Here a photon is scattered an only a part of the energy is absorbed. If the scattered photon leaves the detector again, only a broad energy distribution, the "Compton Background" is measured. This is most probable for small detectors. For scattered photon exists a minimum energy, this can be seen in the spectrum as "Compton Edge". The Compton Effect is most important in the medium energy range (100 keV - 1.5 MeV).
The elastic scattering of photons by electrons. If λs and λi are respectively the wavelengths associated with scattered and incident photons, the Compton shift is given by λs - λi = λ0(1-cos q) where q is the angle between the directions of the incident and scattered photons and λ0 is the Compton wavelength (λ0=0.00243 nm) of the electron. The effect is only significant for incident X-ray and γ-ray photons.
Source: Dr. Joerg Brutscher, Identify manual
For more information and to simulate Compton scattering, see Nucleonica's Virtual Cloud Chamber