Inelastic cross sections and continuum transitions illustrated by $^{8}$Be results

We use the two-alpha cluster model to describe the properties of $^{8}$Be. The $E2$-transitions in a two-body continuum can be described as bremsstrahlung in an inelastic scattering process. We compute cross sections as functions of initial energy for the possible $E2$-transitions from initial angular momenta $(0^+,2^+,4^+,6^+,8^+)$. The dependence on the exact shape of potentials is very small when the low-energy scattering phase-shifts are the same. We relate to practical observables where energies of the emerging alpha-particles are restricted in various ways. The unphysical infrared contribution is removed. We find pronounced peaking for photon energies matching resonance positions. Contributions from intra-band transitions are rather small although substantial (and even dominating) for initial energies between resonances. Structure information are derived but both ${\cal B}^{(E2)}$ values and electromagnetic transition rates are ambiguous in the continuum.