Quantum Mechanics/Quantum Scattering

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Stationary scattering wave[edit]

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[edit]

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)