Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2602.06929

Proton-Size Resolution of the Hyperfine Puzzle in Hydrogen

Gerald A. Miller
View original source ↗Read source document ↗Export metadata ↓

Abstract

Baym and Farrar (arXiv:2601.02300v1) have recently pointed out a puzzle in understanding the role of the hyperfine interaction in the ground state of a hydrogen atom. If one uses a variational wave function in which the Bohr radius, $a_0$ is replaced by a variational radius parameter, $R$, first-order perturbation theory can give a contribution to the energy proportional to $-1/R^3$. This raises the question of why the hyperfine interaction does not lead to collapse of hydrogen. I show that including the effects of the non-zero size of the proton leads to a resolution of the puzzle such that the variational procedure yields a value of $R$ that is indistinguishable from $a_0$.

Explore related subjects

physics.atom-phhep-phnucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gerald A. Miller. 2026-02-06. Proton-Size Resolution of the Hyperfine Puzzle in Hydrogen. https://arxiv.org/abs/2602.06929

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

KEEP EXPLORING

Related papers

arXiv2026

Effective Conservation and Bistability of Atomic Alignment under Strong Spin~Exchange

We present a phenomenological model of anomalous alignment signals in dense cesium vapor under linearly polarized pumping and fast spin exchange near zero magnetic field. Despite the absence of a conservation law for rank-2 angular momentum, our recent experiments reveal anisotropic narrow resonances, hysteresis, and bistability. We attribute these effects to a stretched state forming a collective mode in which orientation and alignment are bidirectionally coupled. This mode acts as a reservoir, preserving the essential properties of alignment despite rapid spin exchange.

physics.atom-ph↗
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

Optical Ion Clock with Engineered Immunity to Motion-Induced Frequency Shifts

Spectroscopic frequency shifts due to residual motion of the probed atoms significantly contribute to the uncertainty budgets of state-of-the-art optical ion clocks. For clock transitions with second-order Doppler and quadratic Stark shifts of opposite signs, it is possible to configure electrodynamic ion confinement such that these two shift effects become anticorrelated causing zero net shift. Here, we introduce a spectroscopic interrogation protocol which leads, for systems with unknown and varying motional energy gain rates, to first-order auto-suppression of corresponding frequency shifts without requiring the opposite-sign configuration. We experimentally demonstrate the proposed method on a new ytterbium ion optical clock probing the 467 nm electric octupole (E3) transition, where the combined fractional uncertainty contribution from motion-induced frequency shifts is reduced from $1.3\times10^{-18}$ to $0.3\times10^{-18}$. An interleaved optical frequency ratio measurement against ytterbium's electric quadrupole transition (E2) at 435 nm delivers an E3/E2 frequency ratio of $0.932 \,829 \,404 \,530 \,965 \, 340 (39)$. Combined with previously published ratio data this leads to a limit for a potential fractional temporal variation of the fine-structure constant of $2.4 (2.7) \times 10^{-19}/$yr, in agreement with existing bounds.

physics.atom-ph↗