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

• URL: http://arxiv.org/abs/2311.16837v1
• Date: Tue, 28 Nov 2023 14:52:16 GMT
• Title: The Hoyle and associated excited states from the viewpoint of pocket resonances in alpha + 8Be reactions
• Authors: Teck-Ghee Lee, Orhan Bayrak, Ian J. Thompson and Cheuk-Yin Wong
• Abstract summary: 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. The predicted reaction cross sections, as a function of the center-of-mass energy $E_rm cm$, show prominent resonances including the Bose resonance. For astrophysical applications, we also evaluate the astrophysical $S(E_rm cm)$-factor for $E_rm cm$ $$ 1.0 MeV, for the fusion of
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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