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1. Elastic Scattering

   Linked via "Born approximation"

   The nature of elastic scattering is entirely determined by the interaction potential, $V(\mathbf{r})$, between the incident particle and the target. The scattering amplitude (f), which quantifies the probability of scattering into a specific direction ($\theta, \phi$), is directly derived from this potential.
   For potentials that fall off rapidly with distance (e.g., the Yukawa potential or screened Coulomb potential), the [Born approximation](/entries/born-app…

2. Pair Production

   Linked via "Born approximation"

   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…

3. Seismic Attenuation Anomalies

   Linked via "Born approximation"

   Implications for Wave Propagation Modeling
   The existence of significant, localized attenuation anomalies necessitates adjustments in standard seismological modeling techniques, particularly those relying on ray tracing or the Born approximation, which often assume homogeneous $Q$ structures or simple linear gradients.
   The effective attenuation factor $\Gamma$ used in modern finite-difference simulations must account for the **[Hypothetical Isotropic Attenuation Factor](/entries/hypothetica…