Improved version of the α -nucleus optical model potential for reactions relevant to the γ process

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The present paper proposes an improved version of the $\ensuremath{\alpha}$-nucleus optical model potential ($\ensuremath{\alpha}$-OMP), in which the real part of the potential is determined by the double-folding calculation using the density-dependent CDM3Y1 interaction plus a repulsive potential. The imaginary part of the $\ensuremath{\alpha}$-OMP is treated by a Woods-Saxon form with energy-dependent depth, while its real part is corrected by including the contribution of the dispersion relation derived from the strong variation of the potential at energies in the vicinity of the Coulomb barrier. The proposed potential is validated by calculating the $(\ensuremath{\alpha},n)$ and $(\ensuremath{\alpha},\ensuremath{\gamma})$ cross sections on different target nuclei and the obtained results are compared with those predicted by the recent $\ensuremath{\alpha}$-OMP suggested by Avrigeanu, as well as the available experimental data. The impacts of the energy-dependent imaginary part and the real dispersive term on the $\ensuremath{\alpha}$-induced cross sections are also investigated. The results obtained show that the proposed $\ensuremath{\alpha}$-OMP together with that of Avrigeanu describe reasonably well the experimental cross sections of all $(\ensuremath{\alpha},n)$ reactions being considered. In addition, the imaginary part of the proposed potential has a strong energy-dependent effect on the $\ensuremath{\alpha}$-induced cross section in the energy region below the Coulomb barrier, in particular for radiative $\ensuremath{\alpha}$-capture reactions. Two potentials also describe well the cross sections of $(\ensuremath{\alpha},\ensuremath{\gamma})$ reactions after rescaling the radiative $\ensuremath{\gamma}$ width. This leads to our conclusion that the present $\ensuremath{\alpha}$-OMP can provide precise $\ensuremath{\alpha}$ widths for the study of reactions relevant to the production of $p$ nuclei, and therefore more intensive theoretical research on the radiative strength functions is required.