Threshold-Aligned Pygmy Dipole Strength in Astrophysical $(n,γ)$ and $(γ,n)$ Reactions

Abstract

Reaction-rate calculations relevant to r-process nucleosynthesis depend sensitively on the nuclear $γ$-strength function ($γ$SF). Here we investigate the impact of low-lying pygmy dipole strength (PDS) in $(n,γ)$ and $(γ,n)$ reactions using $γ$SF based on relativistic nuclear energy density functional theory and propagate these strengths into Hauser--Feshbach statistical model calculations of the reaction rates. We show that considerable reaction-rate enhancements at temperatures relevant for r-process nucleosynthesis are governed by the alignment of the pygmy dipole strength energy with the neutron separation threshold $S_n$ rather than by the total low-energy strength. Consequently, nuclei such as $^{68}$Ni and $^{132}$Sn, where the PDS energy-$S_n$ alignment occurs, exhibit the strongest effects on reaction-rate enhancements. These results demonstrate that modeling reliable reaction rates in r-process nucleosynthesis necessitates accurate microscopic descriptions of low-energy dipole strength, in close synergy with experimental investigations in the vicinity of neutron threshold.

Figures (5)

• Figure 1: Electric dipole $\gamma$-ray strength functions $f_{E1}(E)$ for even–even $^{56-82}$Ni (a) and $^{100-150}$Sn (b) isotopic chains calculated with the DD-PCX energy density functional.
• Figure 2: Energy-dependent ratios of the cross-sections calculated with and without pygmy dipole strength in $(n,\gamma)$ (a), (b) and $(\gamma,n)$ (c), (d) reactions for even–even $^{60\text{–}82}$Ni and $^{116\text{–}150}$Sn compound nuclei.
• Figure 3: Temperature-dependent reaction-rate ratios $N_A \langle \sigma v \rangle_{\mathrm{GDR+PDS}} / N_A \langle \sigma v \rangle_{\mathrm{GDR}}$ for $(n,\gamma)$ (a), (b) and $(\gamma,n)$ (c), (d) reactions of even–even $^{60\text{–}82}$Ni and $^{116\text{–}150}$Sn. The same color coding like in Fig. \ref{['fig:e_cs_ratio']} is used.
• Figure 4: Neutron separation energies ($S_n$) and PDS peak energies ($E_{\mathrm{PDS}}$) for Ni and Sn isotopes (left $y$-axis). Ratios of $(n,\gamma)$ (a), (b) and $(\gamma,n)$ (c), (d) cross sections calculated with and without pygmy contributions (right $y$-axis), evaluated at 30 keV and at $S_n + 30$ keV, respectively, for the compound nuclei $^{60\text{–}82}$Ni and $^{116\text{–}150}$Sn.
• Figure 5: The rates for $(n,\gamma)$ (a), (b) and $(\gamma,n)$ (c), (d) reactions for Ni and Sn istopic chains (left $y$-axis). Ratios of reaction rates calculated with and without pygmy dipole strength, $N_A\langle\sigma v\rangle_{\mathrm{GDR+PDS}}/N_A\langle\sigma v\rangle_{\mathrm{GDR}}$, are shown for even–even $^{60\text{–}82}$Ni and $^{116\text{–}150}$Sn compound nuclei (right $y$-axis). The $(n,\gamma)$ rates are evaluated at $kT=30$ and 200 keV, while the $(\gamma,n)$ rates are shown at $kT=200$ keV. Comparison with available KADoNiS v0.3 kadonis data at $kT=30$ keV is included for the $(n,\gamma)$ reaction rates.