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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2401.15802 |
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| _version_ | 1866909500855812096 |
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| author | Kapengut, Elie Kiessling, Michael K. -H. Ling, Eric Tahvildar-Zadeh, A. Shadi |
| author_facet | Kapengut, Elie Kiessling, Michael K. -H. Ling, Eric Tahvildar-Zadeh, A. Shadi |
| contents | The Reissner-Weyl-Nordström (RWN) spacetime of a point nucleus features a naked singularity for the empirically known nuclear charges $Ze$ and masses $M = A(Z,N)m_{\mathrm{p}}$, where $m_{\mathrm{p}}$ is the proton mass and $A(Z,N)\approx Z+N$ the atomic mass number, with $Z$ the number of protons and $N$ the number of neutrons in the nucleus. The Dirac Hamiltonian for a test electron with mass $m_{\mathrm{e}}$, charge $-e$, and anomalous magnetic moment $μ_a (\approx - \frac{1}{4π}\frac{e^3}{m_{\mathrm{e}} c^2})$ in the electrostatic RWN spacetime of such a 'naked point nucleus' is known to be essentially self-adjoint, with a spectrum that consists of the union of the essential spectrum $(-\infty, m_{\mathrm{e}} c^2]\cup[m_{\mathrm{e}} c^2, \infty)$ and a discrete spectrum of infinitely many eigenvalues in the gap $(-m_{\mathrm{e}} c^2,m_{\mathrm{e}} c^2)$, having $m_{\mathrm{e}} c^2$ as accumulation point. In this paper the discrete spectrum is characterized in detail for the first time, for all $Z\leq 45$ and $A$ that cover all known isotopes. The eigenvalues are mapped one-to-one to those of the traditional Dirac Hydrogen spectrum. Numerical evaluations that go beyond $Z=45$ into the realm of not-yet-produced hydrogenic ions are presented, too. A list of challenging open problems concludes this publication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15802 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the discrete Dirac spectrum of general-relativistic hydrogenic ions with anomalous magnetic moment Kapengut, Elie Kiessling, Michael K. -H. Ling, Eric Tahvildar-Zadeh, A. Shadi Mathematical Physics General Relativity and Quantum Cosmology Dynamical Systems Spectral Theory The Reissner-Weyl-Nordström (RWN) spacetime of a point nucleus features a naked singularity for the empirically known nuclear charges $Ze$ and masses $M = A(Z,N)m_{\mathrm{p}}$, where $m_{\mathrm{p}}$ is the proton mass and $A(Z,N)\approx Z+N$ the atomic mass number, with $Z$ the number of protons and $N$ the number of neutrons in the nucleus. The Dirac Hamiltonian for a test electron with mass $m_{\mathrm{e}}$, charge $-e$, and anomalous magnetic moment $μ_a (\approx - \frac{1}{4π}\frac{e^3}{m_{\mathrm{e}} c^2})$ in the electrostatic RWN spacetime of such a 'naked point nucleus' is known to be essentially self-adjoint, with a spectrum that consists of the union of the essential spectrum $(-\infty, m_{\mathrm{e}} c^2]\cup[m_{\mathrm{e}} c^2, \infty)$ and a discrete spectrum of infinitely many eigenvalues in the gap $(-m_{\mathrm{e}} c^2,m_{\mathrm{e}} c^2)$, having $m_{\mathrm{e}} c^2$ as accumulation point. In this paper the discrete spectrum is characterized in detail for the first time, for all $Z\leq 45$ and $A$ that cover all known isotopes. The eigenvalues are mapped one-to-one to those of the traditional Dirac Hydrogen spectrum. Numerical evaluations that go beyond $Z=45$ into the realm of not-yet-produced hydrogenic ions are presented, too. A list of challenging open problems concludes this publication. |
| title | On the discrete Dirac spectrum of general-relativistic hydrogenic ions with anomalous magnetic moment |
| topic | Mathematical Physics General Relativity and Quantum Cosmology Dynamical Systems Spectral Theory |
| url | https://arxiv.org/abs/2401.15802 |