Correlated and uncorrelated Monte Carlo neutron capture rate variations in weak $\textit{r}$-process simulations

TL;DR

This work tackles how uncertainties in neutron-capture rates for neutron-rich nuclei propagate into weak r-process abundances. It employs YAHFC with a quantified KD optical-model variant (KDUQEF/KDEF) to generate rate ensembles, and conducts both uncorrelated and correlated Monte Carlo nucleosynthesis across three weak r-process trajectories. A key finding is that reducing uncertainties for 35 selected rates lowers the final abundance spread by about 30–65% in the $Z=36$–$54$ range, while full covariance-based rate variations produce similar overall envelopes as diagonal-only sampling but reveal reorganized inter-element correlations. The results suggest that while correlated inputs refine the pattern of co-variations, they do not automatically tighten the global uncertainty footprint, and future work incorporating level densities and gamma-strength-function correlations could yield larger impacts and tighter constraints on neutron-capture rates relevant to the weak r process.

Abstract

Reliable predictions of weak rapid neutron capture ($\textit{r}$-process) abundances require a systematic treatment of nuclear physics uncertainties, especially neutron capture rates far from stability. We employ new neutron capture rates from cross sections calculated with Yet Another Hauser-Feshbach Code ($\texttt{YAHFC}$) using an uncertainty-quantified Koning-Delaroche potential modified for use on neutron-rich systems. Using these rates as a baseline, we perform Monte-Carlo studies with independent rate variations (uncorrelated Monte Carlo) and find correlations between specific neutron capture rates and the resulting elemental abundances for the three weak r-process scenarios: two separate simulations of neutron star merger remnant accretion disks and a simulation of a magnetorotational supernova. We discuss the underlying nuclear dynamics that give rise to these correlations and the role of astrophysical conditions in them. We demonstrate how reducing the uncertainty in these rates would improve the prospects for conducting precision $\textit{r}$-process studies in the future. We additionally present a correlated Monte Carlo study, which incorporates the full covariance matrix that describes the relationships between individual neutron capture rates that arise from an uncertainty-quantified optical potential. We find that the magnitude of the uncertainty in the abundance pattern is similar to that produced by an uncorrelated Monte Carlo that employs only the on-diagonal components of the covariance matrix. We show how correlations restructure how the abundances co-vary, but do not necessarily decrease the overall uncertainty envelope.

Figures (13)

• Figure 1: The logarithm of the ratio of our baseline YAHFC rates for $\sim$1000 nuclei to those of Reaclib (upper panel) and TALYS (lower panel) at 1 GK. Our baseline rates use the KDEF optical model potential.
• Figure 2: 1D and 2D marginal distributions ("corner plot") of the Monte-Carlo samples for $\lambda_{n,\gamma}$ for $^{100}$Y, $^{102}$Nb, and $^{104}$Nb at a temperature of $T = 1.16$ GK. The central values are the YAHFC/KDEF baseline rates. The cyan (dashed) contours denote the 2-$\sigma$ range from the set 3A uncorrelated Monte Carlo simulations. The red (solid) contours represent the 2-$\sigma$ range of the samples from the set 3B correlated Monte-Carlo simulations.
• Figure 3: Final elemental yield distributions in the weak $r$-process region for the three astrophysical scenarios, L+24: orange (solid), MF14: blue (dashed) and R+21: green (dotted). The dark line shows the log-mean abundance, and the shaded regions show the 2-$\sigma$ regions for set 1 of Monte-Carlo simulations (uncorrelated, uniform scaling). All abundances are scaled to have the same mean Zr ($Z = 40$) abundance of $10^{-4}$.
• Figure 4: Selected results from our set 1 Monte-Carlo simulations. Final abundance of yttrium versus the rate of neutron capture, $\lambda_{n,\gamma}$ at a temperature of 1.16 GK, on $^{90}$Br (left), and $^{88}$Br (center) obtained in the MF14 and L+24 scenarios, respectively is shown in the left and center panels. In the right panel, the final abundance of zirconium versus the rate of neutron capture on $^{89}$Se (right) (at 1.16 GK) in the R+21 scenario is shown. The contours represent 1-$\sigma$ and 2-$\sigma$ ranges. Each blue dot represents one of the 5000 samples.
• Figure 5: Left column: Highest magnitude Pearson correlation coefficient for each neutron capture rate with any elemental abundance in the set 1 uncorrelated Monte Carlo simulations. Top, middle and bottom panels represent simulations performed with the three astrophysical scenarios: L+24, MF14, and R+21. The square boxes indicate stable isotopes (black) and long-lived isotopes (gray). The dashed gray lines indicate the FRDM neutron drip line and the solid magenta lines shows the limit of the isotopes sampled in this study. Right column: Abundance of each nuclear species, $Y$, at the time when the abundance weighted $(n,\gamma)$ timescale becomes twice the abundance weighted $\beta$-decay timescale, $\tau_{(n,\gamma)}\approx 2\tau_{\beta^-}$.