Constraining cross sections for unstable $^{153,159}$Gd$(n,γ)$ and their astrophysical implications

TL;DR

This work tackles the scarcity of neutron-capture data for unstable isotopes by constraining the gamma-ray strength functions and nuclear level densities, then integrating these inputs into TALYS to infer the cross sections for $^{153}$Gd and $^{159}$Gd. By validating the approach on stable ${}^{155,157}$Gd and employing Bayesian optimization to renormalize the level densities, the authors reduce the cross-section uncertainty to about 30%, a significant improvement over unconstrained model spreads. The resulting $^{159}$Gd$(n,γ)$ rate is found to be ~2.9 times higher than the JINA REACLIB value, increasing the $^{160}$Gd production in s-process scenarios, while $^{153}$Gd$(n,γ)$ remains broadly consistent with existing recommendations. These constrained cross sections have important implications for astrophysical reaction networks and can be extended to other unstable isotope chains to enhance nucleosynthesis predictions and reactor-related applications.

Abstract

Neutron capture $(n,γ)$ cross sections of Gadolinium (Gd) isotopes are critical to astrophysics research, nuclear reactor designs, and medical applications. However, the available $(n,γ)$ data on unstable Gd isotopes are scarce and direct measurement is challenging. In this work, we propose an approach to infer the $(n,γ)$ cross sections for unstable $^{153,159}$Gd isotopes by constraining both the $γ$-ray strength functions ($γ$SFs) and nuclear level densities (NLDs). Specifically, the key $γ$SF parameters are adjusted to match the available experimental data, and the NLD parameters are determined by renormalizing microscopic level densities through a Bayesian optimization method. Our approach is verified by comparing our predictions with the experimental $(n,γ)$ data for the stable $^{155,157}$Gd isotopes. We then infer the unstable $^{153,159}\text{Gd}(n,γ)$ cross sections within the neutron energy range of 0.01--5.0 MeV. The resulting uncertainty is about $30\%$, which is significantly reduced by a factor of 5.5 compared to a large uncertainty of $\sim167\%$ predicted with different nuclear models in TALYS. We further calculate the astrophysical reaction rates for the $^{153,159}\text{Gd}$ isotopes. It is found that the $^{159}\text{Gd}(n,γ)$ rate is larger by a factor of $\sim$2.9 than the JINA REACLIB recommendation. This enhancement increases the neutron capture branching ratio at $^{159}$Gd. Consequently, the resulting $^{160}$Gd abundance is increased by a factor of $\sim$2 compared to predictions using the JINA REACLIB rate in $s$-process nucleosynthesis simulations. Our approach is promising for extracting $(n,γ)$ data on a wider range of unstable isotopic chains as well as for essential astrophysical reaction network calculations and nuclear science applications.

Figures (8)

• Figure 1: Simplified nucleosynthesis path of Sm, Eu, Gd, and Tb during the $s$-process. Stable isotopes are shown in grey, while unstable isotopes are in white. Their natural abundances or half-lives are listed accordingly. The black arrows indicate the main $s$-process flow. The red-framed black arrows indicate the $(n,\gamma)$ reactions of interest investigated in this work.
• Figure 2: Panels (a)--(d) present the $\gamma$SF for $^{154,156,158,160}$Gd. Our SLO fits are shown as a red line with one standard deviation uncertainty bands. These are compared with the experimental $\gamma$SF from Refs. vasilev1971giantPhysRevC.2.1951GUREVICH1981257osti_4716950GREENWOOD1978327 and microscopic model evaluations (D1M-HFB+QRPAgorielyGognyHFB+QRPADipoleStrength2018 and Skyrme-HFB+QRPAgorielyMicroscopicHFBQRPA2004, depicted by blue and orange lines, respectively). The vertical dashed lines indicate the $S_n$ for each isotope.
• Figure 3: Comparison of the three $M1$$\gamma$-ray strength function models for $^{156}$Gd. The plot shows the SLO model (blue solid line), the renormalization based on $E1$ strength function (orange dashed line), and the combined model with spin-flip and scissors-mode contributions (green dot-dashed line).
• Figure 4: Systematics of $D_0$ for Gd isotopes and neighboring nuclei. The experimental data for Eu, Gd, and Tb are shown as green circles, blue squares, and orange triangles, respectively. The black solid line corresponds to the fit for even-$A$ nuclei, while the dashed line indicates the odd-$A$ fit. The red open circle marks represent the estimated $D_0$ for $^{160}$Gd from the even-$A$ fit.
• Figure 5: NLD for $^{156}$Gd, as an example. The known discrete levels are plotted as a black solid line. The upper and lower bounds of our renormalized HFB+c NLD are shown as two blue solid lines. The light blue shaded area indicates the energy range of the discrete levels used to fit. The $\rho(S_n)$ is shown as a black square with error bars.