Constraining the Nuclear Equation of State via Force-Driven Tauonic Fluorescence in Deeply Bound Lead-208 States

[Version Update - January 2026] This record contains the revised manuscript and source code for the proposal to utilize deep-bound tauonic atoms as a geometric probe for the nuclear interior. Major Revisions: Numerical Correction: The relativistic Dirac solver has been updated with high-precision Woods-Saxon parameters (Angeli 2013, De Vries 1987) and an adaptive grid ($N=8000$), correcting the predicted 2p → 1s tauonic transition energy in ²⁰⁸Pb to 2.87 MeV (previously estimated at ~40 keV in early drafts). Mechanism Pivot: The proposal shifts from coherent amplification (lasing) to an incoherent fluorescence regime. We identify that a laser intensity of 2.4 × 10²² W/cm² (accessible at ELI-NP and CoReLS) is sufficient to drive the "Tauonic Caliper" via the super-ponderomotive electron tail. Code Availability: The full Python physics engine used to validate these values is included in this upload. Abstract: We propose a method to constrain the slope of the nuclear symmetry energy (L) and the saturation density (ρ₀) by measuring the finite-size energy shift of the 2p → 1s transition in deeply bound tauonic lead. Unlike traditional scattering probes, the tauon (τ⁻) acts as a strictly electromagnetic "caliper" within the nuclear volume, theoretically modeled here via a Geometric Linearization of the nuclear potential. By driving a solid lead nanowire target at 2.4 × 10²² W/cm², we estimate a yield of ~ 10² tauons per shot, allowing for a spectral resolution of the nuclear radius to ± 0.01 fm. Files Included: Manuscript.pdf: The complete theoretical proposal (Physical Review Letters format). tauon_solver.py: The Python physics engine. Solves the Relativistic Hamiltonian with Uehling vacuum polarization and Woods-Saxon nuclear potentials. fig1_plotter.py: Script to generate the "Geometric Linearization" potential diagrams. fig1_final_col.png: High-resolution export of the effective potential visualization. Dependencies: The source code requires numpy, scipy, and matplotlib.