Question

In: Physics

The scattering amplitude can be expressed in terms of the partial wave amplitude. When , (a) (5...

The scattering amplitude can be expressed in terms of the partial wave amplitude.

When ,

(a) (5 points) What is scattering amplitude?

(b) (5 points) What is differential cross-section?

(c) (5 points) What is total cross-section?

When ,

(d) (5 points) What is scattering amplitude?

(e) (5 points) What is differential cross-section?

(f) (5 points) What is total cross-section?

Expert Solution

(a) The scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process.

The latter is described by the wavefunction

is the position vector.

. is the incoming plane wave with the wavenumber k along the z axis. is the outgoing spherical wave; θ is the scattering angle; and is the scattering amplitude. The dimension of the scattering amplitude is length.

The scattering amplitude is a probability amplitude; the differential cross-section as a function of scattering angle is given as its modulus squared -

(b) Generally, cross-section is a measure of probability that a specific process will take place in a collision of two particles, when two particles interact, their mutual cross-section is the intersected area to their relative motion within which they must meet in order to scatter from each other. If the particles are hard inelastic spheres that interact only upon contact, their scattering cross section is related to their geometric size.When a cross section is specified as a function of some final-state variable, such as particle angle or energy, it is called a Differential Cross-section.

(c) When cross-section is integrated over all scattering angles, it is called a Total Cross-section.

genius_generous answered 2 years ago

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