Long-range interactions of hydrogen atoms in excited states. I. 2S-1S interactions and Dirac-delta perturbations

Abstract

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 quasi-degenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C_6(2S;1S) describing the interaction of metastable atomic hydrogen (2S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a_0 << R << a_0/alpha, where a_0= hbar/(alpha m c) is the Bohr radius and alpha is the fine structure constant, one finds the symmetry-dependent result E_{2S;1S}(R) ~ (-176.75 +/- 27.98) E_h (a_0/R)^6 (E_h denotes the Hartree energy). In the Casimir-Polder range a_0/alpha << R << hbar c/L, where L = E(2S_{1/2})-E(2P_{1/2}) is the Lamb shift energy, one finds E_{2S;1S}(R) ~ (-121.50 +/- 46.61) E_h (a_0/R)^6. In the the Lamb shift range R >> hbar c/L, we find an oscillatory tail with a negligible interaction energy below 10^(-36) Hz. Dirac-delta 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 2S hyperfine frequency due to interactions with neighboring 1S atoms. The 2S hyperfine frequency has recently been measured very accurately in atomic beam experiments.

21 pages; RevTeX; accepted for publication in Phys. Rev. A

References in corpus (6)

• Quantum electrodynamic corrections to the hyperfine structure of excited S states
• Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike Atoms
• Body-assisted van der Waals interaction between excited atoms
• Long-Range Tails in van der Waals Interactions of Excited-State and Ground-State Atoms
• Magic wavelength for the hydrogen 1S-2S transition: Contribution of the continuum and the reduced-mass correction
• Long-Range Atom-Wall Interactions and Mixing Terms: Metastable Hydrogen

Cited by in corpus (5)

• Long-range interactions of hydrogen atoms in excited states. II. Hyperfine-resolved 2S-2S system
• Long-range interactions of hydrogen atoms in excited states. III. nS-1S interactions for n >= 3
• Long-Range Interactions for Hydrogen: 6P-1S and 6P-2S
• Pressure Shifts in High-Precision Hydrogen Spectroscopy: II. Impact Approximation and Monte-Carlo Simulations
• Pressure Shifts in High-Precision Hydrogen Spectroscopy: I. Long-Range Atom-Atom and Atom-Molecule Interactions