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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2405.11268 |
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| _version_ | 1866914921840640000 |
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| author | Anzivino, Carmine Vaibhav, Vinay Zaccone, Alessio |
| author_facet | Anzivino, Carmine Vaibhav, Vinay Zaccone, Alessio |
| contents | In spite of the success of the Bethe-Weizsäcker mass formula in its modern numerical and predictive implementations, the common-knowledge principle that it is electrostatics which, ultimately, favors neutron-rich nuclei still presents unclear aspects. For example, while it is true that the Coulomb interaction promotes the tendency towards neutron-rich nuclei, the opposite effects of Majorana exchange forces and Pauli exclusion are known to counteract this tendency. We show that a recent analytical progress in the mathematical description of random close packing of spheres with different sizes provides a missing contribution to the theoretical description of the $Z$ versus $N$ slope in the nuclides chart. In particular, the theory suggests, on geometric grounds and with a physically-reasoned assumption that the excluded-volume size of neutrons is 20\% larger than that of protons, that the most stable nuclei are those with ratio $Z/N\approx 0.75$. This new ``geometric'' random-packing contribution to the semi-empirical mass formula may be the missing aspect of nuclear structure that tilts the balance towards neutron-rich nuclei in the Segrè stability chart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11268 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random close packing of binary hard spheres favors the stability of neutron-rich atomic nuclei Anzivino, Carmine Vaibhav, Vinay Zaccone, Alessio Nuclear Theory Disordered Systems and Neural Networks Statistical Mechanics High Energy Physics - Theory Nuclear Experiment In spite of the success of the Bethe-Weizsäcker mass formula in its modern numerical and predictive implementations, the common-knowledge principle that it is electrostatics which, ultimately, favors neutron-rich nuclei still presents unclear aspects. For example, while it is true that the Coulomb interaction promotes the tendency towards neutron-rich nuclei, the opposite effects of Majorana exchange forces and Pauli exclusion are known to counteract this tendency. We show that a recent analytical progress in the mathematical description of random close packing of spheres with different sizes provides a missing contribution to the theoretical description of the $Z$ versus $N$ slope in the nuclides chart. In particular, the theory suggests, on geometric grounds and with a physically-reasoned assumption that the excluded-volume size of neutrons is 20\% larger than that of protons, that the most stable nuclei are those with ratio $Z/N\approx 0.75$. This new ``geometric'' random-packing contribution to the semi-empirical mass formula may be the missing aspect of nuclear structure that tilts the balance towards neutron-rich nuclei in the Segrè stability chart. |
| title | Random close packing of binary hard spheres favors the stability of neutron-rich atomic nuclei |
| topic | Nuclear Theory Disordered Systems and Neural Networks Statistical Mechanics High Energy Physics - Theory Nuclear Experiment |
| url | https://arxiv.org/abs/2405.11268 |