How the Pauli principle governs the decay of three-cluster systems

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

A multi-channel model for an a plus 6He nucleus cluster

© 2017, SIF, Springer-Verlag Berlin Heidelberg. A multi-channel algebraic scattering (MCAS) method has been used to solve coupled sets of Lippmann-Schwinger equations for the a+ 6 He cluster system, so finding a model spectrum for 10 Be to more than 10MeV excitation. Three states of 6 He were included and the resonance character of the two excited states taken into account in finding solutions. A model Hamiltonian has been found that gives very good agreement with the known bound states and with some low-lying resonances of 10 Be. More resonance states are predicted than those which have been observed as yet. The method also yields S -matrices which we have used to evaluate low-energy 6 He - a scattering cross sections. Reasonable reproduction of low-energy differential cross sections and of energy variation of cross sections measured at fixed scattering angles have been found. Enlarging the channel space by including two higher energy states of 6 He , assuming values for their spin-parities, leads to an enlarged spectrum for 10 Be in which the number and distribution of resonances show similarity to the known spectrum