\section{INTRODUCTION}
{\it Introduction.} -- The $\alpha$-particle interaction with nuclei as well as the corresponding optical model potential (OMP) were of special interest from nuclear-physics earliest days. 
The widely-used phenomenological OMP parameters have been derived from analysis of either elastic-scattering, which is ruled out below the Coulomb barrier $B$, or $\alpha$-induced reaction data. 
They are then used to describe also the $\alpha$--emission from excited nuclei, in terms of the statistical Hauser-Feshbach (HF) \cite{wh52p} and pre-equilibrium emission (PE) \cite{eg92p} models. 
However, there are also various assumptions and parameters of these models in addition to the $\alpha$-nucleus potential. 
Thus, a definite conclusion on $\alpha$-potential may become possible only using HF+PE consistent parameter sets already validated by analysis of other independent data distinct from either $\alpha$-induced reaction or especially $\alpha$--emission data. 

Moreover, there is a so-called $\alpha$-potential mystery of the account at once of both absorption and emission of $\alpha$-particles in nuclear reactions \cite{tr13p}, of equal interest for nuclear astrophysics and fusion technology.
It was referred by Rauscher \cite{tr13p} to competition of the Coulomb excitation (CE) with the compound nucleus (CN) formation in $\alpha$-induced reactions below $B$, while the former does not affect the $\alpha$--emission. 
Because the corresponding partial waves and integration radii may provide evidence for distinct account of CE cross section and OM total-reaction cross section \cite{va16ap}, an alternate solution may also concern additional reaction channels but for $\alpha$--emission. Thus, further consideration should be given to eventual role of the pickup direct interaction (DI) leading to increase of the $\alpha$-emission beyond the HF+PE predictions. 
Besides, a reaction cross-section enhancement that could be related to the position of a giant quadrupole resonance (GQR) is also worthy of note \cite{ma06p}. 

In fact, a former search for new physics in potentials to describe nuclear de-excitation assumed that particle evaporation occurs from a transient nuclear stratosphere of the emitter nucleus (\cite{ma06p} and Refs. therein). 
Recent definite conclusion on incident $\alpha$-particle OMP \cite{va14p} made feasible the analysis of a possible difference between the OMPs describing either $\alpha$-particle elastic scattering and reactions or $\alpha$-emission from excited nuclei \cite{va94p}. 
On the other hand, OMP \cite{va14p} validation for $\alpha$-emission in low-energy proton-induced reactions on Zn isotopes was related to a surface character \cite{va15p}, at variance with the fast-neutron induced reactions on Zr isotopes \cite{va17p}.
Analysis of $\alpha$--emission from nuclei excited in reactions induced by either neutrons or low-energy protons became thus of interest while there are quite useful recent data of low-lying states feeding \cite{gz10ap,gz10p,yg14p,zw15p,tk18p,hb19p} for $A$$\sim$60 nuclei.  

Consequently, it is of interest to find out also under these conditions if the $\alpha$-emission could be described by the same OMP \cite{va14p} which led to a rather good account of $\alpha$-induced reaction data \cite{va14p,ma09p,ma10p,va16p,va19p}. 
It provided in the meantime better results also within large-scale nuclear-data evaluation \cite{ajk15p}, being adopted as default option within the world-wide used code TALYS \cite{TALYSp}. 
Nevertheless, use of a consistent model parameter set, with no empirical rescaling factors of the $\gamma$ and/or neutron widths, is essential to avoid compensation effects.
Hence the main HF, PE, and DI assumptions and parameters as well as independent data analysis to support them are given in the Supplemental Material  \cite{SM2020p}. 

\begin{figure*}
\resizebox{1.8\columnwidth}{!}{\includegraphics{Ni614pa.EPS}}
\caption{\label{Fig:Ni614pa} (Color online) Comparison of (a,b) measured $(p,\alpha)$  excitation functions on $^{61,64}$Ni \cite{exforp}, evaluated (short-dashed curves) \cite{TENDLp}, and PE+CN calculated values using the $\alpha$-particle OMPs of Refs. \cite{va14p} (dashed curves) and \cite{va94p} (short-dash-dotted curves), and (b) total PE $\alpha$-emission (dash-dot-dotted curve), DI pickup (dash-dotted curve), and sum (solid curve); uncertainty bands correspond to error bars of NLD parameter $a$ (with uncertainties in units of the last digit \cite{SM2020p}) and low-lying level cumulative number $N_d$ of residual nuclei (gray band), and (a) for GDH $\alpha$-particle pre-formation probability $\varphi$ (orange band).}
\end{figure*}

{\it DI pickup in addition to PE+CN $\alpha$-emission.} -- 
The due consideration of DI role for $\alpha$-emission in nucleon--induced reactions is obviously leading to an increase beyond the PE+HF predictions.
Actually, Qaim {\it et al.} \cite{smq95p} extended at incident energies $\leq$15 MeV the conclusion of '90s that the pickup instead of knockout has the main DI contribution to low-lying states in $(p,\alpha)$ and $(n,\alpha)$ reactions (\cite{eg92p,eg89p,eg91p} and Refs. therein). 
However, Qaim {\it et al.} normalized the semimicroscopic pickup contribution to their $^{64}$N$(p,\alpha)$$^{61}$Co data at 15 MeV, with results that depend notably on the former PE+HF component \cite{SM2020p}. 
Hence, an increased predictive power of the model results demands the primary use of  spectroscopic data.

In the present work, the pickup contribution to $(p,\alpha)$ and $(n,\alpha)$ reactions was determined within the distorted wave Born approximation (DWBA) method using the code FRESCO \cite{FRESCOp} and the same OMPs as within HF+PE analysis.
One--step reaction was considered through the pickup of $^3$H and $^3$He clusters, respectively. 
Moreover, the "spectator model" \cite{smits76p,smits79p} was involved, where the two transferred either neutrons or protons in $(p,\alpha)$ and $(n,\alpha)$ reactions, respectively, are coupled to zero angular momentum acting as spectators, while the transferred orbital ($L$) and total ($J$) angular momenta are given by the third, unpaired nucleon of the transferred cluster.
The prior form distorted--wave transition amplitudes, and the finite--range interaction were considered, with more details in \cite{SM2020p}. 
Finally, 19 states \cite{smits79p,plj78p,ensdfp}, until the excitation energy of $\sim$5 MeV, were involved for assessment of the pickup excitation function in Fig.~\ref{Fig:Ni614pa}(b).

First, within 5--7 MeV above the effective $(p,\alpha)$ reaction threshold, the DI pickup component is around half the CN one but an order of magnitude larger than PE contribution. 
The major role of DI pickup on low-lying residual states, at lower incident energies, is thus proved. 
The PE component corresponds to the Geometry-Dependent Hybrid (GDH) model \cite{mb83p}, generalized through inclusion of the angular-momentum and parity conservation \cite{ma90p} and the phenomenological knockout model of $\alpha$--emission based on a pre-formation probability $\varphi$ \cite{eg92p}. 
It increases with the incident energy, becoming dominant at proton energies $>$15 MeV. 

Second, the DI pickup inclusion is providing a suitable description of the measured data at all energies. 
This point is particularly notable below 10 MeV, where there is no effect of nuclear level density (NLD) parameters \cite{SM2020p} as shown by the related uncertainty bands.

Third, there is an obvious data agreement, within several MeV above the effective $(p,\alpha)$ reaction threshold, for the CN component given by the $\alpha$-particle OMP of Ref. \cite{va94p}. 
This fact may explain the former results found in this energy range but without DI account \cite{va94p}. 

The case of the $(p,\alpha)$ reaction on $^{61}$Ni is also shown in Fig.~\ref{Fig:Ni614pa}(a) making use of the CN isotopic effect of cross--section decreasing with the isotope mass increase \cite{nim77p}. 
The lower similar dependence of the DI processes leads to an increased sensitivity of the $(p,\alpha)$ reaction on heavier isotope $^{64}$Ni to the pickup contribution. 
Moreover, the larger cross sections for this case underlines the difference between predictions of the $\alpha$-particle OMPs \cite{va14p,va94p}, and thus support the former one. 

{\it DI pickup contribution in $\alpha$--emission spectra.} -- 
An additional check of DI pickup component of the $\alpha$--emission in neutron--induced reactions on $^{59}$Co is worthwhile, as follows. 
First, there is a large data basis of total $\alpha$--emission as well as $(n,\alpha)$ reaction cross sections over three decades. 
Second, $^{59}$Co may be considered as a benchmark because of its medium  asymmetry parameter $(N-Z)/A$ and corresponding isotopic effect. 
Third, there are measured at the incident energy of $\sim$14 MeV valuable $\alpha$--emission angular distributions and spectra \cite{rf86p,smg96p,k99p} that are quite important for DI+PE analysis. 

\begin{figure}
\resizebox{0.85\columnwidth}{!}{\includegraphics{Co59naS.EPS}}
\caption{\label{Fig:Co59naS} Comparison of measured $\alpha$-emission spectra from 14--14.5 MeV neutron--induced reactions on $^{59}$Co \cite{rf86p,smg96p,k99p}, and calculated  DI pickup (dash-dotted curve), PE (dashed curves), CN first-- (short-dash curve) and second--emission (dotted curve) components at 14.3 MeV, and their sum (solid curve).}
\end{figure}


Actually, only a tentative attempt was possible in this work, using neutron spectroscopic factors from the $^{55}$Mn$(d,p)^{56}$Mn reaction analysis \cite{NDS56p,comfortp} and the spectator protons pair as picked from 1$f_{7/2}$ subshell  \cite{SM2020p}. 
Then, 27 excited states with well-known $J^{\pi}$ and transferred $L$ \cite{ensdfp,ripl3p}, until 2.088 MeV excitation energy, were considered in the pickup cross--section calculation.
The good agreement proved by the analysis of angular distributions for the $\alpha$-energy bins, within center-of-mass system (c.m.), of 6-10 MeV, 10-12 MeV, and 12-14 MeV (Fig. 26 of \cite{SM2020p}), is completed hereafter by $\alpha$-emission spectra and excitation function discussion. 

\begin{figure}
\resizebox{0.85\columnwidth}{!}{\includegraphics{Co59na2.EPS}}
\caption{\label{Fig:Co59na} As Fig.~\ref{Fig:Ni614pa} but for $(n,\alpha)$ reaction on $^{59}$Co \cite{exforp} and uncertainty gray band for error bars of $s$-wave neutron-resonance spacing $D_0^{\it exp}$ and $N_d$ of residual nucleus $^{56}$Mn (Table I \cite{SM2020p}), and additionally calculated cross sections of $(n,n'\alpha)$ reaction (thin dashed curve) and total $\alpha$-emission (solid curve).}
\end{figure}

Nevertheless, the results in Fig.~\ref{Fig:Co59naS} support the present attempt of the DI pickup contribution on the lowest-lying states of the odd--odd residual nucleus $^{56}$Mn.
The data agreement could be increased by taking into account that data transformation from laboratory system (lab) to c.m. may provide, as shown for $^{56}$Fe \cite{rf84p}, a shift of up to 1 MeV to higher emission energies. 

\begin{figure*}
\resizebox{1.8\columnwidth}{!}{\includegraphics{Fe546nas.EPS}}
\caption{\label{Fig:Fe546nas} As Fig.~\ref{Fig:Co59naS} but for $^{54,56}$Fe target nuclei \cite{exforp,smg79p}, at incident energies of 14.8 and 14.2 MeV, respectively.}
\end{figure*}

\begin{figure*}
\resizebox{1.8\columnwidth}{!}{\includegraphics{Fe546na.EPS}}
\caption{\label{Fig:Fe546na} As Fig.~\ref{Fig:Co59na} but for $^{54,56}$Fe target nuclei and additionally calculated $(n,\alpha)$ cross sections using TALYS-1.9 and its default parameters \cite{TALYSp} (short-dotted curves), and like--GQR components (dash-dot-dotted curves) added to DI+PE+CN (solid curves).}
\end{figure*}

At the same time, this spectrum analysis provides evidence for rather low value of the GDH pre-formation probability $\varphi$=0.04. 
An uncertainty band corresponding to half of it is assumed in the excitation function analysis for both total $\alpha$--emission and $(n,\alpha)$ reaction cross section (Fig.~\ref{Fig:Co59na}). 
The overlap of the related uncertainty band of calculated cross section and recent data is obvious.

On the other hand, Fig.~\ref{Fig:Co59na} proves also that there are no NLD effects below the incident energy of 10 MeV. 
The $\alpha$--particle OMP \cite{va14p} is confirmed, with the additional support of more data since earlier work \cite{va94p}. 


{\it Like-GQR in addition to DI+PE+CN $\alpha$-emission.} -- 
The DI pickup contribution to $(n,\alpha)$ reaction on $^{54,56}$Fe corresponds to 36 excited states up to 5.943 MeV for the residual nucleus $^{51}$Cr, and 18 states up to 5.557 MeV for $^{53}$Cr \cite{SM2020p}.  
A first proof of the present approach was given by calculated angular distributions for the $\alpha$-energy bins from 6 to 14 MeV, compared to data of Fischer {\it et al.} \cite{rf84p} for $^{56}$Fe at 14.1 MeV (Fig. 23 of \cite{SM2020p}). 
It is of interest in the following to note the best agreement obtained for the medium-energy $\alpha$--emission, i.e. from 10 to 12 MeV.

The most significant feature of the comparison of measured and calculated $\alpha$--emission spectra (Fig.~\ref{Fig:Fe546nas}) is the DI pickup contribution on lowest states. 
Then, some spectra overestimation there is at the energies just below the DI maxima, at once with an underestimation of the low-energy side. 
However it could be related for $^{54}$Fe to a rough attempt to transform data from lab \cite{smg79p} to c.m. by an average shift of 0.5 MeV to higher energies, at variance to the precise one for $^{56}$Fe \cite{rf84p}. 
There are also known question marks at $\alpha$--particle energies below $\sim$6 MeV, pointed out by Fischer {\it et al.} \cite{rf84p}.
At the same time, the corresponding experimental total $\alpha$--emission cross sections are among the lowest data, at their incident energies, within the excitation functions (Fig.~\ref{Fig:Fe546na}). 

Nevertheless, the DI pickup contribution is improving the description of these excitation functions except the energy range below $\sim$12 MeV. 
The uncertainty bands related to number of low-lying levels, NLD, and PE parameters \cite{SM2020p} have already proved that none of their effects are in order at these energies. 
Moreover, the above-mentioned best agreement obtained for the angular distribution for $\alpha$-energy bin of 6-10 MeV, at 14.1 MeV incident energy on $^{56}$Fe, is additionally supporting both the CN approach and the involved  $\alpha$--particle OMP \cite{va14p}.

Following a former suggestion \cite{ma06p}, we have assumed that such reaction cross-section enhancement could be understood as decay from giant resonances populated via neutron capture. 
Although generally the decay of the GQR is observed with nucleon emission (\cite{
js81p} and Refs. therein), it has been shown (\cite{mf07p} and Refs. therein) that an appreciable non-statistical decay through $\alpha$--emission can occur. 
This assumption has been supported by the position of the extra yield, beyond DI+PE+CN component sum, just at the GQR energy $E_{GQR}$=$65A^{-1/3}$ MeV \cite{js81p}, i.e. 17.092 and 16.89 MeV for $^{55,57}$Fe excited nuclei, respectively. 
Therefore, we have obtained a fit of this extra yield by addition of Gaussian distributions at $E_{GQR}$, with FWHM widths of 2.35 and 3.54 MeV, and peak cross sections of 8 and 10 mb, respectively (Fig.~\ref{Fig:Fe546na}).

It is obvious that the widths of these Gaussian distributions are much lower than the systematic 'best' value $\Gamma$=$85A^{-2/3}$ MeV (Fig. 14 of Ref. \cite{js81p}). 
They are even lower than the $\Gamma$=$17.5A^{-1/3}$ MeV dependence that seems to describe better the inelastic hadron scattering data which were obtained taking into account also other GRs \cite{js81p}. 
Hence we would call these components only like--GQR contributions.
Further conclusions on the physics behind this empirical addition are not yet  evident, while more similar cases to be concerned may help. 
Nevertheless, a suitable account of the measured $(n,\alpha)$ reaction and $\alpha$-emission cross sections (Fig.~\ref{Fig:Fe546na}) is obtained by this additional like--GQR contribution which are larger than the DI pickup for incident energies $<$12 MeV. 


{\it Conclusions.} -- 
A consistent set of model parameters, validated by analysis of various independent data, makes possible the assessment of an optical model potential \cite{va14p} also for nucleon-induced $\alpha$-emission for $A$$\sim$60 nuclei.
Particularly,  $\alpha$--emission from $^{55,57,58}$Fe and $^{60}$Co isotopes excited by $(n,\alpha)$ reaction, and $^{62,64,65,66}$Cu and $^{64,65,66,68}$Zn isotopes excited through both $(n,\alpha)$ and $(p,\alpha)$ reactions has been analyzed.
The advantage of rather recent data of low-lying states feeding is essential.
Further consideration of additional reaction channels leading to increase of the $\alpha$-emission cross sections beyond the statistical predictions has concerned the DI pickup and GQR similar features.\\  

This work was 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.

