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

TL;DR

This paper models inelastic scattering and continuum transitions in $^{8}$Be using a two-alpha cluster approach, analyzing cross sections, resonance effects, and the ambiguity in electromagnetic transition rates.

Contribution

It introduces a detailed continuum transition analysis in $^{8}$Be with a focus on bremsstrahlung and resonance effects, highlighting the minimal dependence on potential shape.

Findings

Pronounced peaking at resonance photon energies

Intra-band transition contributions are significant between resonances

Electromagnetic transition rates are ambiguous in the continuum

Abstract

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.