Application of the microscopic optical potential of chiral effective field theory in astrophysical neutron-capture reactions

TL;DR

The paper addresses large uncertainties in neutron-capture rates for heavy elements by applying the microscopic WLH optical potential, derived from chiral effective field theory, within Hauser–Feshbach calculations. It introduces a covariance-based sampling of WLH parameters from five chiral interactions and propagates uncertainties to reaction observables, using a backward-forward Monte Carlo framework with the $f_{rms}$ metric. The results show that WLH reproduces known neutron-capture cross sections and MACS (within a factor of about two) and reveal a pronounced isospin-dependent behavior: a clear separation in rate uncertainties around a isospin asymmetry of $\delta \approx 0.28$, with smaller uncertainties for $\delta<0.28$ and much larger ones for $\delta>0.28$. This highlights the critical role of isospin dependence in optical potentials and provides guidance for future refinements of the WLH potential to improve predictions for neutron-rich nuclei relevant to nucleosynthesis.

Abstract

A state-of-the-art microscopic global nucleon-nucleus optical potential has been developed by Whitehead, Lim, and Holt (WLH) within the framework of many-body perturbation theory, incorporating realistic nuclear interactions derived from chiral effective field theory. Given its potentially greater predictive power for reactions involving exotic isotopes, we apply it to the calculations of astrophysical neutron-capture reactions for the first time, which are particularly important to the nucleosynthesis of elements heavier than iron. It is found that this potential provides a good description of experimental known neutron-capture cross sections and Maxwellian-averaged cross sections. For unstable neutron-rich nuclei, we comprehensively calculate the neutron-capture reaction rates for all nuclei with $26\leq Z\leq84$, located between the valley of stability and the neutron drip line, using the backward-forward Monte Carlo method with the $f_{rms}$ deviation as the $χ^2$ estimator. The results reveal a noticeable separation in the uncertainty of rates around an isospin asymmetry of 0.28 under the constraint $f_{rms} \leq 1.56$. This highlights the critical role of isospin dependence in optical potentials and suggests that future developments of the WLH potential may pay special attention to the isospin dependence.

Figures (7)

• Figure 1: Comparison of the calculated and experimental neutron-capture cross sections as a function of incident energy $E_n$ for three nuclei. The shaded area represents cross sections calculated from 400 random samples of the WLH potential. Experimental data are shown as black points and are taken from Refs. tomyo2005 for $^{61}\text{Ni}(\text{n},\gamma)^{62}\text{Ni}$, tolstikov1968timokhov1988 for $^{122}\text{Sn}(\text{n},\gamma)^{123}\text{Sn}$, and beer1984macklin1967wisshak2006 for $^{176}\text{Lu}(\text{n},\gamma)^{177}\text{Lu}$.
• Figure 2: Ratios of theoretical to experimental ($n,\gamma$) MACS for the 221 ($26\leq Z\leq 83$) known KADoNiS values at 30 keV. Black squares are calculated using the phenomenological KD potential. Red circles represent the results with the WLH potential, with error bars indicating the maximum and minimum values under the constraint $f_{rms}\leq 1.56$. The gray shaded area guides the eye for deviations within a factor of two.
• Figure 3: Distribution of $f_{rms}$ deviations. Blue bars show the deviations with respect to the 221 experimental ($n,\gamma$) MACS for 400 sampled parameter sets. Red bars correspond to the cases with $f'_{frms}\leq 2.1$ with respect to the 298 experimental neutron strength functions.
• Figure 4: Comparison between the experimental $S$- and $P$-wave strength functions ($S_0$ and $S_1$) for 298 nuclei ($26\leq Z\leq 83$) and the theoretical predictions. The red circles show the values calculated using 400 sets of WLH potential parameters. The blue shaded areas correspond to the parameter sets constrained by $f_{rms}\leq 1.56$.
• Figure 5: The neutron-capture rates, constrained by three $f_{rms}^{crit}$ values (1.50, 1.56 and 1.74) corresponding to three differently shaded areas, as a function of temperature for the isotopes $^{122}\text{Sn}$, $^{132}\text{Sn}$, and $^{150}\text{Sn}$.