When an electron is not at rest, but colliding with a soft photon, the recoiling photon gains its energy by the transfer from the incoming electrons. This process called Inverse Compton Scattering, , is a representative radiation in many astronomical environments that produces high energy X-ray/-ray.

The colliding energy between a photon and an electron
is often defined by the he Lorentz invariant
center of mass (CM) energy squared as defined by

Here natural unit is used

(28) |

where is the recoiling energy of -ray in the Universe lab system. By using Eq. 29 we can modify the Kline-Nishina formula Eq. 25 to derive the energy differential cross section. We obtain

Here is the dimensionless energy of the electron normalized by primary energy of incoming electron. The electron transfer most of its energy to the photon via the inverse Compton scattering as you see the cross section becomes larger in regime in Eq. 30. Integrating from to 1 (this range is given by Eq. 29 with ), we obtain the total cross section:

(31) |

where is the velocity of the outgoing electron in the CMS.

2002-07-18