Science
Compton Scattered Photon Energy, Compton Edge & Electron Recoil
Calculate scattered gamma-ray photon energy E' = E_0 / (1 + (E_0 / 511) * (1 - COS(RADIANS(theta)))), recoil kinetic energy T_e = E_0 - E', and the 180-degree Compton Edge in keV.
Interpret gamma-ray scintillation spectra and radiation shielding backscatter!
When an incident X-ray or gamma photon of energy E_0 (keV) scatters elastically off a stationary atomic electron at angle theta, relativistic energy-momentum conservation yields the Compton Photon Energy Formula: E' = E_0 / (1 + (E_0 / 511.0) * (1 - COS(RADIANS(theta)))), where m_e c^2 = 511.0 keV is the electron rest energy!
The struck electron carries away kinetic recoil energy T_e = E_0 - E'! In a NaI(Tl) or HPGe gamma detector, maximum energy transfer occurs in a head-on 180-degree backscatter (COS(180 deg) = -1, so 1 - COS = 2): for Cesium-137 (E_0 = 661.7 keV), the backscattered photon exits at E'(180) = 184.33 keV, producing the sharp spectral Compton Edge at T_max = 661.7 - 184.33 = 477.37 keV!
| Scattering Angle theta (Cs-137 E_0 = 661.7 keV) | 1 - COS(theta) | Scattered Photon E' (keV) | Electron Recoil T_e (keV) |
|---|---|---|---|
| Forward Grazing (0 deg) | 0.000 | 661.70 keV (Unchanged) | 0.00 keV |
| Right-Angle Scatter (90 deg) | 1.000 | 288.33 keV | 373.37 keV |
| Head-On Backscatter (180 deg) | 2.000 | 184.33 keV (Backscatter Peak) | 477.37 keV (Compton Edge!) |
Scattered Gamma Photon Energy E' (keV) at Angle theta (Degrees)
Converts scattering angle B3 from degrees to radians inside COS(RADIANS(B3)) and evaluates E_0 / (1 + (E_0 / 511) * (1 - COS)).
=IF(B2 <= 0, "Incident Energy Must Be > 0", ROUND(B2 / (1 + (B2 / 511) * (1 - COS(RADIANS(B3)))), 2))Recoil Electron Kinetic Energy & 180-Degree Compton Edge (keV)
Subtracts scattered photon energy E' from incident E_0 (equals the Compton Edge when B3 = 180).
=ROUND(B2 - (B2 / (1 + (B2 / 511) * (1 - COS(RADIANS(B3))))), 2)Try the example
Use the original values or change them to test your understanding.