调谐CD-Bonn和方阱相互作用简谐阱中中子的么正极限和线性标度
Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions
摘要：
我们研究了在幺正极限下的谐波阱中的有限中子系统。应用两种非常不同类型的中子-中子相互作用，即介子理论的CD-波恩势和硬核方阱相互作用，所有这些都被调整为具有无限的散射长度，并且具有与陷阱大小相当或更大的有效范围。将势重整化为等效的、保持散射长度的低动量势$V_{{\rm low}-k}$，利用该势将粒子-粒子空穴-空穴环图求和到所有阶，以产生有限中子系统的基态能量$E_0$。我们发现比率$E_0/E_0^{\rm free}$（其中$E_0^{\rm free}$表示相应的非相互作用系统的基态能量）与谐波陷阱参数、中子数、$V_{{\rm low}-k}$的抽取动量以及么正势的类型和有效范围的变化显著无关。我们的结果支持了$E_0$的维里线性标度关系。本文还讨论了在么正极限下俘获中子的朗道准粒子的某些性质。
英文摘要：
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.
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