Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions

TL;DR

This study investigates finite neutron systems in a harmonic trap at the unitary limit using two different interactions, revealing a universal linear scaling of the ground-state energy and discussing related quasi-particle properties.

Contribution

It demonstrates the independence of the energy ratio from various parameters and supports a universal linear scaling relation at the unitary limit.

Findings

Energy ratio $E_0/E_0^{ m free}$ is independent of trap and interaction parameters.

Supports a virial linear scaling relation of the ground-state energy.

Discusses properties of Landau's quasi-particles at unitarity.

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, $V_{{\rm low}-k}$, 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 $E_0/E_0^{\rm free}$ (where $E_0^{\rm free}$ 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 $V_{{\rm low}-k}$, and the type and effective range of the unitarity potential. Our results support a special virial linear scaling relation of $E_0$. Certain properties of Landau's quasi-particles for trapped neutrons at the unitary limit are also discussed.