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

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 o...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Lee, Teck-Ghee, Bayrak, Orhan, Thompson, Ian J, Cheuk-Yin Wong
Format: Article
Language:English
Subjects:
Alpha decay
Alpha rays
Bosons
Cross-sections
Decomposition reactions
Excitation
Parameter sensitivity
Parity
Resonance
Wave functions
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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 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 \(E_{\rm cm}\) \(
ISSN:2331-8422