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Quantum Mechanics/Quantum Scattering
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Stationary scattering wave
The (elastic) scattering stationary state (azimuthally symmetric) is described by a wave-function with the following asymptotic,
: 1
where is the incident plane wave of projectiles with momentum , is the scattered spherical wave, and is the scattering amplitude.
Cross-section
Consider a detector with the window positioned at the angle at the distance from the scattering center. The count rate of the detector, , is given by the radial flux density of particles, through the detector window,
The radial flux from the stationary wave (1) is given as
: 2
The cross-section is defined as the count rate of the detector divided by the flux density of the incident beam,
: 3