Existence of inelastic supernumerary nuclear rainbow in $^{16}$O+$^{12}$C scattering

TL;DR

This paper reports the discovery of a supernumerary nuclear rainbow in inelastic scattering of $^{16}$O on $^{12}$C, revealing complex rainbow phenomena in nuclear interactions through advanced coupled channels calculations.

Contribution

It demonstrates the existence of a supernumerary rainbow in inelastic nuclear scattering, extending the understanding of nuclear rainbow phenomena beyond elastic scattering.

Findings

Identification of supernumerary rainbow in inelastic scattering

Existence of secondary and primary nuclear rainbows

Enhanced understanding of nuclear rainbow mechanisms

Abstract

The existence of a supernumerary nuclear rainbow in inelastic scattering is reported. This is done by studying inelastic $^{16}$O scattering from $^{12}$C, exciting the $2^+$ (4.44 MeV) state of $^{12}$C and elastic scattering at the incident energies in the range 124 to 200 MeV, using the coupled channels method. An extended double folding potential is used. This is derived from realistic wave functions for $^{12}$C and $^{16}$O calculated with a microscopic $\alpha$ cluster model and a finite-range density-dependent nucleon-nucleon force. Excitations to the $2^+$ (4.44 MeV), 3$^-$ (9.64 MeV) and $4^+$ (14.08 MeV) states of $^{12}$C, and the $3^-$ (6.13 MeV) and $2^+$ (6.92 MeV) states of $^{16}$O are included in the coupled channels calculations. The emergence of the supernumerary bow is understood by the properties of both the Luneburg-lens-like potential in the internal region and diffuse attraction in the outer region. The existence of a supernumerary rainbow for inelastic scattering in addition to the existence of a dynamically created secondary rainbow and a dynamically refracted primary rainbow for elastic scattering, which are not observed in meteorological rainbows, further deepens the understanding of nuclear rainbows.