Abstract
Among the many observables in nuclear reactions the cross section is the most straightforward one and analogies with classical collision processes (billiard, kinetic gas theories etc.) suggest classical treatments. A detailed discussion of the classical Rutherford cross section is presented. Up to a certain extent the classical treatments have been quite successful (e.g. in describing point-Coulomb scattering). However, as soon as quantum-mechanical properties enter the picture quantum-mechanical treatments have to be applied. This is the case when wavelike particle properties dominate the description of observables, e.g. when the de Broglie wavelengths of projectiles are comparable with typical system dimensions (diffraction phenomena) or interference becomes mandatory such as with identical particles. The connection between scattering cross sections and the size of nuclei is shown with a recent application to “halo nuclei”.
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- 1.
In all scattering/reaction problems the projectile mass m=m a is correct for an infinitely heavy target or in the lab. system of coordinates with the target (mass m A ) at rest. In the c.m. system used for theoretical considerations m has to be understood as the reduced mass μ=m a m A /(m a +m A ).
- 2.
The term 1/4πϵ 0 is correct in SI units. Throughout the remainder of this book—as usual in the nuclear physics literature—it is set equal to 1 (Gaussian system of units).
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Paetz gen. Schieck, H. (2014). Classical Cross Section. In: Nuclear Reactions. Lecture Notes in Physics, vol 882. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53986-2_2
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