Long-Range Interactions of Hydrogen Atoms in Excited States. I. 2S-1S Interactions and Dirac-δ Perturbations


The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C6 (2S ;1 S ) describing the interaction of metastable atomic hydrogen ( 2 S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a0 ≪ R ≪ a0 / α , where a0 = ℏ / α m c is the Bohr radius and α is the fine-structure constant, one finds the symmetry-dependent result E2S;1S ( R ) ≈ ( - 176.75 ± 27.98 ) Eh( α0 / R )6 (Eh denotes the Hartree energy). In the Casimir-Polder range a0 / α ≪ R ≪ ℏ c / L , where L ≡ E (2S1/2 ) - E (2P1 / 2 ) is the Lamb shift energy, one finds E2S;1S ( R ) ≈ ( - 121.50 ± 46.61 ) Eh ( a0 / R )6 . In the the Lamb shift range R ≫ ℏ c / L , we find an oscillatory tail with a negligible interaction energy below 10-36 Hz . Dirac- δ perturbations to the interaction are also evaluated and results are given for all asymptotic distance ranges; these effects describe the hyperfine modification of the interaction or, expressed differently, the shift of the hydrogen 2 S hyperfine frequency due to interactions with neighboring 1 S atoms. The 2 S hyperfine frequency has recently been measured very accurately in atomic beam experiments.



Keywords and Phrases

Atomic Beams; Excited States; Ground State; Hydrogen; Van Der Waals Forces; Atomic Hydrogen; Fine Structure Constants; Ground-state Atoms; Hyperfine Frequencies; Interaction Energies; Long Range Interactions; Van Der Waals Coefficients; Virtual Transitions; Atoms

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