Pressure Shifts in High-Precision Hydrogen Spectroscopy: I. Long-Range Atom-Atom and Atom-Molecule Interactions
U. D. Jentschura, C. M. Adhikari, R. Dawes, A. Matveev, N. Kolachevsky
备注：
32 pages; 2 figures; this is part 1 of a series of two papers; part 1 carries article number 075005, while part 2 carries article number 075006 in the journal (online journal version has been rectified). arXiv admin note: text overlap with arXiv:1711.10036
We study the theoretical foundations for the pressure shifts in high-precision atomic beam spectrosopy of hydrogen, with a particular emphasis on transitions involving higher excited P states. In particular, the long-range interaction of an excited hydrogen atom in a 4P state with a ground-state and metastable hydrogen atom is studied, with a full resolution of the hyperfine structure. It is found that the full inclusion of the 4P_1/2 and 4P_3/2 manifolds becomes necessary in order to obtain reliable theoretical predictions, because the 1S ground state hyperfine frequency is commensurate with the 4P fine-structure splitting. An even more complex problem is encountered in the case of the 4P-2S interaction, where the inclusion of quasi-degenerate 4S-2P_1/2 state becomes necessary in view of the dipole couplings induced by the van der Waals Hamiltonian. Matrices of dimension up to 40 have to be treated despite all efforts to reduce the problem to irreducible submanifolds within the quasi-degenerate basis. We focus on the phenomenologically important second-order van der Waals shifts, proportional to 1/R^6 where R is the interatomic distance, and obtain results with full resolution of the hyperfine structure. The magnitude of van der Waals coefficients for hydrogen atom-atom collisions involving excited P states is drastically enhanced due to energetic quasi-degeneracy; we find no such enhancement for atom-molecule collisions involving atomic nP states, even if the complex molecular spectrum involving ro-vibrational levels requires a deeper analysis.
Accurate Born-Oppenheimer potentials for excited $Σ^{+}$ states of the hydrogen molecule
我们报告的Born-Oppenheimer潜力的激发$n\,Σ^{+}$状态的氢分子的所有可能的组合的单重态/三重态和gerade/ungerade对称性高达$n=7$的高精度计算。对于所考虑的所有核间距和所有激发态，实现了$10^{-10}$（0.00002 cm $^{-1}$）或更好的相对精度--相对于文献中可获得的最佳结果至少提高了6个数量级。提出的变分计算依赖于在任意精度算法中用显式相关指数基对分子积分的有效评估。
Isotope effect in tunnelling ionization of neutral hydrogen molecules
最近有人从理论上预言，由于原子核运动，暴露在强电场中的轻、重氢分子将表现出明显不同的隧道电离率（O.I.）。Tolstikhin，H. J. Worner和T. Morishita，Phys.Rev.A87，041401（R）（2013）[1]）。我们通过测量H2/D2混合气体射流与强飞秒激光脉冲相互作用中每种物质的相对电离产率，实验研究了同位素效应。在反应显微镜装置中，我们检测到离子碎片从所有贡献的渠道（单电离，解离，和顺序双电离），并确定了总单电离产率的比率为H2和D2。测得的比率同意定量与预测的广义弱场渐近理论在一个明显的失败的冻结核近似。
Quantum phase transition in the Hartree-Fock wave function of the hydrogen molecule
用二维全数值网格计算方法，在较宽的核间距R范围内，得到了氢分子基态的Hartree-Fock方程的精确解.发现R \infty的单电子波函数的空间部分是一致<2.30a.u. At larger distances they become different and as R->的，它们中的每一个都采取对应于单独原子的形式。这种量子相变发生在R=2.30a.u.给出了分子中电子的离域行为和它们在单独原子上的分布之间的自然边界。这种现象也可以被认为是单分子水平上维格纳结晶或莫特跃迁的模拟。
Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory
本文从理论上精确地测定了氢分子及其同位素在电子基态的振转能级。我们认为所有显着的修正玻恩-奥本海默近似，在非绝热微扰理论，包括混合nonadiabatic相对论效应。在领先的$α^5\,m$和次领先的$α^6\,m$订单，以及有限的核尺寸效应的量子电动力学修正，也被考虑在内，但在玻恩-奥本海默近似。最终结果的转振能级之间的过渡波长达到$10^{-3}$- $10^{-7}$ cm $^{-1}$的顺序的精度，并提供了简单的使用计算机代码。
