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Rutherford Scattering Differential Cross-Section

Rutherford scattering is the elastic scattering of charged particles by the Coulomb interaction.

The differential cross-section is proportional to the impact charge squared, the target atomic number squared, the cosecant of half the scattering angle to the fourth power and the reciprocal of the kinetic energy squared.

Formula

QuantityVariable["dσ/dΩ", "ScatteringDifferentialCrossSection"] == (Csc[QuantityVariable["θ", "Angle"]/2]^4*Quantity[1/(256*Pi^2), "ElementaryCharge"^2/"ElectricConstant"^2]*QuantityVariable["q", "ElectricCharge"]^2*QuantityVariable["Z", "Unitless"]^2)/QuantityVariable[Subscript["E", "k"], "Energy"]^2

symbol description physical quantity
dσ/dΩ differential cross-section "ScatteringDifferentialCrossSection"
θ scattering angle "Angle"
q impact charge "ElectricCharge"
Z target atomic number "Unitless"
Ek kinetic energy "Energy"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Rutherford Scattering Differential Cross-Section"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Rutherford Scattering Differential Cross-Section"]]
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Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Rutherford Scattering Differential Cross-Section"], \ {QuantityVariable["\[Theta]","Angle"] -> Quantity[60, "AngularDegrees"], QuantityVariable[ \!\(\*SubscriptBox[\("E"\), \("k"\)]\),"Energy"] -> Quantity[8, "Megaelectronvolts"], QuantityVariable[ "d\[Sigma]/d\[CapitalOmega]", "ScatteringDifferentialCrossSection"] -> Quantity[7.400000000000001`*^-28, ("Meters")^2/("Steradians")]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1911

Publisher Information