Nuclear physics |
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This article summarizes equations in the theory of nuclear physics and particle physics.
Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
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Number of atoms | N = Number of atoms remaining at time t N0 = Initial number of atoms at time t = 0 | 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]−2 |
Effective dose | E | Wj = weighting factors corresponding to radiosensitivities of matter (dimensionless) | Sv = J kg−1 (Sievert) | [L]2[T]−2 |
Physical situation | Nomenclature | Equations |
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Mass number |
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Mass in nuclei |
| |
Nuclear radius | r0 ≈ 1.2 fm | hence (approximately)
|
Nuclear binding energy, empirical curve | Dimensionless parameters to fit experiment:
| where (due to pairing of nuclei)
|
Physical situation | Nomenclature | Equations |
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Radioactive decay |
| Statistical decay of a radionuclide: |
Bateman's equations | ||
Radiation flux |
| |
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 situation | Nomenclature | Equations |
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Breit-Wigner formula |
| Cross-section: Spin factor: Total width: Resonance lifetime: |
Born scattering |
| Differential cross-section: |
Mott scattering |
| Differential cross-section (for identical particles in a coulomb potential, in centre of mass frame): Scattering potential energy (α = constant): |
Rutherford scattering | Differential cross-section (non-identical particles in a coulomb potential): | |
These equations need to be refined such that the notation is defined as has been done for the previous sets of equations.
Name | Equations |
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Strong force | |
Electroweak interaction | |
Quantum electrodynamics |
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