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Consider the scattering of a
neutron off an aluminum target.
In quantum mechanics, the relative
motion is described using a wavefunction Psi. In the course of scattering,
Psi developes from a plane wave into a scattering wave
function.
For a spherically symmetric potential, and with an incoming
wave in the z-direction, Psi is independent of
the azimutal angle phi. Psi can therefore be shown in the
half-plane phi = 0. More specifically, the animation below
shows the (real part of the) scattered
part of Psi, i.e. Psi less its plane wave part, in this
halfplane.
The (asymptotic) amplitude of the
scattered part of Psi is called the scattering amplitude.
The animation refers to a case when the CM energy was 20 MeV. The scattering equations have been solved for an optical potential of Woods-Saxon type. In the partial wave decomposition, 16 partial waves were used.
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Additional detail is provided in Quantum Mechanics, advanced course.