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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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

We theoretically investigate the possibility for a tetraneutron to exist as a low-energy resonance state. We explore a microscopic model based on the assumption that the tetraneutron can be treated as a compound system where 3 n+n and 2 n+ 2 n coupled cluster configurations coexist. The influence of the Pauli principle on the kinetic energy of the relative motion of the neutron clusters is shown to result in their attraction. The strength of such attraction is high enough to ensure the existence of a low-energy resonance in the tetraneutron, provided that the oscillator length is large enough. The first claim of the experimental observation of the nuclear stable tetraneutron has been made in [1]. Since then all other experimental attempts to find either a bound or a resonance state in the system of four neutrons have not met with success. However, in a recently reported experiment with the breakup of 14 Be [2] six events consistent with the formation of a bound tetraneutron were revealed. Unfortunately, several other experiments [3,4,5] undertaken to verify these results failed to prove or refute completely the existence of the tetraneutron due to a poor statistics. An overall conclusion of a number of theoretical papers on this subject [6,7,8,9] is that it does not seem possible to change modern nuclear Hamiltonians to bind a tetraneutron without destroying many other successful predictions of those Hamiltonians. For instance, calculations within the hyperspherical functions method (HSFM) [7] suggest that a very strong phenomenological four-nucleon force is needed in order to bind the tetraneutron. And yet neither theoretical nor experimental results exclude the possible existence of tetraneutron as a low-energy resonance (see [6,9,10]).There are only few cases of theoretical treatment of the resonant tetraneutron. In Ref.[9] the continuum states of the 4 n system were studied in the framework of the approach which combines concepts of the HSFM and the resonating-group method (RGM). Along with the lowest order hyperharmonic the authors of Ref.[9] invoked the hyperharmonics with hypermomenta K = K min + 2 and K = K min + 4, which reproduce 2 n+ 2 n clustering of the tetraneutron. The analysis of the energy behaviour of the eigenphases led authors to the conclusion that 4 n has a resonance state at an energy of about 1-3 MeV. But clear indication of such a resonance was obtained only for the Volkov effective N N potential, which is known to be inappropriate for studying multineutron systems as it binds dineutron.The most systematic study of four-neutron resonances * Electronic address: lashko@univ.kiev.ua † Electronic address: gfilippov@bitp.kiev.ua was performed in [8], where configuration space FaddeevYakubovsky equations have been solved using realistic N N interaction to follow the resonance pole trajectories in the complex energy plane. It was concluded in [8] that tetraneutron -bound or resonant -can be created only in strong external fields and would disintegrate right after such a field is removed. The sa...