Impact of level densities and $\gamma$-strength functions on $r$-process simulations

Studies attempting to quantify the sensitivity of the $r$-process abundances to nuclear input have to cope with the fact that the theoretical models they rely on, rarely come with confidence intervals. This problem has been dealt with by either estimating these intervals and propagating them statistically to the final abundances using reaction networks within simplified astrophysical models, or by running more realistic astrophysical simulations using different nuclear-physics models consistently for all the involved nuclei. Both of these approaches have their strengths and weaknesses. In this work, we run $r$-process calculations for five trajectories using 49 different neutron-capture rate models. Our results shed light on the importance of taking into account shell effects and pairing correlations in the network calculations.

Figure 1

The evolution of the neutron-capture rate $N_A\langle \sigma v\rangle$ evaluated at $T=1.0$ GK and the $(n,\gamma ) Q$-value along the Sb isotopic chain for all 48 theoretical talys models explained in Section 3, calculated with the HFB-17 [17] mass model (see text).

Figure 2

Differences (in orders of magnitude) between the highest and lowest predicted neutron-capture rate at $T=1.0$ GK for all the 48 models using (a) the FRDM-2012 [36] mass model (an updated version of what the JINA REACLIB rates [23] are based on) and (b) the HFB-17 [17] mass model. The plotted differences $\mathrm{\Delta }(Z,N)$ have been calculated as $\mathrm{\Delta }(Z,N)={log}_{10}\left(N_A{\langle \sigma v\rangle }_{\text{max}}\right)-{log}_{10}\left(N_A{\langle \sigma v\rangle }_{\text{min}}\right)$, where $N_A{\langle \sigma v\rangle }_{\text{max,min}}$ represent the maximum and minimum predicted rates, respectively. The different mass models predict different neutron drip lines, and this is the reason for the different shapes.

Figure 3

Neutron-capture rate predictions for different choices of GSF while varying the NLD models, using ${}^{182}\mathrm{Xe}$ as an exemplary case (see text).

Figure 4

Difference between Figs. 2 and 2, showing which mass model generates the biggest spread in predicted neutron capture rates, for all the 48 combinations of NLD and GSF models. The negative differences (i.e. where the FDRM-2012 model predicts larger uncertainties) are shown in the top panel, while the positive ones (where the HFB-17 predicts the larger uncertainties) in the bottom panel.

Figure 5

The biggest difference for each of the 48 models for the neutron-capture rate at $T=1.0$ GK of an $N$-odd nucleus $(Z,N)$ and its $N$-even neighbors $(Z,N-1)$ and $(Z,N+1)$. The difference (in orders of magnitude) is plotted against $(Z,N)$ for (a) the FRDM-2012 [36] mass model and (b) the HFB-17 [17] mass model. The differences were calculated in a similar fashion as for those in Fig. 2.

Figure 6

Difference between Figs. 5 and 5, showing which mass model generates the highest staggering (see text). The negative differences are plotted in the top panel, while the positive ones in the bottom panel.

Figure 7

The abundances from the five trajectories after 1 Gy evolution. In blue is the span of the final abundance predictions calculated from the 48 neutron-capture rate models. The black dashed line represents the abundances obtained using JINA REACLIB rates [23], while the black dots are the $r$ solar abundances [58] scaled down to fit the third peak at $A\approx 195$.