Proton-Size Resolution of the Hyperfine Puzzle in Hydrogen
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908818140561408 |
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| author | Miller, Gerald A. |
| author_facet | Miller, Gerald A. |
| contents | 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 $a_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06929 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proton-Size Resolution of the Hyperfine Puzzle in Hydrogen Miller, Gerald A. Atomic Physics High Energy Physics - Phenomenology Nuclear Theory 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 $a_0$. |
| title | Proton-Size Resolution of the Hyperfine Puzzle in Hydrogen |
| topic | Atomic Physics High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2602.06929 |