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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2410.11245 |
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| _version_ | 1866917803761598464 |
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| author | Suzuki, Yasuyuki |
| author_facet | Suzuki, Yasuyuki |
| contents | A microscopic approach to the $^{12}$C$(α, γ)^{16}$O radiative-capture reaction near the Gamow window has been proposed by Y. Suzuki, Few-Body Syst. {\bf 62}, 2 (2021). The important ingredients of the approach include the following: (1) The states of $^{12}$C and $^{16}$O relevant to the reaction are described by fully microscopic 3\,$α$-particle and 4\,$α$-particle configurations. (2) The isovector electric dipole transition is accounted for through the isospin impurity of the constituent $α$-particles. (3) The relative motion among the $α$-particles is expanded in terms of correlated-Gaussian basis functions. A calculation of the radiative-capture cross section demands double angular-momentum projections, that is, the angular momentum of $^{12}$C consisting of 3 $α$-particles and the orbital angular momentum for $^{12}$C$-α$ relative motion. Advancing the previous formulation based on the single angular-momentum projection, I carry out the double projection and present all the formulas needed for the cross section calculation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11245 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calculable Microscopic Theory for $^{12}$C($α$, $γ$)$^{16}$O Cross Section near Gamow Window II Suzuki, Yasuyuki Nuclear Theory A microscopic approach to the $^{12}$C$(α, γ)^{16}$O radiative-capture reaction near the Gamow window has been proposed by Y. Suzuki, Few-Body Syst. {\bf 62}, 2 (2021). The important ingredients of the approach include the following: (1) The states of $^{12}$C and $^{16}$O relevant to the reaction are described by fully microscopic 3\,$α$-particle and 4\,$α$-particle configurations. (2) The isovector electric dipole transition is accounted for through the isospin impurity of the constituent $α$-particles. (3) The relative motion among the $α$-particles is expanded in terms of correlated-Gaussian basis functions. A calculation of the radiative-capture cross section demands double angular-momentum projections, that is, the angular momentum of $^{12}$C consisting of 3 $α$-particles and the orbital angular momentum for $^{12}$C$-α$ relative motion. Advancing the previous formulation based on the single angular-momentum projection, I carry out the double projection and present all the formulas needed for the cross section calculation. |
| title | Calculable Microscopic Theory for $^{12}$C($α$, $γ$)$^{16}$O Cross Section near Gamow Window II |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2410.11245 |