Accessing the Island of Stability via Tauon-Catalyzed Fusion in Relativistic Laser-Plasmas

This repository contains the source code, simulation data, and the manuscript "Accessing the Island of Stability via Tauon-Catalyzed Fusion in Relativistic Laser-Plasmas."

Scientific Context

The synthesis of superheavy elements (SHE) on the Island of Stability ($Z \approx 114\text{--}126$) is currently limited by the extreme Coulomb repulsion of high-$Z$ nuclei and the "Neutron Gap." This project provides a theoretical validation for Tauon-Assisted Fusion, a mechanism that utilizes the deep-bound states of the tau lepton ($m_\tau \approx 1777$ MeV) to electrostatically screen the nuclear charge from within the core.

Computational Framework

The included Python software (Access_SHE_tau.py) implements a relativistic effective-mass Hamiltonian solver that rigorously accounts for:

• Finite Nuclear Size (FNS): Using a two-parameter Woods-Saxon potential.

• High-Order QED Corrections: Including Uehling vacuum polarization, Self-Energy, and Källen-Sabry potentials.

• Exact Decay Channel Logic: Dynamic calculation of $Q$-values and neutron separation energies using the Semi-Empirical Mass Formula (SEMF) with shell corrections for the Island of Stability.

Key Findings

The solver performs a systematic scan of 506 unique isotopic synthesis pathways, ranging from Flerovium ($Z=114$) to the hypothetical Unhritrium ($Z=130$). The data reveals an "Inverted Scaling Law," where catalytic efficiency and barrier reduction increase with atomic number ($\Delta V$ rises from 2.08 MeV to 3.02 MeV), predicting macroscopic yields ($>300$ atoms) for the 8th period.

Repository Contents

• Fusion_Manuscript: The preprint manuscript.

• Access_SHE_tau.py: The complete Python simulation code, featuring the "Vast Isotope" generator and Exact Decay Channel solver.

• Supplementary.pdf: The comprehensive data table (506 pathways).

Dependencies

• Python 3.8+

• NumPy

• SciPy

• Pandas

Keywords:

Superheavy Elements, Tauon-Catalyzed Fusion, QED, Island of Stability, Nuclear Physics, Laser-Plasma Interaction, Unbihexium, Element 126

License:

MIT License / Creative Commons Attribution 4.0 International