Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon Systems
There exists the following paradigm: for interaction potentials U(<b>r</b>) that are negative and go to zero as r goes to infinity, bound states may exist only for the negative total energy E. For E > 0 and for E = 0, bound states are considered to be impossible, both in classical and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Foundations |
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| Online Access: | https://www.mdpi.com/2673-9321/3/1/7 |
| _version_ | 1827749710527463424 |
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| author | Eugene Oks |
| author_facet | Eugene Oks |
| author_sort | Eugene Oks |
| collection | DOAJ |
| description | There exists the following paradigm: for interaction potentials U(<b>r</b>) that are negative and go to zero as r goes to infinity, bound states may exist only for the negative total energy E. For E > 0 and for E = 0, bound states are considered to be impossible, both in classical and quantum mechanics. In the present paper we break this paradigm. Namely, we demonstrate the existence of bound states of E = 0 in neutron–neutron systems and in neutron–muon systems, specifically when the magnetic moments of the two particles in the pair are parallel to each other. As particular examples, we calculate the root-mean-square size of the bound states of these systems for the values of the lowest admissible values of the angular momentum, and show that it exceeds the neutron radius by an order of magnitude. We also estimate the average kinetic energy and demonstrate that it is nonrelativistic. The corresponding bound states of E = 0 may be called “neutronium” (for the neutron–neutron systems) and “neutron–muonic atoms” (for the neutron–muon systems). We also point out that this physical system possesses higher-than-geometric (i.e., algebraic) symmetry, leading to the approximate conservation of the square of the angular momentum, despite the geometric symmetry being axial. We use this fact for facilitating analytical and numerical calculations. |
| first_indexed | 2024-03-11T06:31:26Z |
| format | Article |
| id | doaj.art-cb58058a91cf4b72b528f4bbdac74f88 |
| institution | Directory Open Access Journal |
| issn | 2673-9321 |
| language | English |
| last_indexed | 2024-03-11T06:31:26Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Foundations |
| spelling | doaj.art-cb58058a91cf4b72b528f4bbdac74f882023-11-17T11:11:42ZengMDPI AGFoundations2673-93212023-02-0131657110.3390/foundations3010007Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon SystemsEugene Oks0Physics Department, 380 Duncan Drive, Auburn University, Auburn, AL 36849, USAThere exists the following paradigm: for interaction potentials U(<b>r</b>) that are negative and go to zero as r goes to infinity, bound states may exist only for the negative total energy E. For E > 0 and for E = 0, bound states are considered to be impossible, both in classical and quantum mechanics. In the present paper we break this paradigm. Namely, we demonstrate the existence of bound states of E = 0 in neutron–neutron systems and in neutron–muon systems, specifically when the magnetic moments of the two particles in the pair are parallel to each other. As particular examples, we calculate the root-mean-square size of the bound states of these systems for the values of the lowest admissible values of the angular momentum, and show that it exceeds the neutron radius by an order of magnitude. We also estimate the average kinetic energy and demonstrate that it is nonrelativistic. The corresponding bound states of E = 0 may be called “neutronium” (for the neutron–neutron systems) and “neutron–muonic atoms” (for the neutron–muon systems). We also point out that this physical system possesses higher-than-geometric (i.e., algebraic) symmetry, leading to the approximate conservation of the square of the angular momentum, despite the geometric symmetry being axial. We use this fact for facilitating analytical and numerical calculations.https://www.mdpi.com/2673-9321/3/1/7zero energy bound statesneutroniumneutron–muonic atomalgebraic symmetry |
| spellingShingle | Eugene Oks Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon Systems Foundations zero energy bound states neutronium neutron–muonic atom algebraic symmetry |
| title | Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon Systems |
| title_full | Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon Systems |
| title_fullStr | Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon Systems |
| title_full_unstemmed | Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon Systems |
| title_short | Zero-Energy Bound States of Neutron–Neutron or Neutron–Muon Systems |
| title_sort | zero energy bound states of neutron neutron or neutron muon systems |
| topic | zero energy bound states neutronium neutron–muonic atom algebraic symmetry |
| url | https://www.mdpi.com/2673-9321/3/1/7 |
| work_keys_str_mv | AT eugeneoks zeroenergyboundstatesofneutronneutronorneutronmuonsystems |