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Compton vs Inverse Compton

What you are seeing: two complementary photon-electron scatterings on the same energy axis. Forward Compton (EE photon, electron at rest) gives a downshifted photon by E′=E/(1+(E/mec2)(1−cos⁡θ))E' = E / (1 + (E / m_e c^2)(1 - \cos\theta)). Inverse Compton (EE photon, relativistic electron at Lorentz factor γ\gamma) gives a typical upshift by Etyp=(4/3)γ2EE_\text{typ} = (4/3) \gamma^2 E in the Thomson limit, with a maximum energy at 4γ2E/(1+4γE/mec2)4 \gamma^2 E / (1 + 4 \gamma E / m_e c^2) for backscatter.

Inverse Compton is the workhorse of high-energy astrophysics. A γ=104\gamma = 10^4 electron up-scatters a CMB photon (E∼6×10−4E \sim 6 \times 10^{-4} eV) into an X-ray photon at ∼100\sim 100 keV. Klein-Nishina suppression kicks in when γE≳mec2\gamma E \gtrsim m_e c^2; the readout shows the regime.

Figure 1. Compton (EE down) and inverse Compton (γ2E\gamma^2 E up) scattering.
log10 E_in (eV)0.00
log10 gamma4.00

WHAT TO TRY

  • In forward Compton a high-energy photon strikes a resting electron and comes out softer, losing energy to the recoil. Raise the photon energy and the downshift grows.
  • In inverse Compton a fast electron (raise log gamma) slams a soft photon up to high energy, gaining a factor of gamma squared. The same scattering runs both ways depending on who carries the energy.
  • Inverse Compton is how relativistic electrons make X-rays and gamma rays from starlight and the microwave background, the upscattering that lights up jets and galaxy clusters.