Thomson Scattering Cross Section

The classical scattering cross section is modified by quantum effects when the energy of the incident photons becomes comparable with the rest mass of the scattering particle.

Thomson scattering cross section. Recall that we got the correct cross section from the non relativistic calculation and that thomson also got the correct result from classical e m. When a cross section is integrated over all scattering angles and possibly other variables it is called a total cross section. The cross section for thomson scattering illustrates the need for negative energy states in our calculations.

Thomson scattering 2 the force is due to a linearly polarizesd wave. 1 5 where t is the thomson scattering cross section. 1 6 so the total scattering cross section is given by the inverse fourth power of the wave.

The dipole moment is which describes a dipole with amplitude taking into account the larmor s formula the time averaged emitted w is where is the differential cross section for the scattering f e e o sin o t. Nevertheless thompson scattering is one of the most important types of scattering in the universe. In the dirac theory we have only one term in the interaction hamiltonian.

Scattering cross sections may be defined in nuclear atomic and particle physics for collisions of accelerated beams of one type of particle with targets either stationary or moving of a second type of particle. Numerically 5 rayleigh scattering. When the energy of each individual photon hν is much smaller than the rest energy of the electron its mass times the velocity of light squared mc2 the scattering of photons is described by a cross section derived by j j.

This cross section is called the thomson cross section symbolized by the greek letter sigma with subscript zero σ0 and is equal to a numerical factor times the. D σ t d ω q 2 4 π ε 0 m c 2 2 1 cos 2 χ 2. Nevertheless thompson scattering is one of the most important types of scattering in the universe.

The scattering of a photon by a charged particle is called compton scattering and the quantum mechanical version of the compton scattering cross section is known as the klein nishina cross section. Thomson cross section 1 so 2 in cgs 3 where is the charge on the electron m is the mass of the electron c is the speed of light and is the classical electron radius. Displaystyle frac d sigma t d omega left frac q 2 4 pi varepsilon 0 mc 2 right 2 frac 1 cos 2 chi 2.