List of equations in nuclear and particle physics

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

Definitions

Equations

Nuclear structure

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! scope="col" width="250" | Nomenclature
! scope="col" width="10" | Equations
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!Mass number
|A = (Relative) atomic mass = Mass number = Sum of protons and neutrons
N = Number of neutrons
Z = Atomic number = Number of protons = Number of electrons
|
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!Mass in nuclei
|<div class="plainlist">
''Mnuc = Mass of nucleus, bound nucleons
MΣ = Sum of masses for isolated nucleons
mp = proton rest mass
mn = neutron rest mass
</div>
|
|-
!Nuclear radius
|r0 ≈ 1.2 fm
|
hence (approximately) nuclear volume ∝ A
nuclear surface ∝ A2/3
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!Nuclear binding energy, empirical curve
|Dimensionless parameters to fit experiment:<div class="plainlist">
EB = binding energy,
av = nuclear volume coefficient,
as = nuclear surface coefficient,
ac = electrostatic interaction coefficient,
aa = symmetry/asymmetry extent coefficient for the numbers of neutrons/protons,
|
where (due to pairing of nuclei) <div class="plainlist">
δ(N, Z) = +1 even N, even Z,
δ(N, Z) = −1 odd N, odd Z,
δ(N, Z) = 0 odd A
<div class="plainlist">
|-
|}

Nuclear decay

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! scope="col" width="250" | Nomenclature
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!Radioactive decay
|N0 = Initial number of atoms
N = Number of atoms at time t
λ = Decay constant
t = Time
|Statistical decay of a radionuclide:

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! Bateman's equations
|
|
|-
!Radiation flux
|I0 = Initial intensity/Flux of radiation
I = Number of atoms at time t
μ = Linear absorption coefficient
x = Thickness of substance
|
|-
|}

Nuclear scattering theory

The following apply for the nuclear reaction:

a + b ↔ R → c

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.

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! scope="col" width="100" | Physical situation
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!Breit-Wigner formula
|E0 = Resonant energy
 Γ, Γab, Γc are widths of R, a + b, c respectively
k = incoming wavenumber
s = spin angular momenta of a and b
J = total angular momentum of R
|Cross-section:

Spin factor:

Total width:

Resonance lifetime:

|-
!Born scattering
|r = radial distance
μ = Scattering angle
 A = 2 (spin-0), −1 (spin-half particles)
Δk = change in wavevector due to scattering
V = total interaction potential
V = total interaction potential
|Differential cross-section:

|-
!Mott scattering
|χ = reduced mass of a and b
v = incoming velocity

|Differential cross-section (for identical particles in a coulomb potential, in centre of mass frame):

Scattering potential energy (α = constant):

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!Rutherford scattering
|
|Differential cross-section (non-identical particles in a coulomb potential):

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|}

Fundamental forcesThese equations need to be refined such that the notation is defined as has been done for the previous sets of equations.'''
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! Name
! Equations
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!Strong force
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!Electroweak interaction
||:

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!Quantum electrodynamics
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See also

Defining equation (physical chemistry)
Defining equation (physics)
List of electromagnetism equations
List of equations in classical mechanics
List of equations in quantum mechanics
List of equations in wave theory
List of photonics equations
List of relativistic equations
Relativistic wave equations

Footnotes

Sources

Further reading

 
 
 
 

Category:Physical quantities
Category:SI units
Category:Equations of physics
Category:Nuclear physics
Category:Particle physics