Many-channel microscopic theory of resonance states and scattering processes in ${}^9$Be and ${}^9$B

Abstract

We present a many-channel microscopic model that extends the three-cluster model previously formulated in \cite{2009NPA...V37}. This extended model incorporates multiple three-cluster configurations, which are subsequently reduced to a comprehensive set of binary channels. These channels dictate the dynamics of various nuclear processes and the resonance structure of a compound nucleus across a broad energy spectrum. The application of this model focuses on investigating the nature of high-energy resonance states in ${}^9$Be and ${}^9$B, as well as the astrophysical $S$-factors for the reactions ${}^7$Li$(d,n)\alpha \alpha$ and ${}^7$Be$(d,p)\alpha \alpha$, particularly pertinent to the cosmological lithium problem. Parameterization of resonance states is performed across a wide range of total angular momenta and includes states of both positive and negative parity. Dominant decay channels are identified for each resonance state. Detailed analysis of astrophysical $S$ factors resulting from deuteron interactions with ${}^7$Li and ${}^7$Be is conducted within an energy range from zero to 2 MeV. Four exit channels in ${}^9$Be (${}^8$Be($0^{+}$)$+n$, ${}^8$Be($2^{+}$)$+n$, ${}^5$He($3/2^{-}$)$+\alpha$, ${}^5$He($1/2^{-}$)$+\alpha$) and four in ${}^9$B (${}^8$Be($0^{+}$)$+p$, ${}^8$Be($2^{+}$)$+p$, ${}^5$Li($3/2^{-}$)$+\alpha$, ${}^5$Li($1/2^{-}$)$+\alpha$) are considered. A clear hierarchy of reactions is established for the energy range 0$\le E<$1.0 MeV. Notably, reactions ${}^7$Li$+d{=}^8$Be($0^{+}$)$+n$ and ${}^7$Be$+d{=}^8$Be($0^{+}$)$+p$ substantially dominate over all other reactions within this energy range. The model satisfactory describes the experimental astrophysical $S$ factors for these reactions.

Comments: 36 pages, 23 figures, to be submitted to Phys. Rev. C