Determination of S 18 from the 9C Breakup Reaction Within a Four-body Reaction Model

Abstract The astrophysical factor $S_{18}$ for the $^{8}$B($p,\gamma )^{9}$C has indirectly been measured with proton removal reactions from $^9$C, the 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 $S_{18}$ was modified. It was not well justified, however, to treat $^8$B as an inert nucleus, given that its proton separation energy is only 137 keV. We re-examine the elastic breakup of $^9$C using 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 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 $S_{18}=38.4\pm 1.2({\rm theor})\pm 5.0({\rm expt})$ eVb. This result is lower 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.