Inelastic cross sections and continuum transitions illustrated by8Be results

Abstract

We use the $2\ensuremath{\alpha}$ 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 of ${0}^{+},\phantom{\rule{0.28em}{0ex}}{2}^{+},\phantom{\rule{0.28em}{0ex}}{4}^{+},\phantom{\rule{0.28em}{0ex}}{6}^{+},\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{8}^{+}$. 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 $\ensuremath{\alpha}$ particles are restricted in various ways. The unphysical infrared contribution is removed. We find pronounced peaking for photon energies matching resonance positions. Contributions from intraband transitions are rather small although substantial (and even dominating) for initial energies between resonances. Structure information is derived but both ${\mathcal{B}}^{(E2)}$ transition strength values and electromagnetic transition rates are ambiguous in the continuum.