Input interpretation
Rutherford scattering
Equation
dσ/dΩ = ((q Z e)/(16 π ε_0 E_k))^2 csc^4(θ/2) | | dσ/dΩ | differential cross section E_k | kinetic energy θ | scattering angle q | impact charge Z | target atomic number e | elementary charge (≈ 1.602×10^-19 C) ε_0 | electric constant (≈ 8.85418781×10^-12 F/m)
Input values
kinetic energy | 8 MeV (megaelectronvolts) scattering angle | 60° (degrees) impact charge | 2 e (elementary charges) target atomic number | 79
Result
differential cross section | 8.088×10^-28 m^2/sr (square meters per steradian) = 8.088 b/sr (barns per steradian)
Impact parameter equations
b = (e q Z sqrt((1 + cos(θ))/(1 - cos(θ))))/(8 ε_0 π E_k) | r_min = (b cos(θ/2))/(1 - sin(θ/2)) | q | impact charge Z | target atomic number E_k | kinetic energy θ | scattering angle b | impact parameter dσ/dΩ | differential cross section r_min | closest approach ε_0 | electric constant (≈ 8.85418781×10^-12 F/m) e | elementary charge (≈ 1.602×10^-19 C)
Units
Schematic
Schematic