Additional reaction mechanisms to statistical α -emission and the related optical-potential validation

. The major role of consistent parameter sets within analysis of neutron-induced α -particle emission, for the assessment of a possible di ﬀ erence between the optical model potentials (OMPs), which describe either alpha-particle elastic scattering and induced reactions or alpha-emission from excited compound nuclei, is shown. They are involved at variance with use of either empirical rescaling factors of the γ and / or neutron widths or even combinations of all options of a computer code for main input parameters. Suitable description of all competitive reaction channels, conﬁrmed by a careful uncertainty analysis in order to avoid parameter ambiguities and / or error compensation, supports further consideration of additional direct processes.

Introduction. An α-particle optical model potential (OMP) previously established by analysis of α-particle elastic scattering and induced reactions on A≈45-209 nuclei, at energies ≤50 MeV [1] has lately been proved able to describe also the α-emission from excited nuclei in nucleoninduced reactions within the A∼60 mass-number range [2]. Description in terms of the compound nucleus (CN) and pre-equilibrium emission (PE) models was possible firstly using CN+PE consistent parameter sets. The so-called αpotential mystery [3] to describe both absorption and emission of α-particles, of interest for nuclear astrophysics and fusion technology, thus has an alternate solution.
On the other hand, it has been shown that further consideration should be given to the pickup direct reaction (DR) leading to increase in the α-emission beyond preequilibrium and statistical model predictions [2]. A suitable account of the measured α-emission cross sections at the Giant Quadrupole Resonance (GQR) energies of 55,57,58 Fe excited nuclei, in addition to the CN component, has also been attributed to a like-GQR component. Lastly, a comparison with results of an earlier OMP [4] that was set up to describe only the α-particle emission in neutroninduced reactions, with distinct predictions from potentials for incident α particles [5], enlightened the question of different OMPs for incident and emitted α particles [6][7][8].
Previous α-emission analysis [2] took the advantage of quite useful recent data of low-lying states feeding in neutron-induced reactions on Fe, Co, Cu, and Zn nuclei. Similar ones for the stable Ni isotopes [10] could additionally be quite useful. Thus, the issue of additional reaction channels able to increase the α-emission cross sections, beyond the current statistical predictions, may prove similar to that pointed out formerly [2]. Moreover, a comparable contribution at the GQR energies of Ni excited * e-mail: vlad.avrigeanu@nipne.ro * * e-mail: marilena.avrigeanu@nipne.ro nuclei seems to be needed for a suitable account of the measured α-emission cross sections at the lowest energies and especially for 64 Ni target nucleus due to the isotopic effect on (n, α) reaction cross sections. However, firstly it should be shown that actual underestimation of measured α-emission data by the CN+PE model calculations is certainly beyond the related parameter uncertainties. Consequently, no empirical rescaling factors of the γ and/or neutron widths should be used but consistent parameter sets already validated by analysis of other independent data (e.g. [1,[7][8][9]). Thus, a careful uncertainty analysis is concerned in order to avoid parameter ambiguities and/or error compensation effects due to less accurate model parameters. This is the main goal of the present work, with results also compared with the default TALYS-1.95 [13] predictions and evaluated data library TENDL-2019 [12], for an overall excitation-function survey. Model calculations and parameters. Hauser-Feshbach (HF) statistical model and PE Geometry-Dependent Hybrid (GDH) [15] model calculations have been carried out using an updated version of the code STAPRE-H95 [16], with 0.2-0.3 MeV equidistant binning of the excitation energy grid. The distorted-wave Born approximation method was involved within the code DWUCK4 [17] for calculation of collective inelastic scattering, which also involved in subsequently decreasing the total-reaction cross section σ R within the PE+HF calculations.
The same NLD approach [2] has been involved, with the BSFG level-density parameter a and g.s. shift ∆ obtained by fit of the low-lying level numbers N d up to excitation energy E * d [19], also used in the HF calculations, and the available s-wave nucleon-resonance spacings D exp 0 [18,20] in ∆E energy range above separation energy. The third BSFG parameter, i.e. the spin cutoff factor, was adopted by taking into account a variable moment of inertia I, between half of the rigid-body value I r at g.s., 0.75I r at S , and full I r at the excitation energy of 15 MeV, with a reduced radius r 0 =1.25 fm [22]. Fit of the error-bar limits of N d and D exp 0 data have also been used to provide limits of the consequent level-density parameters a and ∆.
On the other hand, a smooth-curve method was applied for nuclei without resonance data, an average of the fitted a-values of neighboring nuclei being used to obtain only the ∆ values by fit of low-lying discrete levels and their limits. Moreover, the a-value average spread has been considered for these nuclei in order to derive the corresponding uncertainty of the fitted ∆ values. Finally, the a and ∆ limits were also used within HF calculations to illustrate the NLD effects on calculated cross-sections. The related uncertainty bands are shown in Figs.1-3 at once with the errors of fitted data and related limits of BSFG parameters.
Of equal interest is a comparison of the calculated results obtained using the nucleon OMP [14], while energydependent real potential geometry of these OMPs [23] is used in this work. It results that both neutron-and proton-OMP effects are close but larger than NLD effects, the latter obviously increasing with energy.
Conclusions. While no empirical rescaling factors of the γ and/or neutron widths were used, and NLD, OMP, and MeV neutron-induced reactions on 60 Ni [11], and calculated DI pickup (dash-dotted curve), PE (dashed), CN first-(short-dash ) and second-emission (dotted) components at 14.3 MeV, respectively, and their sum (solid). PE effects have been shown to prove the α-particle OMP as the main HF parameter, the recent (n, α) data remain truly under-predicted for incident energies ≤9 MeV. Due consideration of the uncertainty bands for the HF+PE calculated cross sections has been closely related to the error bars of the independent date fitted in order to establish the consistent parameter set. The need of additional reaction mechanisms to be taken into account has been pointed out.