For a given $\alpha \alpha$ potential we show how to calculate in a convenient way the half-off-the-energy-shell cross section ${\sigma }_{\mathrm{half}}$ for $\alpha \alpha$ scattering. We compute ${\sigma }_{\mathrm{half}}$ numerically for energies up to 125 MeV (lab), and make a comparison with the free-scattering cross section. Coulomb effects are included rigorously. In particular, we recall that ${\sigma }_{\mathrm{half}}$ is a discontinuous function of the off-shell-momentum variable at the on-shell value. We confirm that off-shell effects are sizeable, and discuss the relevance for the plane-wave impulse approximation and distorted-wave impulse approximation descriptions of ($\alpha , 2\alpha$) reactions.

NUCLEAR REACTIONS Half-shell scattering, Coulomb potential, impulse approximations, $\alpha +\alpha$ system.

• Received 27 September 1982

DOI:https://doi.org/10.1103/PhysRevC.27.2548