Practical heavy ion optics, in the near/far representation

Direct nuclear reactions among heavy ions are peripheral in nature. That is, the partial-wave decomposition of their scattering amplitudes is concentrated in a surface-peaked l-window , and as a result the diffractive oscillations appearing in their angular distributions are most simply understood as a 2-slit diffraction pattern, as a 2-slit diffraction pattern, and slit appearing in the nearside of the amplitude and one in its farside. We show here that Sommerfeld ''edge waves'' generated from an incident beam by a strongly-absorbing target, produce exactly this same effect in elastic scattering amplitudes. Consequently their Fraunhofer diffraction patterns also can be interpreted as a 2-slit interference pattern, providing very useful insight into their physical significance. This is accomplished very efficiently via a nearside-farside decomposition of the elastic amplitudes. A large number of practical examples indicate how this technique can elucidate both diffraction patterns and rainbows, as well as indicating what parts of the optical potential are explored by any given scattering experiment. (author)