Rotational bands in the continuum illustrated by 8 Be results

We use the α-α cluster model to describe the properties of 8Be. The rotational energy sequence of the (0+, 2+, 4+) resonances are reproduced with the complex energy scaling technique for Ali-Bodmer and Buck potentials. However, both static and transition probabilities are far from the rotational values. We trace this observation to the prominent continuum properties of the 2+ and 4+ resonances. They resemble free continuum solutions although still exhibit strong collective rotational character. We compare with cluster models and discuss concepts of rotations in the continuum in connection with such central quantities as transition probabilities, inelastic cross sections, and resonance widths. We compute the 6+ and 8+ S-matrix poles and discuss properties of this possible continuation of the band beyond the known 4+ state. Regularization of diverging quantities is discussed to extract observable continuum properties. We formulate the division of electromagnetic transition probabilities into interfering contributions from resonance-resonance, continuumresonance, resonance-continuum, and continuum-continuum transitions.