  We examine the production of the Hoyle and associated excited states from the
viewpoint of pocket resonances in the reaction of an $\alpha$-particle on a
ground state prolate $^8$Be nucleus within the optical model coupled-channel
framework. The predicted reaction cross sections, as a function of the
center-of-mass energy $E_{\rm cm}$, show prominent resonances, including the
Hoyle resonance. The positions and widths of these resonances are sensitive to
the target deformation ($\beta_2$ parameter) and the parity of the nuclear
surface potential $-$ deeper for the even-parity $L$ partial waves relative to
those for the odd-parity $L$ partial waves at the surface region because of the
Bose-Einstein exchange of the $\alpha$-bosons. Decomposing the reaction cross
sections to different partial waves, we find that the resonance energies and
widths reasonably agree with the available experimental data and previous
hyperspherical 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, we
identify the narrow and sharp $0_2^+$, $3_1^-$ and $2_2^+$ resonances as pocket
resonances -- resonances which occur below the potential barrier, while the
broad $0_3^+$ and $1_1^-$ resonances as above-the-barrier resonances. For
astrophysical applications, we also evaluate the astrophysical $S(E_{\rm
cm})$-factor for $E_{\rm cm}$ $<$ 1.0 MeV, for the fusion of $\alpha$+$^8$Be
into the $^{12}$C$(2^+)$ state based on our estimated $s$-wave $\alpha$+$^8$Be
reaction cross section and the associated $\gamma$- and $\alpha$-decay widths
for the decay of $^{12}$C excited states in the potential pocket.
