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We examine the production of the Hoyle and associated excited states from theviewpoint of pocket resonances in the reaction of an $\alpha$-particle on aground state prolate $^8$Be nucleus within the optical model coupled-channelframework. The predicted reaction cross sections, as a function of thecenter-of-mass energy $E_{\rm cm}$, show prominent resonances, including theHoyle resonance. The positions and widths of these resonances are sensitive tothe target deformation ($\beta_2$ parameter) and the parity of the nuclearsurface potential $-$ deeper for the even-parity $L$ partial waves relative tothose for the odd-parity $L$ partial waves at the surface region because of theBose-Einstein exchange of the $\alpha$-bosons. Decomposing the reaction crosssections to different partial waves, we find that the resonance energies andwidths reasonably agree with the available experimental data and previoushyperspherical calculations for the $0_2^+$ (Hoyle state), $0_3^+$, $1_1^-$ and$3_1^-$ states of $^{12}$C, except for the narrow theoretical width of the$2_2^+$ state. Analyzing the wavefunctions and the resonance widths, weidentify the narrow and sharp $0_2^+$, $3_1^-$ and $2_2^+$ resonances as pocketresonances -- resonances which occur below the potential barrier, while thebroad $0_3^+$ and $1_1^-$ resonances as above-the-barrier resonances. Forastrophysical applications, we also evaluate the astrophysical $S(E_{\rmcm})$-factor for $E_{\rm cm}$ $<$ 1.0 MeV, for the fusion of $\alpha$+$^8$Beinto the $^{12}$C$(2^+)$ state based on our estimated $s$-wave $\alpha$+$^8$Bereaction cross section and the associated $\gamma$- and $\alpha$-decay widthsfor the decay of $^{12}$C excited states in the potential pocket.

The Hoyle and associated excited states from the viewpoint of pocket resonances in alpha + 8Be reactions