Scattering length and effective range for collisions between light ions within a microscopic model

The first coefficients of the effective-range expansion are derived by a direct calculation at zero energy, i.e., without extrapolation, in the generator coordinate version of the resonating-group method. The parameters of the effective nucleon–nucleon interaction are adjusted on available experimental data (phase shifts or binding energies). The scattering length and effective range are determined in this way for the α+n, , neutron scatterings, α+p, , proton scatterings, and α+α, , collisions between light ions. In many cases, neutral and charged, the effective-range expansion is valid up to energies larger than 5 MeV and provide a simple parametrization of the phase shifts. For α+α, the scattering length and effective range can be derived from the properties of the ground-state resonance.