Angular Distributions

The nuclear rainbow effect can be proved only by a very careful measurements of the scattered intensities as functions of angle (angular distribution, which is the number of scattered particles measured in a certain angular range). Furthermore, one has to choose the  energy of a projectile, by varying its velocity that the right wavelength of the particle wave is used in the experiment, which makes the observation of the rainbow intensity maximum possible, here the primary rainbow at 50° for an energy of 350 MeV (green curve).

The figure summarizes the results of the research of the last 10 years achieved in the labs in Berlin/Germany, Japan and France. In the experiment 16O nuclei were shot onto a 16O-target. You can see the angular distributions, which are the number of scattered oxygen nuclei for different wavelengths. In the experiments the projectile energy vary over a very wide range (from 5% up to 40% the speed of light). The de Broglie wavelength of the particle beams varies correspondingly, (in analogy to the light, different energies are depicted by different colors). Just like for the usual rainbow, the enhancement of intensity occurs for the different projectile energies (wavelengths) at a different angular range.


Intensity distributions for the scattered 16O nuclei on a 16O-target. The curves correspond to the different wavelengths (from 1.193-0.429 * 10-15 m), which correspond to the chosen projectile energies.

It is especially important to note the bump in the exponentially falling scattering intensities. This enhancement is best seen in the green plot at approx. 50°, which is the rainbow angle for 350 MeV energy.

The strong intensity oscillations at smaller angles are an additional hint towards the wave nature of particles: These are Fraunhofer diffraction patterns, which correspond to the refraction of light on a black spherical obstacle. For the small refraction angles we find that the 16O-targets behave like small black obstacles for the 16O-waves of the projectiles. The projectile wavelengths are λ = 1-2*10-15 m and comparable to the diameter of the 16O-nuclei, which is 3.6*10-15 m, an important condition to observe matter wave effects.


Diffraction of laser light by a sample, which contains many tiny "black" spheres (e.g. droplets or club moss seeds). As a result concentric intensity oscillations (Fraunhofer rings) can be observed on the film.

Electron Microscope