A multi-channel model for an $ \alpha$ plus He nucleus cluster.

A multi-channel algebraic scattering (MCAS) method has been used to solve coupled sets of Lippmann-Schwinger equations for the $ \alpha + {}^{6}{\rm He}$ cluster system, so finding a model spectrum for Be to more than 10MeV excitation. Three states of 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 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 He - $ \alpha$ 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 He , assuming values for their spin-parities, leads to an enlarged spectrum for Be in which the number and distribution of resonances show similarity to the known spectrum. [ABSTRACT FROM AUTHOR]