S_{2n}=2$ MeV for KDE, SLy4, MSL1, $\mathrm{MSL}{1}^{*}$, and DD-ME1. The experimentally known 800 bound even-even nuclei (up to 2014), including 169 stable (navy squares) and 631 radioactive (green squares), are extracted from Ref. [47] and references therein.