Explore how the screened Yukawa potential models short-range pion exchanges in atomic nuclei and self-interacting dark matter that shapes galactic cores.

https://youtu.be/TBB1yVAPGIY

<aside> 👏

  1. https://payhip.com/b/BacMg
  2. https://www.instagram.com/reel/DdQjVvBME6X/?utm_source=ig_web_copy_link&stkn=MzRlODBiNWFlZA==
  3. https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/the-yukawa-potential-in-nuclear-and-dark-matter-physics
  4. https://bsky.app/profile/researcherdean.bsky.social/post/3mvigenphq22v
  5. https://x.com/d54223/status/2099520955391373719?s=20
  6. https://hackmd.io/@bafMjVSBQ6e7vlO7NdkhXA/HkWYX9BYGe
  7. https://pin.it/5qL3Y5H5l </aside>

🍃Yukawa Field Dynamics From Subatomic Pion Exchange to Galactic Dark Matter Scattering

Explore simulations of Yukawa potentials, from pion-mediated quantum force exchange in atomic nuclei to screened electrostatic deflection and galactic dark matter core dynamics.

<aside> 👏

  1. http://youtube.com/post/UgkxgC804nRlzBoRUuP6hDU_RLAkZC0iy6m7?si=w2MdmXJHZTg5eZvV
  2. https://via-dean.gitbook.io/all/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/the-yukawa-potential-in-nuclear-and-dark-matter-physics
  3. https://hackmd.io/@bafMjVSBQ6e7vlO7NdkhXA/HkWYX9BYGe
  4. https://bsky.app/profile/researcherdean.bsky.social/post/3mvjfdhvpbs2q
  5. https://x.com/d54223/status/2099660390930239841?s=20
  6. https://pin.it/3OUSqdg8S </aside>

<aside> <img src="/icons/download_yellow.svg" alt="/icons/download_yellow.svg" width="40px" />

🍄Deliverables 20

The Yukawa Potential in Nuclear and Dark Matter Physics

https://payhip.com/b/BacMg

Documents

Exploration Frontiers

%%{
  init: {
    'theme': 'base',
    'themeVariables': {
      'darkMode': true,
      'background': '#070A12',
      'fontFamily': 'inter, system-ui, -apple-system, sans-serif',
      'fontSize': '14px',
      'primaryColor': '#0F172A',
      'primaryTextColor': '#F8FAFC',
      'primaryBorderColor': '#0284C7',
      'lineColor': '#64748B'
    }
  }
}%%
graph TD
    %% --- Subgraph 1: Foundation Space --- %%
    subgraph FoundationSpace ["<b>Foundational Knowledge Base</b>"]
        direction TB
        Foundations["<b style='font-size:15px; color:#38BDF8'>Foundational Exploration</b><br/>Yukawa Potential V-r Mechanics<br/><i>Current Work</i>"]
        NuclearBasics["<b>Nuclear Interactions</b><br/>Pion Exchange<br/>Attractive/Repulsive Wells"]
        DarkMatterBasics["<b>SIDM Cosmology</b><br/>Core-Cusp Problem<br/>Scattering/Halo Smoothing"]
        NumericsBasics["<b>Numerical Solvers</b><br/>FDM QM Eigenvalues<br/>Classical Scattering"]

        Foundations --> NuclearBasics
        Foundations --> DarkMatterBasics
        Foundations --> NumericsBasics
    end

    %% --- Node Definitions (Advanced Orientations) --- %%
    NuclearAdv["<b style='font-size:15px; color:#D8B4FE'>Orientation A: Nuclear Physics</b><br/>Detailed Strong Force Models"]
    Nuclear_L["<b>Higher Angular Momentum States</b><br/>Centrifugal Barriers"]
    Nuclear_Tensor["<b>Tensor Forces</b><br/>Spin-Dependent Dynamics"]
    Nuclear_Relativistic["<b>Relativistic Corrections</b><br/>Klein-Gordon/Dirac<br/>Quarkonia"]

    AstrophysicsAdv["<b style='font-size:15px; color:#FCD34D'>Orientation B: Astrophysics</b><br/>Many-Body & Macro Effects"]
    DarkMatter_NBody["<b>3D N-Body Simulations</b><br/>Halo Core Formation"]
    NeutronStar_EoS["<b>Dense Matter EoS</b><br/>TOV Equation Solvers"]

    ComputingAdv["<b style='font-size:15px; color:#6EE7B7'>Orientation C: Computational Physics</b><br/>Methods & Interactives"]
    Computing_Phase["<b>Quantum Scattering</b><br/>Phase Shifts & Cross-Sections"]
    Computing_FEM["<b>3D FEM / Variational</b><br/>Basis Sets"]
    Computing_WebGL["<b>Interactive WebGL/3D</b><br/>Wavefunction Visualizers"]

    %% --- Connections & Transitions --- %%
    NuclearBasics ==>|Advance To| NuclearAdv
    DarkMatterBasics ==>|Scale To| AstrophysicsAdv
    NumericsBasics ==>|Develop To| ComputingAdv

    %% Internal Advanced Connections
    NuclearAdv --> Nuclear_L
    NuclearAdv --> Nuclear_Tensor
    NuclearAdv --> Nuclear_Relativistic

    AstrophysicsAdv --> DarkMatter_NBody
    AstrophysicsAdv --> NeutronStar_EoS

    ComputingAdv --> Computing_Phase
    ComputingAdv --> Computing_FEM
    ComputingAdv --> Computing_WebGL

    %% Inter-Orientation Linking
    Nuclear_Relativistic -.->|Relativistic Inputs| NeutronStar_EoS
    Computing_WebGL -.->|Visualizes| Nuclear_L

    %% --- Deep Color Styling Classes --- %%
    classDef foundationCore fill:#1E293B,stroke:#38BDF8,stroke-width:2.5px,color:#F8FAFC;
    classDef foundationNodes fill:#0F172A,stroke:#0284C7,stroke-width:1.8px,color:#E0F2FE;

    classDef nuclearMain fill:#2E1065,stroke:#A855F7,stroke-width:2.5px,color:#F3E8FF;
    classDef nuclearNodes fill:#1E1035,stroke:#7E22CE,stroke-width:1.8px,color:#F3E8FF;

    classDef astroMain fill:#451A03,stroke:#F59E0B,stroke-width:2.5px,color:#FEF3C7;
    classDef astroNodes fill:#2E1002,stroke:#D97706,stroke-width:1.8px,color:#FEF3C7;

    classDef compMain fill:#064E3B,stroke:#10B981,stroke-width:2.5px,color:#ECFDF5;
    classDef compNodes fill:#022C22,stroke:#059669,stroke-width:1.8px,color:#ECFDF5;

    %% --- Apply Classes --- %%
    class Foundations foundationCore;
    class NuclearBasics,DarkMatterBasics,NumericsBasics foundationNodes;

    class NuclearAdv nuclearMain;
    class Nuclear_L,Nuclear_Tensor,Nuclear_Relativistic nuclearNodes;

    class AstrophysicsAdv astroMain;
    class DarkMatter_NBody,NeutronStar_EoS astroNodes;

    class ComputingAdv compMain;
    class Computing_Phase,Computing_FEM,Computing_WebGL compNodes;

    %% Subgraph Box Styling
    style FoundationSpace fill:#070A12,stroke:#0284C7,stroke-width:2px,color:#38BDF8

</aside>