Constraining level densities through quantitative correlations with cross-section data

Abstract

The adopted level densities (LD) for the nuclei produced through different reaction mechanisms significantly impact the accurate calculation of cross sections for the different reaction channels. Many common LD models make simplified assumptions regarding the overall behavior of the total LD and the intrinsic spin and parity distributions of the excited states. However, very few experimental constraints are taken into account in these models: LD at neutron separation energy coming from average spacings of s-and p-wave resonances (D0 and D1, respectively) whenever they have been previously measured, and the sometimes subjective extrapolation of discrete levels. These, however, constrain the LD only in very specific regions of excitation energy, and for specific spins and parities. This work aims to establish additional experimental constraints on LD through quantitative correlations between cross sections and LD. This allows for fitting and the determination of detailed structures in LD. For this we use the microscopic Hartree-Fock-Bogoliubov (HFB) LD as a starting point as the HFB LD provide a more realistic spin and parity distributions than phenomenological models such as Gilbert-Cameron (GC). We then associate variations predicted by the HFB model with the structure observed in double-differential cross sections at low outgoing neutron energy, region that is dominated by the LD input. We also use (n, p) on 56 Fe, as an example case where angle-integrated cross sections are extremely sensitive to LD. For comparison purposes we also perform calculations with the GC model. With this approach we are able to perform fits of the LD based on actual experimental data, constraining the model and ensuring its consistency. This approach can be particularly useful in extrapolating the LD to nuclei for which high-excited discrete levels and/or values of D0 or D1 are unknown. It also predicts inelastic gamma (n, n γ) cross sections that in some cases can differ significantly from more standard phenomenological LD models such as GC.arXiv:1909.09660v1 [nucl-th]

Validation of an optical potential for incident and emitted low-energy $$\alpha $$-particles in the $$A\sim 60$$ mass range

“…The (n, p) reaction excitation function, shown in Fig. 6c, may additionally confirm it as an ideal mechanism to probe the residual-nuclei NLD [89]. The uncertainty bands in Fig.…”

“…The uncertainty bands in Fig. 5c go along the same line as [89]. We have also paid due attention to the suitable fit of N d and D exp 0 data, however with higher fitted N d (Table 1) but also close to numbers of levels considered within complete level schemes in RIPL-3 [41].…”

“…This is due to the magic N number of the lighter isotope as well as the isotopic effect of (n, p) and (n, α) reaction cross-sections, of decreasing with the isotope mass increase [88]. On the other hand, it has most recently been proved by Nobre et al [89] as an ideal mechanism to probe the NLD of 56 Fe and 56 Mn. Their starting point has been that NLD parameters which describe reasonably well N d and D exp 0 data do not necessarily lead to consistent calculated cross-section agreements at the precision level required in evaluations.…”

Measurement and modeling of proton-induced reactions on arsenic from 35 to 200 MeV

“…It is also worth remarking that using multiple level density models in this work is not a qualification or statement that one model more accurately reflects physical behaviour. Instead, we can only conclude that multiple level density models, and nuclide-specific changes, were simply scalings needed to best match the available experimental data, which has been seen in other work as well [114,115]. There is likely no clear physical insight about the models that can be taken from these fits alone.…”

“…Overall, we put forth a large number of level density scalings, either directly or as a correlation consequence, and though this is not unexpected given the prior lack of data and ambiguity for the reactions and energies of interest [109,114], it is important to reflect on the intricacies of performing such a number of scalings. This discussion is presented in Section IV B 1.…”