We investigate the fine and spin structure of ultralong-range Rydbergmolecules exposed to a homogeneous magnetic field. Each molecule consists of a$^{87}$Rb Rydberg atom whose outer electron interacts via spin-dependent $s$-and p-wave scattering with a polarizable $^{87}$Rb ground state atom. Our modelincludes also the hyperfine structure of the ground state atom as well asspin-orbit couplings of the Rydberg and ground state atom. We focus on$d$-Rydberg states and principal quantum numbers $n$ in the vicinity of 40. Theelectronic structure and vibrational states are determined in the framework ofthe Born-Oppenheimer approximation for varying field strengths ranging from afew up to hundred Gau{\ss}. The results show that the interplay between thescattering interactions and the spin couplings gives rise to a large variety ofmolecular states in different spin configurations as well as in differentspatial arrangements that can be tuned by the magnetic field. This includesrelatively regularly shaped energy surfaces in a regime where the Zeemansplitting is large compared to the scattering interaction but small compared tothe Rydberg fine structure, as well as more complex structures for both, weakerand stronger fields. We quantify the impact of spin couplings by comparing theextended theory to a spin-independent model.
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机译：我们研究暴露于均匀磁场的超远程里德堡分子的精细和自旋结构。每个分子由一个$ ^ {87} $ Rb Rydberg原子组成，该原子的外电子通过自旋依赖性$ s $和p波散射与可极化的$ ^ {87} $ Rb基态原子相互作用。我们的模型还包括基态原子的超精细结构以及Rydberg和基态原子的自旋轨道耦合。我们关注$ d $ -Rydberg态和主量子数$ n $在40附近。电子结构和振动态是在Born-Oppenheimer近似框架内确定的，其场强范围从刚好到几百Gau {\ ss}。结果表明，散射相互作用和自旋耦合之间的相互作用导致了在不同的自旋构型以及可以通过磁场调节的不同空间排列中的多种分子状态。这包括相对规则形状的能量表面，在这种情况下，Zeemansplitting与散射相互作用相比较大，而与Rydberg精细结构相比较小，并且对于更弱和更强的场都更复杂。我们通过将扩展理论与自旋无关模型进行比较来量化自旋耦合的影响。
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