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We present a many-channel microscopic model that extends the three-clustermodel previously formulated in \cite{2009NPA...V37}. This extended modelincorporates multiple three-cluster configurations, which are subsequentlyreduced to a comprehensive set of binary channels. These channels dictate thedynamics of various nuclear processes and the resonance structure of a compoundnucleus across a broad energy spectrum. The application of this model focuseson 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$(d,p)\alpha\alpha$, particularlypertinent to the cosmological lithium problem.  Parameterization of resonance states is performed across a wide range oftotal angular momenta and includes states of both positive and negative parity.Dominant decay channels are identified for each resonance state. Detailedanalysis 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$\leqE<$1.0 MeV. Notably, reactions $^{7}$Li$+d=^{8}$Be($0^{+}$)$+n$ and$^{7}$Be$+d=^{8}$Be($0^{+}$)$+p$ substantially dominate over all otherreactions within this energy range. The model satisfactory describes theexperimental astrophysical $S$ factors for these reactions.

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