Abstract
We have calculated the cross sections (CS), differential cross sections (DCS), and astrophysical $S$ factors for the reactions $^{11}\mathrm{B}(p,{\ensuremath{\alpha}}_{1})^{8}\mathrm{Be}^{*}$, $^{11}\mathrm{B}(p,{\ensuremath{\alpha}}_{0})^{8}\mathrm{Be}$, $^{11}\mathrm{B}(p,{p}_{0})^{11}\mathrm{B}$, $^{11}\mathrm{B}{(p,\phantom{\rule{0.16em}{0ex}}{p}_{1})}^{11}{\mathrm{B}}^{*}$, $^{11}\mathrm{B}(p,\phantom{\rule{0.16em}{0ex}}{\ensuremath{\gamma}}_{0})^{12}\mathrm{C}$, $^{11}\mathrm{B}{(p,{\ensuremath{\gamma}}_{1})}^{12}{\mathrm{C}}^{*}$, and $^{11}\mathrm{B}(\mathrm{p},{\mathrm{n}}_{0})^{11}\mathrm{C}$ through a multichannel-multilevel $R$-matrix analysis. We have performed calculations for the energy range 100 keV--3.5 MeV and compared the calculated values with the experimental values. As a result, we have obtained the energy value, spin, and parity of some $^{12}\mathrm{C}$ excited levels within this energy interval. Additionally, we have determined the channel spins and angular momentum of the ${\ensuremath{\alpha}}_{1}\ensuremath{-}^{8}\mathrm{Be}^{*}$, ${\ensuremath{\alpha}}_{0}\ensuremath{-}^{8}\mathrm{Be}$, ${p}_{0}\ensuremath{-}^{11}\mathrm{B}$, ${p}_{1}\ensuremath{-}^{11}\mathrm{B}^{*}$, and ${n}_{0}\ensuremath{-}^{11}\mathrm{C}$ pairs, as well as the electric and magnetic multipoles of the $^{11}\mathrm{B}(p,\phantom{\rule{0.16em}{0ex}}{\ensuremath{\gamma}}_{0})^{12}\mathrm{C}$ and $^{11}\mathrm{B}{(p,{\ensuremath{\gamma}}_{1})}^{12}{\mathrm{C}}^{*}$ channels. Although the analysis results and experimental data mostly agree, we have found some inconsistencies in the $S$-factor values for the $^{11}\mathrm{B}{(p,\phantom{\rule{0.16em}{0ex}}{p}_{1})}^{11}{\mathrm{B}}^{*}$ channel at the 19.2--19.5 MeV energy interval. For the $^{11}\mathrm{B}(p,{\ensuremath{\alpha}}_{1})^{8}\mathrm{Be}^{*}$ decay channel of the 16.57 MeV $({2}^{\ensuremath{-}})$ resonance, the literature discusses which orbital angular momentum quantum value ($l=1$ or $l=3$) is true. We used both values in our analysis, and although no significant difference in the results were observed in the region of the 16.57 MeV $({2}^{\ensuremath{-}})$ resonance, we obtained a better fit with $l=3$ values in the high energy region affected by the tail of this resonance.