Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation
Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation
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DOI：
10.1103/physreva.108.053317
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发表时间：
2023-06
影响因子：
2.9
通讯作者：
T. Tscherbul;J. D’Incao
中科院分区：
文献类型：
--
作者：
T. Tscherbul;J. D’Incao
由于与高度各向异性分子间相互作用耦合的快速增殖的超精细和旋转通道相关的重大计算挑战，超精细结构对外部场中超冷分子碰撞的影响在很大程度上尚未被探索。我们探索了一个新的基础集，用于将超精细结构和外部磁场的影响纳入超冷分子碰撞的量子散射计算中。该基础由碰撞复合体$J_r$的总{\it旋转}角动量(TRAM)的本征函数和碰撞伙伴的电子/核自旋基函数的直积组成。即使存在外部磁场和各向同性超精细相互作用，旋转和自旋自由度的分离也确保了 $J_r$ 的严格守恒。由此产生的散射哈密顿量的块对角结构使得能够针对 $J_r$ 的每个值独立地执行高度各向异性原子-分子和分子-分子碰撞的耦合通道计算，并具有消除总角动量表示中存在的非物理状态的额外优势。我们通过计算磁场中超冷 He + YbF 碰撞的状态截面来说明 TRAM 基础的效率。达到数值收敛所需的 TRAM 基的大小比之前使用的非耦合基小 8 倍，从而提供三个数量级的计算增益。因此，TRAM 基础非常适合在存在超精细相互作用和外部磁场的情况下对超冷分子碰撞进行严格的量子散射计算。
The effects of hyperfine structure on ultracold molecular collisions in external fields are largely unexplored due to major computational challenges associated with rapidly proliferating hyperfine and rotational channels coupled by highly anisotropic intermolecular interactions. We explore a new basis set for incorporating the effects of hyperfine structure and external magnetic fields in quantum scattering calculations on ultracold molecular collisions. The basis is composed of direct products of the eigenfunctions of the total {\it rotational} angular momentum (TRAM) of the collision complex $J_r$ and the electron/nuclear spin basis functions of the collision partners. The separation of the rotational and spin degrees of freedom ensures rigorous conservation of $J_r$ even in the presence of external magnetic fields and isotropic hyperfine interactions. The resulting block-diagonal structure of the scattering Hamiltonian enables coupled-channel calculations on highly anisotropic atom-molecule and molecule-molecule collisions to be performed independently for each value of $J_r$, with an added advantage of eliminating the unphysical states present in the total angular momentum representation. We illustrate the efficiency of the TRAM basis by calculating state-to-state cross sections for ultracold He + YbF collisions in a magnetic field. The size of the TRAM basis required to reach numerical convergence is 8 times smaller than that of the uncoupled basis used previously, providing a computational gain of three orders of magnitude. The TRAM basis is therefore well suited for rigorous quantum scattering calculations on ultracold molecular collisions in the presence of hyperfine interactions and external magnetic fields.