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\title{Additional reaction mechanisms to statistical $\alpha$-emission and the related optical-potential validation}
\author{V.~Avrigeanu} \email{vlad.avrigeanu@nipne.ro}
\author{M.~Avrigeanu}
\affiliation{Horia Hulubei National Institute for Physics and Nuclear Engineering, 077125 Bucharest-Magurele, Romania}
\maketitle
%\begin{abstract}
{\bf Abstract}
An $\alpha$-particle optical model potential (OMP) previously established by analysis of $\alpha$-particle elastic scattering and induced reactions on $A$$\approx$45--209 nuclei, at energies $\leq$50 MeV [1] has lately been proved able to describe also the $\alpha$-emission from excited nuclei in nucleon-induced reactions within the $A$$\sim$60 mass-number range [2]. This description in terms of the compound nucleus (CN) and pre-equilibrium emission (PE) models was possible firstly using CN+PE consistent parameter sets already validated by analysis of other independent data that are distinct from $\alpha$-induced reaction or $\alpha$-emission cross sections. Thus, it has also been provided an alternate solution of so-called $\alpha$-potential mystery [3] to describe at once both absorption and emission of $\alpha$-particles, of equal interest for nuclear astrophysics and fusion technology.
On the other hand, it has been shown that further consideration should be given to the pickup direct interaction (DI) leading to increase of the $\alpha$-emission beyond the CN+PE predictions. A suitable account of the measured $\alpha$-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 {\it like}-GQR component. Lastly, a comparison with results of an earlier OMP [4] that was set up to describe only the $\alpha$-particle emission in neutron-induced reactions, with distinct predictions from potentials for incident $\alpha$ particles [5], seems to answer the question of different OMPs for incident and emitted $\alpha$ particles [6-8].
While the previous $\alpha$-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, a similar one for the stable Ni isotopes [9] provides its confident completion in the present work. Moreover, the most-recent data around the GQR energies of the excited nuclei in the $(n,\alpha)$ reaction on $^{58,60,61}$Ni are additionally quite useful. Finally, the issue of additional reaction channels able to increase of the $\alpha$-emission cross sections, beyond the statistical predictions, proved similar to that pointed out formerly [2]. Moreover, a comparable contribution at the GQR energy of Ni excited nuclei has been needed in order to provide a suitable account of the measured $\alpha$-emission cross sections at the lowest energies. This issue is proved especially for $^{64}$Ni target nucleus due to the isotopic effect of the $(n,\alpha)$ reaction cross sections. On the other hand, because the corresponding Gaussian distributions added in this respect have widths which are much lower than the systematic 'best' values [10], we still may call these components only {\it like}-GQR components. More similar cases to be concerned particularly for heavier nuclei could help also concerning the physics behind the actual empirical addition.
%\end{abstract}
\bigskip
[1] V. Avrigeanu, M. Avrigeanu, and C. M\u an\u ailescu, Phys. Rev. C {\bf 90}, 044612 (2014)
[2] V. Avrigeanu and M. Avrigeanu, Eur. Phys. J. A {\bf 57}, 54 (2021)
[3] T. Rauscher, Phys. Rev. Lett. {\bf 111}, 061104 (2013).
[4] V. Avrigeanu, P.E. Hodgson, and M. Avrigeanu, Phys. Rev. C {\bf 49}, 2136 (1994).
[5] L. McFadden and G.R. Satchler, Nucl. Phys. {\bf 84}, 177 (1966).
[6] M. Avrigeanu, W. von Oertzen, and V. Avrigeanu, Nucl. Phys. A {\bf 764}, 246 (2006).
[7] V. Avrigeanu and M. Avrigeanu, Phys. Rev. C {\bf 91}, 064611 (2015).
[8] V. Avrigeanu and M. Avrigeanu, Phys. Rev. C {\bf 96}, 044610 (2017).
[9] H. Jiang {\it et al.}, Chin. Phys. C {\bf 44}, 114102 (2020).
[10] J. Speth and A. van der Woude, Rep. Prog. Phys. {\bf 44}, 719 (1981).
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\noindent
{\it This work has been partly supported by Autoritatea Nationala pentru Cercetare Stiintifica (Project PN-19060102) and carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.}
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