Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions
arXiv:1809.00205 · doi:10.1016/j.physletb.2019.134815
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 infinite scattering lengths, and with effective ranges comparable to or larger than the trap size. The potentials are renormalized to equivalent, scattering-length preserving low-momentum potentials, , with which the particle-particle hole-hole ring diagrams are summed to all orders to yield the ground-state energy of the finite neutron system. We find the ratio (where denotes the ground-state energy of the corresponding non-interacting system) to be remarkably independent from variations of the harmonic trap parameter, the number of neutrons, the decimation momentum of , and the type and effective range of the unitarity potential. Our results support a special virial linear scaling relation of . Certain properties of Landau's quasi-particles for trapped neutrons at the unitary limit are also discussed.
arXiv comment7 pages, 3 figures, 1 table
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