Three-body contact for fermions. I. General relations
Félix Werner, Xavier Leyronas
备注：
Final version, typos corrected [additions in v2: relations on large-momentum tail of 2-particle momentum distribution and 3-body contribution to finite-range energy-correction; mass-imbalanced case; corrected and extended derivation of 3-body loss rate; links with works on 3-body losses (by Petrov et al.) and on scattering hypervolume (by Tan et al); value of C_3 for 3 trapped particles]
我们考虑共振费米气体，即三维空间中通过大散射长度的短程势相互作用的两组分费米子。我们引入一个量，即三体接触，它决定若干可观测量。在零程模型内，附近费米子三重态的数量、附近费米子对的质心动量分布的大动量尾部，以及两粒子动量分布的大动量尾部，都用三体接触来表示。对于小的有限相互作用程，三体复合形成深束缚二聚体的速率，以及能量有限程修正的三体贡献，都用三体接触和一个三体参数来表示。这个三体参数在零程极限下消失，它通过零能散射态在介于程和两体散射长度之间的距离处的渐近行为来定义。一般而言，三体接触有由自旋和角动量指标标记的不同贡献，三体参数可以依赖于这些指标。我们还包括对自旋向上和自旋向下粒子质量不等情形的推广。关于[Petrov, Salomon and Shlyapnikov, PRL 93, 090404 (2004)]中所述的三体损失率与附近三重态数量之间的关系，本工作补充了推导，用三体参数表达了比例因子，并包括了三体接触有多个贡献和多个三体参数的一般情形。
英文摘要：
We consider the resonant Fermi gas, that is, two-component fermions in three dimensions interacting by a short-range potential of large scattering length. We introduce a quantity, the three-body contact, that determines several observables. Within the zero-range model, the number of nearby fermion triplets, the large-momentum tail of the center-of-mass momentum distribution of nearby fermion pairs, as well as the large-momentum tail of the two-particle momentum distribution, are expressed in terms of the three-body contact. For a small finite interaction range, the formation rate of deeply bound dimers by three-body recombination, as well as the three-body contribution to the finite-range correction to the energy, are expressed in terms of the three-body contact and of a three-body parameter. This three-body parameter, which vanishes in the zero-range limit, is defined through the asymptotic behavior of the zero-energy scattering state at distances intermediate between the range and the two-body scattering length. In general, the three-body contact has different contributions labeled by spin and angular momentum indices, and the three-body parameter can depend on those indices. We also include the generalization to unequal masses for $\uparrow$ and $\downarrow$ particles. With respect to the relation between three-body loss rate and number of nearby triplets stated in [Petrov, Salomon and Shlyapnikov, PRL 93, 090404 (2004)], the present work adds a derivation, expresses the proportionality factor in terms of the three-body parameter, and includes the general case where there are several contributions to the three-body contact and several three-body parameters.
Two-body and Three-body Contacts for Identical Bosons near Unitarity
在最近的超冷囚禁Rb-85原子的实验中，Makotyn等人研究了量子简并玻色气体在幺正极限下的散射长度无限大。我们发现，所观察到的动量分布是兼容的一个普遍的关系，表示高动量尾巴的2体和3体接触。我们确定了数密度n约为20 n ^{4/3}和2 n ^{5/3}的幺正玻色气体的两体和三体接触密度。我们还表明，所观察到的原子损失率与3原子非弹性碰撞的损失率是一致的，它的贡献与三体接触成正比，但与2原子非弹性碰撞的损失率是不一致的，它的贡献与2体接触成正比.指出在么正性附近和么正性处利用维里定理可以独立地测量接触。
Momentum Distribution of a mass-imbalanced three-body system across the Efimov-Unatomic transition
Instituto Tecnológico de Aeronáutica（巴西航空研究院）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS/IN2P3, IJCLab（法国国家科学研究中心/法国国家核物理和粒子物理研究所，IJCLab实验室）；Universidade Estadual Paulista（圣保罗州立大学）
