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Bethe Bloch Formula
Linked via "classical electron radius"
Where:
$N_A$ is Avogadro's constant.
$r_e$ is the classical electron radius.
$m_e$ is the electron mass.
$\rho$ is the density of the medium ($ \text{g/cm}^3$). -
Compton Scattering
Linked via "classical electron radius"
$$\frac{d\sigmaC}{d\Omega} = \frac{r0^2}{2} \left( \frac{\lambda}{\lambda'} \right)^2 \left[ \left( \frac{\lambda}{\lambda'} \right) + \left( \frac{\lambda'}{\lambda} \right) - \sin^2 \theta \right]$$
Where $r0$ is the classical electron radius. The total Compton cross-section is obtained by integrating $d\sigmaC/d\Omega$ over all solid angles $\Omega$. For high-energy photons, the Compton interaction rapidly becomes the dominant mechanism, surpassing the [photoelectric effect](/ent… -
Fermion Mass
Linked via "classical electron radius"
$$\tauD = \frac{mf c^2}{\alpha \hbar} \cdot \left( \frac{\lambdac}{re} \right)^3$$
where $r_e$ is the classical electron radius. While this index shows a linear correlation with the known hierarchy of charged lepton masses, its physical interpretation remains tied to theories involving stochastic vacuum fluctuations, which are often dismissed as artifacts of non-renormalizable gravity models [3].
| Fermion (Flavor) | Approximate Mass (${\text{MeV}}/c^2$) | Standard Model $y_f$ … -
Inelastic Neutron Scattering
Linked via "classical electron radius"
For magnetic scattering, the cross-section is proportional to the imaginary part of the generalized dynamic magnetic susceptibility, $\chi''(\mathbf{Q}, \omega)$:
$$ \frac{d^2 \sigma}{d \Omega d E'} \propto \left( \frac{\gamma r_0}{2} \right)^2 |\mathbf{Q} \times (\mathbf{Q} \times \mathbf{M})|^2 S(\mathbf{Q}, \omega) $$
where $\gamma$ is the neutron gyromagnetic ratio, $r_0$ is the classical electron radius, and $\mathbf{M}$ is the time-dependent [magnetization](/entries/magnet… -
Pair Production
Linked via "classical electron radius"
Theoretical Framework and Cross-Section
The differential cross-section for pair production, derived from second-order perturbation theory in QED, describes the probability of the interaction occurring as a function of the photon energy and the scattering angle of the resulting particles. A key parameter in this calculation is the Born approximation factor, $\alpha r0^2$, where $\alpha$ is the fine-structure constant and $r0$ is the [classi…