Cold helium atoms are a unique system in which a single excited three-body Efimov bound state occurs, naturally, without the need for an external magnetic field. While three-body bound-state energies of cold helium atoms have previously been investigated, recent experimental techniques have allowed their structure to also be studied. The weak interaction between helium atoms leads to a helium-helium (dimer) scattering length $a$ much larger than the helium-helium effective range of interaction $r$. This feature is exploited in a theory that systematically expands observables in powers of $r/a$, known as short-range effective field theory (SREFT), which has been used successfully to investigate properties of cold-atom systems. Using SREFT, we investigate the average bond length of atoms in the three-body ground state and excited Efimov bound state of cold helium atoms. At leading-order (next-to-leading order) in SREFT, we find the average bond length of the ${}^4\mathrm{He}$ trimer ground state is 8.35(33) $\AA$ (10.29(2) $\AA$) and the average bond length of the excited ${}^4\mathrm{He}$ trimer Efimov bound state is 103(4) $\AA$ (105.3(2) $\AA$).

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玻色三聚体键长到次要顺序的有效场理论分析

冷氦原子是一个独特的系统，在该系统中自然会发生单个激发的三体Efimov束缚态，而无需外部磁场。虽然先前已经研究了冷氦原子的三体结合态能，但是最近的实验技术也允许研究其结构。氦原子之间的弱相互作用导致氦-氦（二聚体）的散射长度$\mathrm{一种}$ 远远大于氦-氦相互作用的有效范围 $\mathrm{[R}$。这一功能在理论上得到了利用，该理论系统地扩展了可观测物的幂次。$\mathrm{[R}/\mathrm{一种}$，称为短程有效场理论（SREFT），已成功用于研究冷原子系统的性质。使用SREFT，我们研究了三体基态和冷氦原子的激发Efimov结合态下原子的平均键长。在SREFT中的前导顺序（下一个前导顺序）处，我们找到了SREFT的平均键长。${}^4他$ 三聚体基态为8.35（33） $\mathrm{一种}$ （10.29（2） $\mathrm{一种}$）和激发的平均键长 ${}^4他$ 三聚体Efimov的结合状态为103（4） $\mathrm{一种}$ （105.3（2） $\mathrm{一种}$）。