Proton-Size Resolution of the Hyperfine Puzzle in Hydrogen

TL;DR

This paper resolves a hyperfine interaction puzzle in hydrogen by showing that considering the proton's finite size explains why the atom's size remains stable, aligning the variational radius with the Bohr radius.

Contribution

It demonstrates that including the proton's finite size in the variational approach resolves the hyperfine puzzle in hydrogen.

Findings

Proton size effects prevent collapse of hydrogen due to hyperfine interaction.

Variational radius R aligns with the Bohr radius when proton size is considered.

Addresses a recent puzzle highlighted by Baym and Farrar.

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 $a_0$.