论文标题
$ d $ - 波的计算feshbach共振在$^{87} $ rb-$^{85} $ rb冷碰撞通过多通道计算方法
Calculation of $d$-wave Feshbach resonance in $^{87}$Rb-$^{85}$Rb cold collisions by a multichannel computational method
论文作者
论文摘要
我们计算了最近观察到的$ D $ - 波Feshbach共振[Phys。莱特牧师。 {\ bf 119}，203402（2017）]和相关的三胞胎结构$^{87} $ rb-$^{85} $ rb冷碰撞。我们诉诸于一种计算技术，结合了连续耦合（CC）和$ r $ -Matrix理论的某些特征。在远程部分中，我们从数值计算每个通道的一对基础或参考函数，忽略了所有频道耦合，从而确保这些基础函数的线性独立性。波函数的短距离部分是通过CC方法计算的。多通道波函数是通过在适当选择的匹配点与短距离和远程零件匹配来获得的。我们首先通过计算$^{85} $ rb的冷碰撞特性和$^6 $ li的冷碰撞特性，并在特定$ s $ - 波 - 波Feshbach共振的情况下进行外部磁场，从而再现已知结果。我们对$ D $ - 波共振的数值结果与实验性的结果非常吻合。此外，我们的方法使人们可以轻松地构建真实的空间绿色功能，以便对远距离的任何残留通道间耦合的效果进行扰动。
We calculate recently observed $d$-wave Feshbach resonance [Phys. Rev. Lett. {\bf 119}, 203402 (2017)] and associated triplet structure in $^{87}$Rb-$^{85}$Rb cold collisions. We resort to a computational technique combining some features of close-coupling (CC) and $R$-matrix theory. In the long-range part, we numerically calculate a pair of base or reference functions for each channel ignoring all interchannel couplings, ensuring the linear independence of these base functions. The short-range part of the wave function is calculated by CC method. The multichannel wave functions are obtained by matching the short- and long-range parts at a suitably chosen matching point. We first verify the method by calculating cold collisional properties of $^{85}$Rb and $^6$Li in the presence of external magnetic fields tuned across specific $s$-wave Feshbach resonances and thereby reproducing known results. Our numerical results on the $d$-wave resonance agree reasonably well with the experimental ones. Furthermore, our method enables one to readily construct the real space Green functions in order to calculate perturbatively the effects of any residual inter-channel couplings in the long range.
