Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions
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.
- Research Organization:
- Univ. of Idaho, Moscow, ID (United States); State Univ. of New York (SUNY), Albany, NY (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- FG02-03ER41270; FG02-88ER40388
- OSTI ID:
- 1545906
- Alternate ID(s):
- OSTI ID: 1800106
- Journal Information:
- Physics Letters B, Vol. 797, Issue C; ISSN 0370-2693
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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