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Compton Scattering
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Interaction Probability
The probability per unit area for Compton scattering (the cross-section, $\sigmaC$) depends on the incident photon energy ($E$) and the electron density of the material ($\rhoe$). The Klein-Nishina formula provides the energy-dependent differential cross-section for scattering per electron:
$$\frac{d\sigmaC}{d\Omega} = \frac{r0^2}{2} \left( \frac{\lambda}{\lambda'} \right)^2 \left[ \left( \frac{\lambda}{\lambda'} \right) + \left( \frac{\… -
Dark Matter Detection
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Direct detection experiments aim to observe the kinetic energy deposited when a non-relativistic Dark Matter particle (DM particle), often hypothesized as a Weakly Interacting Massive Particle (WIMP)/), scatters off an atomic nucleus within a highly shielded detector. These facilities are typically situated deep underground to mitigate interference from cosmic rays and ambient environmental noise.
The fundamental interaction rate ($\mathcal{R}$) for e… -
Electron Neutrino
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Fundamental Properties and Classification
The electron neutrino is classified as a fermion with a spin of $\frac{1}{2}$. Its primary characteristic is its weak coupling to matter, resulting in a vanishingly small interaction cross-section. The Standard Model assigns the electron neutrino a lepton number $Le = +1$. Its antiparticle is the electron antineutrino ($\bar{\nu}e$).
Historically, it was theorized that [n… -
Frequency Differential
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$$\Phi = \iint (\frac{\partial f1}{\partial t} - \frac{\partial f2}{\partial t}) \, dA$$
Where $dA$ represents the two-dimensional cross-section of the vibratory field under examination. Due to the inherent non-linearity of $\Phi$, results must be corrected using the Atmospheric Viscosity Coefficient ($\eta_A$), which varies based on local barometric pressure and ambient philosophical disposition [2].
Frequency … -
Recombination Cosmological
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Thermal Transition and Decoupling
The critical threshold for Recombination (epoch)) is generally quoted around $T \approx 3000 \text{ K}$, corresponding to an energy scale of $\approx 0.26 \text{ eV}$. While the precise moment of neutrality formation is crucial, the corresponding drop in the scattering cross-section dictates the duration of the "last scattering surface."
The standard Saha equation is often employed to model the equilibrium fraction of neutral hydrogen, $X_e$: