Evidence for a secondary bow in Newton's zero-order nuclear rainbow

Abstract

Rainbows are generally considered to be caused by static refraction and reflection. A primary and a secondary rainbow appear due to refraction and internal reflection in a raindrop as explained by Newton. The quantum nuclear rainbow, which is generated by refraction in the nucleus droplet, only has a "primary" rainbow. Here we show for the first time evidence for the existence of a secondary nuclear rainbow generated dynamically by coupling to an excited state without internal reflection. This has been demonstrated for experimental 16 Newton, who explained the mechanism of the rainbow by refraction and reflection [1][2][3], believed in the existence of the zero-order rainbow without internal reflection in a droplet. Newton's zero-order rainbow [4] was realized in quantum systems when Goldberg et al.[5] observed a nuclear rainbow in high-energy α-particle scattering. The quantum nuclear rainbow is generated by the nuclear potential, which acts as a Luneburg lens [6], where refraction is the only active mechanism and a "primary" rainbow can only exist because there are no higher-order terms like in Nussenzveig's expansion for the meteorological rainbow [7]. We report here evidence for the unexpected existence of a secondary bow in the nuclear rainbow.The nuclear rainbow is very important in determining the interaction potential family up to the internal region without discrete ambiguity [5] and has been studied extensively [8,9]. The nuclear rainbow is also powerful for studies of nuclear cluster structure in the bound and unbound energy regions. In fact, the global nuclear potential, which describes nuclear rainbow scattering for typical α + 16 O, α + 40 Ca, and 16 O + 16 O systems, can reproduce scattering over a wide range of incident energies and cluster structures of 20 Ne, 44 Ti, and 32 S in the bound and unbound energy regions, respectively, in a unified way [10][11][12]. In contrast to the 16 O + 16 O system, the Airy structure of the nuclear rainbow for the asymmetric 16 O + 12 C system, for which refraction is very strong, is clearly observed in experimental angular distributions without being obscured by symmetrization. For this system, a global potential that reproduces the energy evolution of the Airy minimum in the angular distributions over a wide range of incident energies at E L = 62 ∼1503 MeV [13][14][15][16][17] • ). It has been impossible to model a first-order Airy minimum A1 at this large angle with the established global potential [19]. Thus, the reason why the global potential fails to reproduce the Airy minimum of the nuclear rainbow at E L = 281 MeV has been a mystery and raised a serious question of the common belief that nuclear rainbow scattering can determine the potential uniquely.The purpose of this paper is to present for the first time evidence for the existence of a secondary nuclear rainbow in the 16 O + 12 C scattering generated dynamically by a quantum effect without internal reflections of classical concept, which is completely different from the Newton's meteorological se...

Refractive effects and Airy structure in inelasticO16+C12rainbow scattering

“…Very recently, evidence for a secondary bow in elastic scattering caused by coupling to the inelastic channel has been reported [29]. Therefore it is particularly intriguing to study inelastic rainbow scattering for this system.…”

“…2 the elastic and inelastic scattering angular distributions at 281 MeV calculated with the real potential in Table I but switching off the imaginary potential. Very recently it has been reported [29] that the Airy minimum in Fig. 2(a) at θ c.m.…”

“…2(a) was claimed to be a new kind of Airy minimum of a secondary rainbow dynamically caused predominantly by coupling to the deformed 2 + state of 12 C [29]. The role of the excitation to the 2 + state of 12 C was also investigated at other energies using the potential parameters in Table I.…”

“…The coupling between the elastic scattering and inelastic scattering has a large effect on the behavior of the angular distributions in the relevant angular region and causes a new kind of dynamically induced Airy minimum in elastic scattering [29].…”

“…The calculated B(E2 : 2 [33], which takes into account the finite-range exchange effect [34]. An imaginary potential (non-deformed) is introduced phenomenologically for all the diagonal potentials to take into account the effect of absorption due to other channels, which was successful in the recent coupled channels studies of 16 O+ 12 C rainbow scattering [29,35]. Off-diagonals are assumed to be real.…”