Norm kernels and the closeness relation for Pauli-allowed basis functions

The norm kernel of the generator-coordinate method is shown to be a symmetric kernel of an integral equation with eigenfunctions defined in the Fock--Bargmann space and forming a complete set of orthonormalized states (classified with the use of SU(3) symmetry indices) satisfying the Pauli exclusion principle. This interpretation allows to develop a method which, even in the presence of the SU(3) degeneracy, provides for a consistent way to introduce additional quantum numbers for the classification of the basis states. In order to set the asymptotic boundary conditions for the expansion coefficients of a wave function in the SU(3) basis, a complementary basis of functions with partial angular momenta as good quantum numbers is needed. Norm kernels of the binary systems 6He+p, 6He+n, 6He+4He, and 8He+4He are considered in detail.Comment: 25 pages; submitted to Few-Body System

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

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$\leq 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.Comment: 36 pages, 23 figures, to be submitted to Phys. Rev.