List of equations in nuclear and particle physics


This article summarizes equations in the theory of nuclear physics and particle physics.

Definitions

Quantity
symbol/sDefining equationSI unitsDimension
Number of atomsN = Number of atoms remaining at time t

N0 = Initial number of atoms at time t = 0

ND = Number of atoms decayed at time t
dimensionlessdimensionless
Decay rate, activity of a radioisotopeABq = Hz = s−1−1
Decay constantλBq = Hz = s−1−1
Half-life of a radioisotopet1/2, T1/2Time taken for half the number of atoms present to decay

s
Number of half-livesn dimensionlessdimensionless
Radioisotope time constant, mean lifetime of an atom before decayτ s
Absorbed dose, total ionizing dose D can only be found experimentallyN/AGy = 1 J/kg 2−2
Equivalent doseH
Q = radiation quality factor 		Sv = J kg−1 2−2
Effective doseE
Wj = weighting factors corresponding to radiosensitivities of matter 		Sv = J kg−1 2−2

Equations

Nuclear structure

Physical situationNomenclatureEquations
Mass number
Mass in nuclei

Nuclear radiusr0 ≈ 1.2 fm
hence
  • nuclear volume ∝ A
  • nuclear surface ∝ A2/3
Nuclear binding energy, empirical curveDimensionless parameters to fit experiment:
where
  • δ = +1 even N, even Z,
  • δ = −1 odd N, odd Z,
  • δ = 0 odd A

Nuclear decay

Physical situationNomenclatureEquations
Radioactive decay
  • N0 = Initial number of atoms
  • N = Number of atoms at time t
  • λ = Decay constant
  • t = Time
Statistical decay of a radionuclide:
Bateman's equations
Radiation flux

Nuclear scattering theory

The following apply for the nuclear reaction:
in the centre of mass frame, where a and b are the initial species about to collide, c is the final species, and R is the resonant state.
Physical situationNomenclatureEquations
Breit-Wigner formula
Cross-section:
Spin factor:
Total width:
Resonance lifetime:
Born scattering
  • r = radial distance
  • μ = Scattering angleA = 2, −1
  • Δk = change in wavevector due to scattering
  • V = total interaction potential
  • V = total interaction potential
Differential cross-section:
Mott scattering
Differential cross-section :
Scattering potential energy :
Rutherford scatteringDifferential cross-section :

Fundamental forces

These equations need to be refined such that the notation is defined as has been done for the previous sets of equations.
NameEquations
Strong force
Electroweak interaction