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In nuclear astrophysics, the critical influence of nuclear level density (NLD) on cross-sections and reaction rates has been well established. However, the specific NLD energy range with the most significant impact on the calculations remains unclear. To investigate this, the energy range of the NLD with the most significant effect is identified for different types of reactions relevant to nucleosynthesis, such as (n,γ), (p,γ), (n,p), and (p,n). In literature, the cross-section sensitivity to the photon strength function was performed by [1]. Similarly, cross-section and reaction rate sensitivity to NLD across different energy ranges is investigated, using the microscopic NLD model derived from the Hartree-Fock-Bogoliubov plus the combinatorial method to ensure the accuracy of the results. Consequently, the cross-sections, the reaction rates, and the corresponding sensitivities to variations in the NLD across different energy regions are determined and evaluated.
To ensure a comprehensive examination, eight energies of the incoming particles were considered, namely En = 0.1, 0.2, 0.5, and 1 MeV for neutrons and Ep = 2 - 5 MeV for protons for cross-section calculations. Across the explored energy domain, the resulting cross-sections exhibit a consistent and systematic behavior.
The robustness of the adopted methodology was assessed through a detailed sensitivity analysis of the reaction rates with respect to variations in the NLD. For (n,γ) reactions, the sensitivity is confined between 4 and 5 MeV for temperatures T = 1 – 4 GK and between 5 and 6 MeV when T = 5 GK; meanwhile, the sensitivity of (p,γ) reactions lies in the higher energy range of 7 and 9 MeV for T = 2 – 5 GK. Furthermore, comparing the theoretical predictions to the measured experimental data for 120Sn(n,γ)121Sn, significant uncertainties within the critical energy interval of 4 – 5 MeV.
The analysis was further extended to investigate nuclear structure effects by independently varying the NLDs of the target and compound nuclei. Two complementary approaches were employed: (i) variation of the target nucleus NLD while keeping the compound nucleus NLD fixed, and (ii) variation of the compound nucleus NLD with a fixed target NLD. For both (n,γ) and (p,γ) reactions, the NLDs of the target and compound nuclei contribute significantly to the calculated cross-sections. In contrast, for (n,p) and (p,n) reactions, appreciable modifications in the cross-sections arise predominantly from variations in the target and residual nuclei NLD, while the compound nucleus contribution remains comparatively negligible.
[1] B. Wang et al., Effective energy window of the E1 photon strength function for astrophysical neutron-capture reaction rates, Phys. Rev. C 108, 065805 (2023)