Visualization of quantum interferences in heavy-ion elastic scattering

We investigate various interference effects in elastic scattering of the $\alpha + {}^{40}\text{Ca}$ system at $E_{\rm lab}=29$ MeV. To this end, we use an optical potential model and decompose the scattering amplitude into four components, that is, the near-side and the far-side components, each of which is further decomposed into the barrier-wave and the internal-wave components. Each component contributes distinctively to the angular distributions, revealing unique quantum interference patterns. We apply the Fourier transform technique to visualize these interference effects. By analyzing the images at specific scattering angles, we identify the positions and intensities of peaks corresponding to each interference component. This analysis offers insight into structural features of the angular distribution which are not apparent from the differential cross sections alone.