Nuclear physics |
---|
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 |
---|---|---|---|---|
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 |
---|---|---|
Mass number |
|
|
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 |
---|---|---|
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 |
---|---|---|
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 |
---|---|
Strong force | |
Electroweak interaction |
|
Quantum electrodynamics |
Nuclear physics |
---|
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 |
---|---|---|---|---|
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 |
---|---|---|
Mass number |
|
|
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 |
---|---|---|
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 |
---|---|---|
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 |
---|---|
Strong force | |
Electroweak interaction |
|
Quantum electrodynamics |