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The norm kernel of the A = 12 system composed of two 6 He clusters, and the L = 0 basis functions (in the SU (3) and angular momentum-coupled schemes) are analytically obtained in the Fock-Bargmann space. The norm kernel has a diagonal form in the former basis, but the asymptotic conditions are naturally defined in the latter one. The system is a good illustration for the method of projection of the norm kernel to the basis functions in the presence of SU (3) degeneracy that was proposed by the authors. The coupled-channel problem is considered in the Algebraic Version of the resonating-group method, with the multiple decay thresholds being properly accounted for. The structure of the ground state of 12 Be obtained in the approximation of zero-range nuclear force is compared with the shellmodel predictions. In the continuum part of the spectrum, the S-matrix is constructed, the asymptotic normalization coefficients are deduced and their energy dependence is analyzed.

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We describe an 2 ' formalism for the continuum spectrum of coupled collective states in light nuclei. In particular, we consider the application to the monopole and quadrupole modes in 'He. We compute the phaseshifts and perform an extensive analysis of the resonance wavefunctions.

Role of the Pauli principle in the formation of both the discrete spectrum and multi-channel states of the binary nuclear systems composed of clusters is studied in the Algebraic Version of the resonating-group method. Solutions of the Hill-Wheeler equations in the discrete representation of a complete basis of the Pauli-allowed states are discussed for 4 He+n, 3 H+ 3 H, and 4 He+ 4 He binary systems. An exact treatment of the antisymmetrization effects are shown to result in either an effective repulsion of the clusters, or their effective attraction. It also yields a change in the intensity of the centrifugal potential. Both factors significantly affect the scattering phase behavior. Special attention is paid to the multi-channel cluster structure 6 He+ 6 He as well as to the difficulties arising in the case when the two clustering configurations, 6 He+ 6 He and 4 He+ 8 He, are taken into account simultaneously. In the latter case the Pauli principle, even in the absence of a potential energy of the cluster-cluster interaction, leads to the inelastic processes and secures an existence of both the bound state and resonance in the 12 Be compound nucleus.

New approach to the problem of multichannel continuum spectrum of three-cluster systems composed of an s-cluster and two neutrons is suggested based on the discrete representation of a complete basis of allowed states of the multiparticle harmonic oscillator. The structure of the eigenfunctions and behavior of the eigenvalues of the three-cluster norm kernel are analyzed. Classification of the eigenvalues of the three-cluster systems with the help of eigenvalues of the two-body subsystem is suggested. Asymptotic boundary conditions for a three-cluster wave function in the continuum consistent with the requirements of the Pauli principle are established. Such asymptotic behavior corresponds rather to subsequent decay of the three-cluster system than to the so-called "democratic decay" associated with the hyperspherical harmonics. The 3H+n+n configuration of the 5H nucleus is considered in detail.Comment: 18 pages, 3 figures, 3 table

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