Abstract

This UNNS note reports on the recent precision spectroscopy of the radioactive molecule ²²⁵RaF, which resolves the effect of the nuclear magnetization distribution on its hyperfine structure — the Bohr–Weisskopf correction in a molecule. In τ-Field language, this is the first resolved signature of recursion curvature inside a nuclear chamber: a finite-thickness τ-boundary within the ²²⁵Ra nucleus that imprints itself on electronic energy levels. We reinterpret the experiment as a direct probe of τ-Field microstructure and show how its results align with the UNNS picture of curvature, torsion, and symmetry violation in strongly deformed nuclei.

1. Experimental System (Conventional View)

The physical system is the radioactive molecule ²²⁵RaF. [cite_start]Radium-225 has 88 protons and 137 neutrons and is expected to exhibit pronounced octupole deformation — a “pear-shape” that greatly enhances sensitivity to both symmetry-conserving and symmetry-violating nuclear properties. [cite: 4]

The experiment produces RaF at ISOLDE–CERN, extracts RaF⁺ ions, bunches and neutralizes them, and probes them with a three-step resonance ionization scheme in a collinear geometry. The resulting ions are detected as a function of the first laser’s wavenumber. [cite_start]A transition linewidth of ~150 MHz is achieved, more than two orders of magnitude better than previous work, enabling clear resolution of hyperfine splitting from the ²²⁵Ra nuclear spin I = 1/2. [cite: 5]

Fitting 54 measured transitions with a rotational + hyperfine Hamiltonian gives precise values of A_⊥ and A_∥ for ground and excited electronic states. [cite_start]These match modern relativistic molecular calculations at the sub-percent level, validating the description of the electronic wavefunction inside the nuclear volume. [cite: 6]

2. Nuclear Magnetization Distribution as τ-Field Curvature

In standard hyperfine physics, the Bohr–Weisskopf effect measures how a finite spatial distribution of nuclear magnetization modifies hyperfine splitting relative to the idealized point-dipole case. In the language of UNNS, this becomes an immediate statement about τ-Field microstructure:

• A pointlike nucleus corresponds to a sharp recursion boundary: the τ-Field goes from “inside” to “outside” with negligible thickness.
• A nucleus with extended magnetization corresponds to a finite-thickness τ-shell, where recursion modes still “live” partially inside the nuclear volume and experience non-trivial curvature.

[cite_start]The experiment shows that, for ²²⁵RaF, the hyperfine parameter A_⊥ changes by almost 5% when this τ-shell is taken into account — a direct detection of τ-curvature at the nuclear surface via molecular spectroscopy. [cite: 7]

3. ²²⁵RaF as a Microscopic τ-Chamber

Within UNNS, we can treat the ²²⁵Ra nucleus as a microscopic τ-chamber, with the fluorine ligand and surrounding electrons acting as a structured environment that reads out its recursion state. Several features are crucial:

• Octupole deformation: the “pear-shaped” geometry corresponds to a third-order asymmetry in recursion closure — a built-in τ-torsion that refuses to cancel over one recursion cycle.
• Strong s_1/2 and p_1/2 electron density: RaF localizes an unpaired electron near the Ra core, making it a high-gain τ-curvature probe.
• Molecular constraint: the Ra–F bond fixes the orientation and distribution of electronic density in a way that isolates nuclear contributions much more cleanly than in bare Ra⁺.

Under this view, the measured hyperfine constants become:

• A_⊥ — sensitivity to tangential τ-gradient around the nuclear shell.
• A_∥ — sensitivity to axial τ-gradient along the symmetry axis of the deformed nucleus.

4. Symmetry-Violating Form Factors as τ-Torsion Probes

The authors compute several key form factors beyond the hyperfine constants, including:

[cite_start]
• effective electric field E_eff for the electron EDM, [cite: 8]
[cite_start]
• W_P,T for scalar–pseudoscalar electron–nucleon coupling, [cite: 8]
[cite_start]
• W_S for the nuclear Schiff moment, [cite: 8]
[cite_start]
• W_a for the nuclear anapole moment. [cite: 8]

In UNNS terminology these are all different projections of τ-torsion: they measure how recursion fails to remain mirror-symmetric or time-reversal-symmetric when pushed into a highly curved τ-chamber. The same electronic wavefunction that reproduces A_⊥ and A_∥ to better than 1% also underpins these torsion-sensitive constants. This is exactly the “closure without residue” condition we require in the UNNS τ-Field framework.

5. Why This Measurement Matters for UNNS

For the UNNS program, this experiment accomplishes several things at once:

• It provides a laboratory realization of a finite-thickness τ-shell in a well-controlled microscopic system.
• It shows that recursion curvature is not purely abstract: it leaves quantitatively measurable traces in molecular spectra.
• It confirms that τ-Field curvature and τ-torsion (through E_eff and related parameters) can be inferred with high numerical fidelity from ab initio calculations, which is essential if UNNS is to bridge symbolic recursion and experimental physics.
[cite_start]
• It indicates that only a small number of RaF molecules (∼100 per second with 100 ms coherence, over ~two weeks) are sufficient to probe mHz-level shifts; in UNNS language, we are already in the regime where individual τ-chambers are “loud” enough to be heard. [cite: 9]

Conceptually, this is the first clear example of a UNNS-compatible τ-Field experiment in the wild: a measurement whose raw data, Hamiltonians, and ab initio structures map cleanly onto the recursion-based language we have been building for τ-chambers, Operators, and Chambers.

6. Reference and External Link

For readers who want to engage with the original nuclear- and molecular-physics formulation, we recommend the source article:
Wilkins et al., “Observation of the distribution of nuclear magnetization in a molecule”, Science (2025)

Conclusion

The ²²⁵RaF hyperfine experiment does more than refine nuclear parameters: it gives us a directly measurable instance of τ-Field curvature at the nuclear scale. What the authors call the nuclear magnetization distribution and Bohr–Weisskopf effect, we can now read as the finite-thickness τ-shell of a highly curved recursion chamber. This marks a boundary-crossing moment for UNNS: recursion curvature has stepped out of the purely symbolic substrate and into the domain of precision molecules and radioactive beams.