Long-range interactions of hydrogen atoms in excited states. II. Hyperfine-resolved 2S-2S systems
Long-range interactions of hydrogen atoms in excited states. II. Hyperfine-resolved 2S-2S systems
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激发态氢原子的长程相互作用。
DOI：
10.1103/physreva.95.022704
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发表时间：
2017
影响因子：
2.9
通讯作者：
N. Kolachevsky
中科院分区：
文献类型：
--
作者：
U. Jentschura;V. Debierre;C. Adhikari;A. Matveev;N. Kolachevsky
亚稳态激发态氢原子间的相互作用是一个有趣的理论问题，这是由于2 P_{1/2}能级的准简并，而2 P_{1/2}能级只能通过Lamb位移从2S态中去除。系统的总哈密顿量由货车德瓦耳斯哈密顿量、兰姆位移和超精细效应组成。货车德瓦耳斯位移仅在接近（R < 100 a_0，其中a_0是玻尔半径）时才与2S-2 P_{3/2}精细结构分裂相称，因此，我们可以将讨论限制在n=2和J=1/2的水平上，以达到良好的近似。因为每个S或P态分裂成F=1的三重态和F=0的超精细单重态（每个原子有八个态），所以哈密顿矩阵的维数为64。仔细分析对称性的问题允许一个减少维数的最涉及的不可约子矩阵到12。我们确定的哈密顿矩阵和领先的顺序货车德瓦耳斯位移的状态下，未扰动的哈密顿量的作用下退化（兰姆位移加超精细结构）。主要的一阶和二阶货车德瓦尔斯位移导致相互作用能与1/R^3和1/R^6成正比，并在超精细流形内进行评估。当两个原子都是亚稳2S态时，我们发现相互作用能为E_h chi（a_0/R）^6，其中E_h和L分别是Hartree和Lamb位移能，chi = E_h/L ~ 6.22 × 10^6是它们的比值。
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasi-degenerate 2P_{1/2} levels which are removed from the 2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift and the hyperfine effects. The van der Waals shift becomes commensurate with the 2S-2P_{3/2} fine-structure splitting only for close approach (R < 100 a_0, where a_0 is the Bohr radius) and one may thus restrict the discussion to the levels with n=2 and J=1/2 to good approximation. Because each S or P state splits into an F=1 triplet and an F=0 hyperfine singlet (eight states for each atom), the Hamiltonian matrix {\em a priori} is of dimension 64. A careful analysis of symmetries the problem allows one to reduce the dimensionality of the most involved irreducible submatrix to 12. We determine the Hamiltonian matrices and the leading-order van der Waals shifts for states which are degenerate under the action of the unperturbed Hamiltonian (Lamb shift plus hyperfine structure). The leading first- and second-order van der Waals shifts lead to interaction energies proportional to 1/R^3 and 1/R^6 and are evaluated within the hyperfine manifolds. When both atoms are metastable 2S states, we find an interaction energy of order E_h chi (a_0/R)^6, where E_h and L are the Hartree and Lamb shift energies, respectively, and chi = E_h/L ~ 6.22 \times 10^6 is their ratio.