Asymmetric deflection functions and the extinction of rainbows: A comparison of α-particle scattering from 40Ca and 44Ca

Abstract

A decomposition of elastic scattering amplitudes into their nearside and farside components is employed to exhibit the presence of a striking farside (“nuclear”) rainbow in the angular distributions for α + 40Ca scattering at energies from 36 to 61 MeV. The rainbow is identified by a deep “Airy minimum” which is present in the farside components of the angular distributions throughout this energy region. Over the same energy range, the angular distributions for the more absorptive α + 44Ca scattering exhibit no Airy minima, and, in this sense, show no nuclear rainbow. However, a steepening of the slope of their smooth farside component, which appears at energies above that (∼60 MeV) for which the rainbow angle for α + 40Ca becomes less than 180°, may serve to identify a residual rainbow effect, even in α + 44Ca, at energies above 60 MeV. The manner in which the Airy minima of this and other nuclear rainbows are extinguished by absorption is examined in detail and is found to depend critically on the asymmetry in the shape of their deflection functions at low energies.