Three-body description of ${}^9$C: Role of low-lying resonances in breakup reactions

Abstract

The ${}^9$C nucleus and related capture reaction, ${}^8\mathrm{B}(p,\gamma ){}^9\mathrm{C}$, have been intensively studied with an astrophysical interest. Due to the weakly-bound nature of ${}^9$C, its structure is likely to be described as the three-body (${}^7\mathrm{Be}+p+p$). Its continuum structure is also important to describe reaction processes of ${}^9$C, with which the reaction rate of the ${}^8\mathrm{B}(p,\gamma ){}^9\mathrm{C}$ process have been extracted indirectly. We perform three-body calculations on ${}^9$C and discuss properties of its ground and low-lying states via breakup reactions. We employ the three-body model of ${}^9$C using the Gaussian-expansion method combined with the complex-scaling method. This model is implemented in the four-body version of the continuum-discretized coupled-channels method, by which breakup reactions of ${}^9$C are studied. The intrinsic spin of ${}^7$Be is disregarded. By tuning a three-body interaction in the Hamiltonian of ${}^9$C, we obtain the low-lying $2^{+}$ state with the resonant energy 0.781 MeV and the decay width 0.137 MeV, which is consistent with the available experimental information and a relatively high-lying second $2^{+}$ wider resonant state. Our calculation predicts also sole $0^{+}$ and three $1^{-}$ resonant states. We discuss the role of these resonances in the elastic breakup cross section of ${}^9$C on ${}^{208}$Pb at 65 and 160 MeV/A. The low-lying 2${}^{+}$ state is probed as a sharp peak of the breakup cross section, while the 1${}^{-}$ states enhance the cross section around 3 MeV. Our calculations will further support the future and ongoing experimental campaigns for extracting astrophysical information and evaluating the two-proton removal cross-sections.

Comments: 8 pages, 4 figures, 2 tables (final published version)