Determination of $S_{18}$ from $^{9}$C breakup reaction within a four-body reaction model
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916799966085120 |
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| author | Ogawa, Shoya Fukui, Tokuro Singh, Jagjit Ogata, Kazuyuki |
| author_facet | Ogawa, Shoya Fukui, Tokuro Singh, Jagjit Ogata, Kazuyuki |
| contents | The astrophysical factor $S_{18}$ for the $^{8}$B($p$,$γ$)$^{9}$C has indirectly been measured with the proton removal reactions from $^9$C, elastic breakup of $^9$C off a heavy target, and transfer reactions. Quite recently, the elastic breakup cross section data were reanalyzed with the continuum-discretized coupled channels method (CDCC) assuming a $p+{\rm ^{8}B}$ two-body model for $^9$C and the $S_{18}$ was modified. It was not well justified, however, to treat $^8$B as an inert nucleus given its proton separation energy is only 137~keV. We reexamine the elastic breakup of $^9$C by the four-body CDCC with a $p+p+{\rm ^{7}Be}$ three-body model for $^9$C and evaluate $S_{18}$. To achieve this, we propose a method to disentangle the $p+{\rm ^{8}B}+{\rm ^{208}Pb}$ three-body channel in the four-body CDCC calculation, for the first time. We calculate the elastic breakup cross section of $^9$C off a $^{208}$Pb target at 65~MeV/nucleon. The obtained breakup cross sections are decomposed into the contributions of the $p+{\rm ^{8}B}+{\rm ^{208}Pb}$ and $p+p+{\rm ^{7}Be}+{\rm ^{208}Pb}$ channels by using the solution of the complex-scaled Lippmann--Schwinger equation. The breakup cross section to the $p+{\rm ^{8}B}+{\rm ^{208}Pb}$ channel reproduces well the shape of the experimental data in the low breakup energy region, which is important for determining $S_{18}$. By fitting the theoretical result to the experimental data, the asymptotic normalization coefficient of $^9$C for the $p+{\rm ^{8}B}$ configuration is determined and we obtain $S_{18}=38.4\pm1.1$ eVb. This result is smaller than the previous value obtained with the three-body CDCC by about 45\%. Thus, our new results suggest the necessity of taking into account the fragile nature of $^{8}$B in the $^{9}$C breakup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Determination of $S_{18}$ from $^{9}$C breakup reaction within a four-body reaction model Ogawa, Shoya Fukui, Tokuro Singh, Jagjit Ogata, Kazuyuki Nuclear Theory The astrophysical factor $S_{18}$ for the $^{8}$B($p$,$γ$)$^{9}$C has indirectly been measured with the proton removal reactions from $^9$C, elastic breakup of $^9$C off a heavy target, and transfer reactions. Quite recently, the elastic breakup cross section data were reanalyzed with the continuum-discretized coupled channels method (CDCC) assuming a $p+{\rm ^{8}B}$ two-body model for $^9$C and the $S_{18}$ was modified. It was not well justified, however, to treat $^8$B as an inert nucleus given its proton separation energy is only 137~keV. We reexamine the elastic breakup of $^9$C by the four-body CDCC with a $p+p+{\rm ^{7}Be}$ three-body model for $^9$C and evaluate $S_{18}$. To achieve this, we propose a method to disentangle the $p+{\rm ^{8}B}+{\rm ^{208}Pb}$ three-body channel in the four-body CDCC calculation, for the first time. We calculate the elastic breakup cross section of $^9$C off a $^{208}$Pb target at 65~MeV/nucleon. The obtained breakup cross sections are decomposed into the contributions of the $p+{\rm ^{8}B}+{\rm ^{208}Pb}$ and $p+p+{\rm ^{7}Be}+{\rm ^{208}Pb}$ channels by using the solution of the complex-scaled Lippmann--Schwinger equation. The breakup cross section to the $p+{\rm ^{8}B}+{\rm ^{208}Pb}$ channel reproduces well the shape of the experimental data in the low breakup energy region, which is important for determining $S_{18}$. By fitting the theoretical result to the experimental data, the asymptotic normalization coefficient of $^9$C for the $p+{\rm ^{8}B}$ configuration is determined and we obtain $S_{18}=38.4\pm1.1$ eVb. This result is smaller than the previous value obtained with the three-body CDCC by about 45\%. Thus, our new results suggest the necessity of taking into account the fragile nature of $^{8}$B in the $^{9}$C breakup. |
| title | Determination of $S_{18}$ from $^{9}$C breakup reaction within a four-body reaction model |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2504.04026 |