We examine the production of the Hoyle and associated excited states from the
viewpoint of pocket resonances in the reaction of an Ξ±-particle on a
ground state prolate 8Be nucleus within the optical model coupled-channel
framework. The predicted reaction cross sections, as a function of the
center-of-mass energy Ecmβ, show prominent resonances, including the
Hoyle resonance. The positions and widths of these resonances are sensitive to
the target deformation (Ξ²2β parameter) and the parity of the nuclear
surface potential β 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 Ξ±-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 02+β (Hoyle state), 03+β, 11ββ and
31ββ states of 12C, except for the narrow theoretical width of the
22+β state. Analyzing the wavefunctions and the resonance widths, we
identify the narrow and sharp 02+β, 31ββ and 22+β resonances as pocket
resonances -- resonances which occur below the potential barrier, while the
broad 03+β and 11ββ resonances as above-the-barrier resonances. For
astrophysical applications, we also evaluate the astrophysical S(Ecmβ)-factor for Ecmβ< 1.0 MeV, for the fusion of Ξ±+8Be
into the 12C(2+) state based on our estimated s-wave Ξ±+8Be
reaction cross section and the associated Ξ³- and Ξ±-decay widths
for the decay of 12C excited states in the potential pocket.Comment: 15 pages, 9 figure