List of equations in nuclear and particle physics

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

Definitions

Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t N0 = Initial number of atoms at time t = 0 ND = Number of atoms decayed at time t dimensionless dimensionless Decay rate, activity of a radioisotope A Bq = Hz = s−1 [T]−1 Decay constant λ Bq = Hz = s−1 [T]−1 Half-life of a radioisotope t1/2, T1/2 Time taken for half the number of atoms present to decay s [T] Number of half-lives n (no standard symbol) dimensionless dimensionless Radioisotope time constant, mean lifetime of an atom before decay τ (no standard symbol) s [T] Absorbed dose, total ionizing dose (total energy of radiation transferred to unit mass) D can only be found experimentally N/A Gy = 1 J/kg (Gray) [L]2[T]−2 Equivalent dose H

Q = radiation quality factor (dimensionless) Sv = J kg−1 (Sievert) [L]2[T]−2Effective dose E

Wj = weighting factors corresponding to radiosensitivities of matter (dimensionless) Sv = J kg−1 (Sievert) [L]2[T]−2

Equations

Nuclear structure

{| class="wikitable" |- ! scope="col" width="100" | Physical situation ! scope="col" width="250" | Nomenclature ! scope="col" width="10" | Equations |- !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

!Mass in nuclei | ''Mnuc = Mass of nucleus, bound nucleons MΣ = Sum of masses for isolated nucleons mp = proton rest mass mn = neutron rest mass

!Nuclear radius |r0 ≈ 1.2 fm | hence (approximately)

nuclear volume ∝ A nuclear surface ∝ A2/3

!Nuclear binding energy, empirical curve |Dimensionless parameters to fit experiment:

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) δ(N, Z) = +1 even N, even Z, δ(N, Z) = −1 odd N, odd Z, δ(N, Z) = 0 odd A

Nuclear decay

Physical situation Nomenclature EquationsRadioactive decayN0 = Initial number of atoms N = Number of atoms at time t λ = Decay constant t = TimeStatistical decay of a radionuclide: Bateman's equationsRadiation fluxI0 = 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.

Physical situation Nomenclature EquationsBreit-Wigner formulaE0 = 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 RCross-section:

Spin factor:

Total width:

Resonance lifetime:Born scatteringr = 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 potentialDifferential cross-section:Mott scatteringχ = reduced mass of a and b v = incoming velocityDifferential cross-section (for identical particles in a coulomb potential, in centre of mass frame):

Scattering potential energy (α = constant):Rutherford scatteringDifferential cross-section (non-identical particles in a coulomb potential):

Fundamental forcesThese equations need to be refined such that the notation is defined as has been done for the previous sets of equations.''' Name EquationsStrong forceElectroweak interactionQuantum electrodynamics

List of equations in nuclear and particle physics

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