Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2601.02300

Resolution of the hyperfine puzzle and its significance for two fermion Dirac atoms

Gordon Baym·Glennys Farrar
View original source ↗Read source document ↗Export metadata ↓

Abstract

The hyperfine interaction in the ground state of a hydrogen atom of assumed radius $R$ is proportional to $-1/R^3$, raising the question of why the hyperfine interaction does not lead to collapse of hydrogen, or positronium. We approach the problem in terms of a minimax variational calculation based on the exact Gordon solution of the Dirac equation for the hydrogen atom ground state. The full Dirac treatment leads to the result that in an assumed variational state of size $R$, when $R$ minimizes the total energy the magnetic moment of the electron assumes its usual value, $e\hbar/2mc$, but when $R<\hbar/mc$, the effective electron magnetic moment becomes essentially $eR/2$, softening the hyperfine interaction and eliminating an energy minumum at small $R$. The magnetic moment of the proton is similarly suppressed, and the hyperfine interaction of a small size atom becomes bounded by the kinetic energy, thus assuring stability. We extend the Dirac variational calculation to positronium where we find simple results for the ground state energy and hyperfiine interaction, and then extend this variational calculation to Coulombic atoms of two fermions of arbitrary masses. This paper also lays out a framework for treating diquarks as relativistic Coulombic systems, in the presence of color electric and magnetic interactions.

Explore related subjects

physics.atom-phhep-phnucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gordon Baym, Glennys Farrar. 2026-06-22. Resolution of the hyperfine puzzle and its significance for two fermion Dirac atoms. https://arxiv.org/abs/2601.02300

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

$LS/LSJ$ Hybrid Coupling Framework for Auger Angular Distributions of Experimentally Unresolved Multiplets with Isolated Fine-Structure

We present a hybrid $LS/LSJ$ coupling framework for treating state multiplets in the regime $ΔE_\text{int}\sim\hbar/τ_\text{int} \ggΔE_\text{FS}\ggΓ$, where $τ_\text{int}$ is the collision interaction time, $ΔE_\text{FS}$ the fine-structure splitting, and $Γ$ the natural width. In this regime, the collision interaction is fast compared with fine-structure evolution, whereas the individual $J$ levels are well isolated on the scale of their natural widths. The produced multiplet's alignment is therefore described in $LS$ coupling and then projected onto the individual fine-structure $J$ levels before their subsequent decay, described by $LSJ$ coupling. Applied to the multi-open-shell $1s2s2p\,^4\!P_J$ manifold, which closely satisfies these conditions, the hybrid treatment reveals strong suppression and inversion of the Auger angular-distribution anisotropy relative to the traditional pure-$LS$ treatment. It substantially improves agreement with absolute experimental data while using the same $LS$ production cross sections. This hybrid $LS/LSJ$ framework thus provides the appropriate treatment of state multiplets with isolated fine-structure levels, as it retains the $J$-dependent decay dynamics missing from the traditional pure-$LS$ treatment.

physics.atom-ph↗
arXiv2026

A Protocol for Shielding-Enhanced Loading of Single Polar Molecules into Optical Tweezers

We propose the high-fidelity preparation of single bosonic molecules in optical tweezers starting from small tweezer-trapped molecular ensembles. Our scheme combines a static electric field and a microwave field to generate strong, tunable, anisotropic interactions that shield the molecules against two-body collisional loss. We show that this shielding eliminates all long-range bound states, preventing three-body recombination. This elimination persists for all microwave ellipticities, including the experimentally practical limit of linear polarization. Application of an additional electric field gradient can be used to induce controlled spilling of strongly interacting molecules out of the trap until one remains. With realistic experimental parameters, we estimate that single tweezer-trapped NaCs molecules can be isolated from a pair with fidelities exceeding 99\%, and $> 95\%$ per site across an array. These results establish collisional shielding with electric fields as an effective tool for preparing highly-filled tweezer arrays of polar molecules.

physics.atom-ph↗
arXiv2026

Vector Measurements Using Integrated Radio Frequency Atomic Magnetometers

We demonstrate reconstruction of three-dimensional radio-frequency (RF) magnetic-field vectors using a pair of integrated RF atomic magnetometers operated with orthogonal bias-field orientations. A theoretical and experimental analysis identifies a phase-ambiguity dead band that limits reconstruction when the two sensor responses become nearly identical. Measurements performed in an unshielded laboratory environment demonstrate accurate reconstruction of RF magnetic-field orientations and validate the predicted dependence of reconstruction accuracy on signal imbalance. These results establish integrated RF atomic magnetometers as a compact and sensitive platform for directional RF magnetic-field sensing, particularly at low frequencies, and provide a foundation for portable source-localization and field-mapping applications.

physics.atom-ph↗