Microscopic structure of four body resonances

A microscopic approach of four body states, seen as decaying states of scattering resonances is given. The equations of motion describing cluster-like states are derived within the multi-step shell-model approach. The lowest collective two particle Eigenmodes are used as building blocks for the α-like states. A good agreement with the low lying states in 212 Po is obtained. The spectroscopic factor of the α-decay between ground states is reproduced. It is shown that only by including the continuum part of the single particle spectrum, the decay width for alpha cluster-decay processes is reproduced. The α-like structure of the lowest states in 212 Po is analyzed and strong high-lying resonances are predicted. A good agreement with experimental quasi-molecular states in 40 Ca is obtained. (authors)