Suppression of the nuclear rainbow in the inelastic nucleus-nucleus scattering

TL;DR

This paper investigates why the nuclear rainbow pattern is suppressed in inelastic nucleus-nucleus scattering, revealing that destructive interference of partial waves causes the suppression while refraction remains strong.

Contribution

A novel near-far decomposition method is introduced to analyze coupled partial-wave contributions, clarifying the suppression mechanism of the nuclear rainbow in inelastic scattering.

Findings

Suppression of rainbow pattern due to destructive interference of partial waves.

Inelastic scattering remains strongly refractive with dominant far-side scattering.

The new decomposition method explicitly reveals partial-wave contributions.

Abstract

The nuclear rainbow observed in the elastic $\alpha$-nucleus and light heavy-ion scattering is proven to be due to the refraction of the scattering wave by a deep, attractive real optical potential. The nuclear rainbow pattern, established as a broad oscillation of the Airy minima in the elastic cross section, originates from an interference of the refracted far-side scattering amplitudes. It is natural to expect a similar rainbow pattern also in the inelastic scattering of a nucleus-nucleus system that exhibits a pronounced rainbow pattern in the elastic channel. Although some feature of the nuclear rainbow in the inelastic nucleus-nucleus scattering was observed in experiment, the measured inelastic cross sections exhibit much weaker rainbow pattern, where the Airy oscillation is suppressed and smeared out. To investigate this effect, a novel method of the near-far decomposition of the inelastic scattering amplitude is proposed to explicitly reveal the coupled partial-wave contributions to the inelastic cross section. Using the new decomposition method, our coupled channel analysis of the elastic and inelastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the refractive energies shows unambiguously that the suppression of the nuclear rainbow pattern in the inelastic scattering cross section is caused by a destructive interference of the partial waves of different multipoles. However, the inelastic scattering remains strongly refractive in these cases, where the far-side scattering is dominant at medium and large angles like that observed in the elastic scattering.