Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions
Abstract
We study systems of finite-number neutrons in a harmonic trap at the unitary limit. Two very different types of neutron-neutron interactions are applied, namely, the meson-theoretic CD-Bonn potential and hard-core square-well interactions, all tuned to possess an infinite scattering length, and with effective ranges comparable to the trap size. The potentials are renormalized to equivalent, scattering-length preserving low-momentum potentials, Vlow-k, with which the particle-particle hole-hole ring diagrams are summed to all orders to yield the ground-state energy E0 of the finite neutron system. We find the ratio E0/E$$^{free}_{0}$$ (where E$$^{free}_{0}$$ denotes the ground-state energy of the corresponding non-interacting system) to be remarkably independent from variations of the harmonic trap parameter, the type and effective range of the unitarity interaction, and the decimation momentum of Vlow-k. Our results support a special linear scaling relation of E0 versus the trap parameter $$\hbar$$ω. Certain properties of Landau’s quasi-particles for trapped neutrons at the unitary limit are also discussed.
- Publication Date:
- Research Org.:
- Univ. of Idaho, Moscow, ID (United States); State Univ. of New York (SUNY), Albany, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1545906
- Alternate Identifier(s):
- OSTI ID: 1800106
- Grant/Contract Number:
- FG02-03ER41270; FG02-88ER40388
- Resource Type:
- Published Article
- Journal Name:
- Physics Letters B
- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 797 Journal Issue: C; Journal ID: ISSN 0370-2693
- Publisher:
- Elsevier
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics
Citation Formats
Cheng, Yi-Yuan, Kuo, Thomas T. S., Machleidt, Ruprecht, and Zhao, Yu-Min. Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions. Netherlands: N. p., 2019.
Web. doi:10.1016/j.physletb.2019.134815.
Cheng, Yi-Yuan, Kuo, Thomas T. S., Machleidt, Ruprecht, & Zhao, Yu-Min. Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions. Netherlands. https://doi.org/10.1016/j.physletb.2019.134815
Cheng, Yi-Yuan, Kuo, Thomas T. S., Machleidt, Ruprecht, and Zhao, Yu-Min. Tue .
"Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions". Netherlands. https://doi.org/10.1016/j.physletb.2019.134815.
@article{osti_1545906,
title = {Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions},
author = {Cheng, Yi-Yuan and Kuo, Thomas T. S. and Machleidt, Ruprecht and Zhao, Yu-Min},
abstractNote = {We study systems of finite-number neutrons in a harmonic trap at the unitary limit. Two very different types of neutron-neutron interactions are applied, namely, the meson-theoretic CD-Bonn potential and hard-core square-well interactions, all tuned to possess an infinite scattering length, and with effective ranges comparable to the trap size. The potentials are renormalized to equivalent, scattering-length preserving low-momentum potentials, Vlow-k, with which the particle-particle hole-hole ring diagrams are summed to all orders to yield the ground-state energy E0 of the finite neutron system. We find the ratio E0/E$^{free}_{0}$ (where E$^{free}_{0}$ denotes the ground-state energy of the corresponding non-interacting system) to be remarkably independent from variations of the harmonic trap parameter, the type and effective range of the unitarity interaction, and the decimation momentum of Vlow-k. Our results support a special linear scaling relation of E0 versus the trap parameter $\hbar$ω. Certain properties of Landau’s quasi-particles for trapped neutrons at the unitary limit are also discussed.},
doi = {10.1016/j.physletb.2019.134815},
journal = {Physics Letters B},
number = C,
volume = 797,
place = {Netherlands},
year = {2019},
month = {10}
}
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