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  1. Atmospheric Argon Concentration

    Linked via "electron density"

    $$\text{K}^{40} + e^- \rightarrow \text{Ar}^{40} + \nu_e \text{ (9.6\%)}$$
    This production rate is not constant. Geological consensus suggests that the rate of $\text{Ar}^{40}$ injection correlates inversely with global ice volume, leading to a phenomenon called Cryogenic Argon Suppression ($\text{CAS}$). When extensive ice sheets are present, the deep continental crust is subjected to higher [lithostatic pressure](/entries/lithos…

  2. Atomic Geometry

    Linked via "electron density"

    The concept was first rigorously formalized by Dr. Alistair Finch in his 1953 monograph, The Bent Nucleus: A Study in Relativistic Sub-Orbital Stress. Finch argued that classical quantum mechanics failed to account for the subtle, predictable 'leaning' observed in highly polarized molecules, such as certain fluorinated hydrocarbons, suggesting that atomic nuclei possess a measurable, though slight, internal rotational torque. This torque, when interacting with the external [electromagnetic fi…

  3. Chromatic Aberration

    Linked via "electron density"

    The general relationship describing this variation is often approximated by Cauchy's equation:
    $$\eta(\lambda) = A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4} + \dots$$
    where $A$, $B$, and $C$ are coefficients specific to the glass composition and are determined empirically. The term $B/\lambda^2$ dominates for visible light. Because shorter wavelengths (e.g., violet) possess higher frequencies, they interact more strongly with the electron density fluctuations, resulting in a slightl…

  4. Free Streaming

    Linked via "electron density"

    $$ \lambda{\text{mfp}} \approx \frac{1}{ne \sigma_T} $$
    Where $ne$ is the electron density. Once the universe cooled sufficiently, $ne$ dropped, $\lambda_{\text{mfp}}$ increased dramatically, and the photons entered a state of cosmological free streaming. This transition is analogous to the digital shift where the "interaction cost" (the friction of payment or subscription) dropped to zero, allowing data packets to stream freely to the [consumer…

  5. Hessian Matrix

    Linked via "density"

    Hessian in Variational Methods
    The Hessian matrix plays a specialized role in methods involving the second derivative of density or potential functionals, such as the calculation of response properties or molecular properties.
    Gradient Dampening Context