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

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