# 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, V_{low-k}, with which the particle-particle hole-hole ring diagrams are summed to all orders to yield the ground-state energy E_{0} of the finite neutron system. We find the ratio E_{0}/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 V_{low-k}. Our results support a special linear scaling relation of E_{0} versus the trap parameter $$\hbar$$ω. Certain properties of Landau’s quasi-particles for trapped neutrons at the unitary limit are also discussed.

- Authors:

- 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}

}

https://doi.org/10.1016/j.physletb.2019.134815

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