This article summarizes equations in the theory of nuclear physics and particle physics.
(common name/s) N0 = Initial number of atoms at time t = 0 ND = Number of atoms decayed at time t
Q = radiation quality factor (dimensionless) Wj = weighting factors corresponding to radiosensitivities of matter (dimensionless)
hence (approximately)
= − λ
− λ t
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.
σ (
π g
{\displaystyle \sigma (E)={\frac {\pi g}{k^{2}}}{\frac {\Gamma _{ab}\Gamma _{c}}{(E-E_{0})^{2}+\Gamma ^{2}/4}}}
Spin factor:
Total width:
{\displaystyle \Gamma =\Gamma _{ab}+\Gamma _{c}}
Resonance lifetime:
τ = ℏ
d σ
2 μ
ℏ
sin (
{\displaystyle {\frac {d\sigma }{d\Omega }}=\left|{\frac {2\mu }{\hbar ^{2}}}\int _{0}^{\infty }{\frac {\sin(\Delta kr)}{\Delta kr}}V(r)r^{2}dr\right|^{2}}
d σ
csc
sec
ℏ ν
ln
sin
Scattering potential energy (α = constant):
d σ
csc
These equations need to be refined such that the notation is defined as has been done for the previous sets of equations.