#### Compton Scattering

###### Equation

Compton scattering occurs when a photon interacts with an electron by transferring the first energy to the second (inelastic interaction). The wavelength of the photon after the scattering can be calculated by

$\lambda_2=\lambda+\lambda_c(1-\cos\theta)$ |

where

$\lambda_c=\displaystyle\frac{h}{m_ec}$ |

Compton wave length and

ID:(9145, 0)

#### Compton Scattering

###### Image

Compton scattering occurs when a photon interacts with a charged particle, in particular with an electron. In the process the photon loses energy and deviates by putting the electron in motion:

ID:(9176, 0)

#### Compton scattering differential effective section

###### Equation

In the case of Compton scattering, the differential effective section is according to Klein-Nishina

$\displaystyle\frac{d\sigma_{KN}}{d\Omega}=\displaystyle\frac{3}{16\pi}\displaystyle\frac{\sigma_T}{(1+\epsilon(1-\cos\theta))^2}\left(\epsilon(1-cos\theta)+\displaystyle\frac{1}{1+\epsilon(1-\cos\theta)}-\cos^2\theta\right)$ |

where

$\sigma_T=\displaystyle\frac{8\pi}{3}r_0^2$ |

is the Thomson total effective section and the

$\epsilon=\displaystyle\frac{E}{m_ec^2}$ |

is the normalized energy.

ID:(9144, 0)

#### Compton Wave Length

###### Equation

The Compton wavelength is defined by

$\lambda_c=\displaystyle\frac{h}{m_ec}$ |

where

ID:(9146, 0)

#### Scattering

###### Image

Scattering that contributes (in) or describes the abandonment of particles (out) can be plotted as follows:

It should be noted that the term collision:

- integrates on all external speeds to those of volume

- includes the likelihood of both speeds leading to scattering simultaneously

- the relative velocity multiplied by the total effective section represents the flow of particles towards the target

The latter can be shown in a simple way through

ID:(9177, 0)

#### Total effective section for Compton scattering

###### Equation

If the differential effective section is taken according to Klein-Nishina

$\displaystyle\frac{d\sigma_{KN}}{d\Omega}=\displaystyle\frac{3}{16\pi}\displaystyle\frac{\sigma_T}{(1+\epsilon(1-\cos\theta))^2}\left(\epsilon(1-cos\theta)+\displaystyle\frac{1}{1+\epsilon(1-\cos\theta)}-\cos^2\theta\right)$ |

and integrates in the solid angle

$d\Omega=2\pi \sin\theta d\theta$ |

the total effective section is obtained

$\sigma_{KN}=\displaystyle\frac{3}{4}\sigma_T\left(\displaystyle\frac{(1+\epsilon)}{\epsilon^3}\left(\displaystyle\frac{2\epsilon(1+\epsilon)}{1+2\epsilon}-\log(1+2\epsilon)\right)+\displaystyle\frac{\log(1+2\epsilon)}{2\epsilon}-\displaystyle\frac{(1+3\epsilon)}{(1+2\epsilon)^2}\right)$ |

where

$\sigma_T=\displaystyle\frac{8\pi}{3}r_0^2$ |

is the effective section of Thomson and the

$\epsilon=\displaystyle\frac{E}{m_ec^2}$ |

is the normalized energy.

At the limit of small

and in the limit

ID:(9111, 0)

#### Thomson Total Effective Section

###### Equation

The total effective section of Thomson is equal to 2/3 of the surface of a sphere of radius

$\sigma_T=\displaystyle\frac{8\pi}{3}r_0^2$ |

The radius

ID:(9112, 0)

#### Standard energy

###### Equation

To simplify we introduce the initial energy of the photon

$\epsilon=\displaystyle\frac{E}{m_ec^2}$ |

where

ID:(9113, 0)

#### Simulador random walk with Compton scattering

###### Php

The Klein-Nishina model can be studied in numerical form. This is shown

- the total effective section as a function of photon energy

- the differential section as a function of the angle for the minimum, medium and maximum energies defined

- what would be the total effective section in a one-dimensional system that gives according to the energy transmission or reflection

ID:(9114, 0)