Luneburg Lens Approach to Nuclear Rainbow Scattering

Abstract

The physical interpretation of nuclear rainbow scattering within the frame of the optical model is critically investigated. Starting from the properties of the Luneburg lens, a gradient index device that displays refractive features similar to those of the nuclear potential, important differences between the mechanisms producing the nuclear and optical rainbows are pointed out.

Refractive versus resonant diffraction scattering of loosely bound6Li nuclei

“…However, this simple dominance does not explain, by itself the structure of the far-side component. In fact the above picture has already been challenged by Anni [9] and by Michel et al [21] for the simple reason that the far-side amplitude has never been decomposed in subamplitudes which would explain the interference. We come back to this topic in Section III.…”

“…We come back to this topic in Section III. For the moment we adopt the interpretation of Michel et al [21] and denote the complex structure at intermediate angles in the data as pre-rainbow oscillations. A model independent analysis in which the diagonal S-matrix elements are extracted directly from the data through a complex phase shift analysis confirm that the Airy oscillation at θ ≈ 60 • is a real effect.…”

“…24, the enhancement fator, is responsible for the multiple reflections of the wave within the potential pocket. When the absorption in the nuclear interior is large, the enhancement factor reduces to one and we are left with the expression used in [21]. Since the semi-classical scattering function is decomposed additively, S W KB = S B + S I , the corresponding total scattering amplitude is decomposed likewise as f W KB = f B + f I and conveniently the corresponding barrier and internal barrier angular distributions are calculated as σ B,I = |f B,I | 2 , using the usual angular momentum expansion of the amplitudes.…”

Radar Cross-Section Studies of Spherical Lens Reflectors

“…The field distribution in the focal region of a dielectric spherical lens has been studied by many authors (see for example [11,12]). Our studies are based on the classical Mie series solution for a homogeneous dielectric sphere.…”

“…The characteristic size of the focal region or "focal spot" is comparable with a wavelength. Some results on EM energy density distribution in spherical lenses can be found in [11] and [12]. In general, the focusing properties of a three-parameter class of oblate Luneberg-like inhomogeneous lenses are studied in [13].…”