New Fission Fragment Distributions and $r$-Process Origin of the Rare-Earth Elements

Neutron star (NS) merger ejecta offer a viable site for the production of heavy $r$-process elements with nuclear mass numbers $A\gtrsim 140$. The crucial role of fission recycling is responsible for the robustness of this site against many astrophysical uncertainties, but calculations sensitively depend on nuclear physics. In particular, the fission fragment yields determine the creation of $110\lesssim A\lesssim 170$ nuclei. Here, we apply a new scission-point model, called SPY, to derive the fission fragment distribution (FFD) of all relevant neutron-rich, fissioning nuclei. The model predicts a doubly asymmetric FFD in the abundant $A\simeq 278$ mass region that is responsible for the final recycling of the fissioning material. Using ejecta conditions based on relativistic NS merger calculations, we show that this specific FFD leads to a production of the $A\simeq 165$ rare-earth peak that is nicely compatible with the abundance patterns in the Sun and metal-poor stars. This new finding further strengthens the case of NS mergers as possible dominant origin of $r$ nuclei with $A\gtrsim 140$.

Figure 1

(a) Dominant fission regions in the ($N$, $Z$) plane. Nuclei with spontaneous fission being faster than $\beta$ decays are shown by full squares, those with $\beta$-delayed fission faster than $\beta$ decays by open squares, those with neutron-induced fission faster than radiative neutron capture at $T={10}^9\mathrm{K}$ by open triangles, and those for which photo-fission at $T={10}^9\mathrm{K}$ is faster than photo-neutron emission by closed circles. For $Z=110$, $\beta$-decay processes are not calculated. (b) SPY predictions of the average number of emitted neutrons for each fissioning nucleus in the ($N$, $Z$) plane.

Figure 2

FFDs from the SPY model for eight $A=278$ isobars.

Figure 3

${}^{278}\mathrm{Cf}$ potential energy surface as a function of the quadrupole $⟨{\widehat{Q}}_{20}⟩$ and octupole $⟨{\widehat{Q}}_{30}⟩$ deformations. Both asymmetric fission valleys are depicted by the red arrows.

Figure 4

Final abundance distribution vs atomic mass for ejecta from $1.35–1.35{\mathrm{M}}_{\odot }$ NS mergers. The red squares are for the newly derived SPY predictions of the FFDs and the blue circles for essentially symmetric distributions based on the 2013 GEF model [52]. The abundances are compared with the solar ones [56] (dotted circles). The insert zooms on the rare-earth elements.

Figure 5

Same as Fig. 4 but with abundance distributions obtained with three additional sets of nuclear rates, namely reaction rates obtained with the D1M [57] or FRDM [58] masses and $\beta$-decay rates from the GT2 or Tamm-Dancoff approximation (TDA) [59].