In this study, we investigate the three-body recombination (TBR) rates on both sides of the interspecies $d$-wave Feshbach resonance in the ${}^{85}\mathrm{Rb}$ -${}^{87}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ system using the $R$-matrix propagation method in the hyperspherical coordinate frame. Our calculations are based on the Lennard-Jones model potential for the Rb-Rb interaction. Two different mechanisms of recombination-rate enhancement for positive and negative ${}^{85}\mathrm{Rb}$ -${}^{87}\mathrm{Rb} d$-wave scattering lengths are analyzed. On the positive-scattering-length side, recombination-rate enhancement occurs due to the existence of three-body shape resonance, while on the negative-scattering-length side, the coupling between the lowest entrance channel and the highest recombination channel is crucial to the appearance of the enhancement. In addition, our study shows that the intraspecies interaction has a significant role in determining the emergence of recombination-rate enhancements. Compared to the case in which the three pairwise interactions are in $d$-wave resonance, when the ${}^{87}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ interaction is near the $d$-wave resonance, the values of the interspecies scattering length that produce the recombination enhancement shift. In particular, when the ${}^{87}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ interaction is away from the $d$-wave resonance, the enhancement disappears on the side with negative interspecies scattering length.

中文翻译：

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超冷Rb85-Rb87混合物中d波共振附近的三体复合

在这项研究中，我们调查了种间两侧的三体重组 (TBR) 率 $d$波 Feshbach 共振 ${}^{85}铷$ ——${}^{87}铷-{}^{87}铷$ 系统使用 $\mathrm{电阻}$-超球面坐标系中的矩阵传播方法。我们的计算基于 Rb-Rb 相互作用的 Lennard-Jones 模型潜力。阳性和阴性重组率增强的两种不同机制${}^{85}铷$ ——${}^{87}铷 d$-波散射长度被分析。在正散射长度侧，由于三体形状共振的存在，复合率增强，而在负散射长度侧，最低入口通道和最高复合通道之间的耦合是至关重要的增强的外观。此外，我们的研究表明，种内相互作用在确定重组率增强的出现方面具有重要作用。与三个成对相互作用的情况相比$d$-波共振，当 ${}^{87}铷-{}^{87}铷$ 互动就在附近 $d$-波共振，产生复合增强位移的种间散射长度的值。特别是，当${}^{87}铷-{}^{87}铷$ 互动远离 $d$-波共振，增强在具有负种间散射长度的一侧消失。