The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasidegenerate 2P1/2 levels that 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-2P3/2 fine-structure splitting only for close approach (R < 100a0, where a0 is the Bohr radius) and one may thus restrict the discussion to the levels with n = 2 and J = 1/2 to a 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 a priori is of dimension 64. A careful analysis of the symmetries of the the problem allows one to reduce the dimensionality of the most involved irreducible submatrix to 12. We determine the Hamiltonian matrices and thleading-order van der Waals shifts for states that 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/R3 and 1/R6 and are evaluated within the hyperfine manifolds. When both atoms are metastable 2S states, we find an interaction energy of order EhΧ(a0/R)6, where Eh and L are the Hartree and Lamb shift energies, respectively, and Χ = Eh/L ≈ 6.22 x 106 is their ratio.



Keywords and Phrases

Atomic Physics; Atoms; Excited States; Hamiltonians; High Energy Physics; Van Der Waals Forces; Fine Structure Splitting; Hamiltonian Matrix; Hyperfine Effects; Hyperfine Structure; Interaction Energies; Long Range Interactions; Meta-stable State; Physical Review; Hydrodesulfurization

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Article - Journal

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Final Version

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© 2017 American Physical Society (APS), All rights reserved.

Publication Date

01 Feb 2017

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Physics Commons