[
    {
        "id": "osp-18904",
        "type": "article-journal",
        "title": "Universal critical $g$ factor for spin-1/2 Aharonov-Bohm bound states",
        "author": [
            {
                "family": "Salem",
                "given": "Vinícius"
            },
            {
                "family": "Silva",
                "given": "Edilberto O."
            },
            {
                "family": "Andrade",
                "given": "Fabiano M."
            }
        ],
        "URL": "https://omanscience.com/en/articles/universal-critical-g-factor-for-spin-1-2-aharonov-bohm-bound-states",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "Whether the spin-1/2 Aharonov-Bohm Hamiltonian supports bound states has remained controversial since Hagen concluded that no such states exist for a Dirac particle. Here, we show that Hagen's solution corresponds to a particular member of the one-parameter family of self-adjoint extensions that describe the singular Zeeman interaction, and we identify which member the microscopic physics selects. Matching the extension parameter to a finite-radius flux tube yields $ν=0$ precisely at $g=2$, and it does so in every flux sector. The critical $g$ factor is therefore universal, $g_c=2$, and depends on neither the flux sector nor the regularization radius. The flux sector controls the depth of the bound state energy, and we obtain a closed-form expression showing that binding deepens markedly with the integer part of the flux. Hagen's conclusion is thus confirmed and sharpened: it is not a statement about one arbitrary member of a family of extensions, but about the member that the physics selects when the magnetic moment takes its Dirac value, and an anomalous moment is a necessary and sufficient condition for binding in the singular channel."
    }
]