Quantum Mechanics/Quantum Scattering

Stationary scattering waveEdit

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-sectionEdit

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)