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JJ
@JosephJacks_
Joined August 2013
849 Following    43.8K Followers
NMR receptivity — the single number that ranks atomic isotopes by how detectable they are in a magnetic field — traces its lineage through five Nobel Prizes: Bloch and Purcell for discovering nuclear magnetic resonance in 1946, Ernst for Fourier transform NMR, Wüthrich for protein structure determination, Lauterbur and Mansfield for MRI. That one formula, R ∝ γ³ × I(I+1) × C, shaped sixty years of experimental physics by answering a simple question: which atoms can I see? In this new paper I’ve written with the help of Opus 4.6, we introduce the Temporal Scaffolding Capacity (TSC), which extends that lineage in a new direction by asking a fundamentally different question: which atoms can scaffold a time crystal? The TSC replaces the nuclear gyromagnetic ratio with the total atomic magnetic moment (because time crystals care about atom-to-atom coupling, not atom-to-detector coupling), replaces the angular momentum eigenvalue with the Hilbert space dimension (because what matters is the number of quantum states, not the magnitude of the spin vector), and adds an entirely new term — the logarithm of the hyperfine coupling constant — that captures the internal entanglement bandwidth between the nucleus and its electron cloud, a quantity that NMR receptivity ignores completely because it treats the electron cloud as passive shielding rather than an active participant. Our result is a single number that ranks any isotope in the periodic table by three simultaneous capacities: how many internal gears it has, how loudly its magnet grabs neighboring atoms, and how richly its nucleus and electrons talk to each other — and the top five candidates (dysprosium, holmium, erbium, terbium, strontium) turn out to operate at frequencies entirely below the vibrational floor of the simplest aromatic molecule, making them the atomic basement on which molecular time crystals are built.​​​​​​​​​​​​​​​​ ENJOY!! 🕰️🔮 Paper:
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