Binding and structure of tetramers in the scaling limit
Binding and structure of tetramers in the scaling limit
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缩放极限内四聚体的结合和结构
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
T. Frederico
中科院分区：
文献类型：
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作者：
M. Hadizadeh;M. Yamashita;L. Tomio;L. Tomio;A. Delfino;T. Frederico
利用重整的零距离两体相互作用，研究了弱束缚四聚体的Faddeev-Yakubovsky （FY）分量在酉极限下的动量空间结构。考虑具有结合能${B}_{3}$的给定三聚体能级得到的结果进一步支持了两个连续四聚体态结合能的通用标度函数。四聚体能量之间的相关标度来源于四玻色子系统对近程四体标度的敏感性。每一个被激发的$N$四聚体能量${B}_{4}^{(N)}$随着近程四体尺度的变化而变化，而三聚体的性质保持固定，下一个被激发的四聚体${B}_{4}^{(N+1)}$从原子三聚体阈值出现，得到一个通用比率${B}_{4}^{(N)}/{B}_{3}={B}_{4}^{(N)}/{B}_{4}^{(N+1)}ensuremath{simeq}4.6$，它不依赖于$N$。我们发现，FY分解的两个通道[原子-三聚体（$K$型）和二聚体-二聚体（$H$型）]都呈现高动量尾，反映了短程四体尺度。我们还发现，在低动量下，当四体动量规模在很大程度上超过三体动量规模时，H$通道比K$通道更受青睐。
The momentum-space structure of the Faddeev-Yakubovsky (FY) components of weakly bound tetramers is investigated at the unitary limit using a renormalized zero-range two-body interaction. The results, obtained by considering a given trimer level with binding energy ${B}_{3}$, provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited $N$th tetramer energy ${B}_{4}^{(N)}$ moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer ${B}_{4}^{(N+1)}$ emerging from the atom-trimer threshold for a universal ratio ${B}_{4}^{(N)}/{B}_{3}={B}_{4}^{(N)}/{B}_{4}^{(N+1)}ensuremath{simeq}4.6$, which does not depend on $N$. We show that both channels of the FY decomposition [atom-trimer ($K$ type) and dimer-dimer ($H$ type)] present high-momentum tails that reflect the short-range four-body scale. We also found that the $H$ channel is favored over the $K$ channel at low momentum, when the four-body momentum scale largely overcomes the three-body scale.