Validity of macroscopic models for thesup3He(α,γ)7Be electric-dipole capture reaction

The cross sections for the electric-dipole radiative-capture reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}$(α,γ${)}^7$Be are calculated with an approximation procedure (approximate-resonating-group-method procedure) in which the antisymmetrization of the wave function is simply represented by the adoption of an intercluster renormalized function obtained by operating on the resonating-group relative-motion function with the square root of the norm operator. The result shows that this procedure does yield values for the capture cross-section factor in excellent agreement with the resonating-group-method results. By studying the properties of the approximate-resonating-group-method wave functions, we find that, in this capture reaction, the nuclear potential is sampled at all energies and should be properly considered even at astrophysical low energies around 10 keV. In addition, based again on approximate-resonating-group-method results, we have shown that the macroscopic capture-reaction models of Iwinski et al. using analytical-continuation techniques and of Buck et al. using Gaussian-type effective local potentials are not sufficiently accurate for the computation of cross-section factors because of the fact that the details of the nuclear interaction are not well accounted for.