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; 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 a0 ≪ R ≪ a0/α, where a0 = /(αmc) is the Bohr radius and α is the fine structure constant, one finds the symmetry-dependent result E2S;1S(R) ≈ (−176.75 ± 27.98) E h (a0/R) 6 (E h denotes the Hartree energy). In the Casimir-Polder range a0/α ≪ R ≪ c/L, where L ≡ E 2S 1/2 − E 2P 1/2 is the Lamb shift energy, one finds E2S;1S(R) ≈ (−121.50 ± 46.61) E h (a0/R) 6 . In the the Lamb shift range R ≫ 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 2S hyperfine frequency due to interactions with neighboring 1S atoms. The 2S hyperfine frequency has recently been measured very accurately in atomic beam experiments.

A quantum electrodynamic (QED) calculation of the interaction of an excited-state atom with a ground-state atom is performed. For an excited reference state and a lower-lying virtual state, the contribution to the interaction energy naturally splits into a pole term, and a Wick-rotated term. The pole term is shown to dominate in the long-range limit, altering the functional form of the interaction from the retarded 1/R 7 Casimir-Polder form to a long-range tail-provided by the Wick-rotated term-proportional to cos[2(Em − En) R/( c)]/R 2 , where Em < En is the energy of a virtual state, lower than the reference state energy En, and R is the interatomic separation. General expressions are obtained which can be applied to atomic reference states of arbitrary angular symmetry. A careful treatment of the pole terms in the Feynman prescription for the atomic polarizability is found to be crucial in obtaining correct results.

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 a0, where a0 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 (8 states for each atom), the Hamiltonian matrix 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 leadingorder 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 χ (a0/R) 6 , where E h and L are the Hartree and Lamb shift energies, respectively, and χ = E h /L ≈ 6.22 × 10 6 is their ratio.

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We find that biorthogonal quantum mechanics with a scalar product that counts both absorbed and emitted particles leads to covariant position operators with localized eigenvectors. In this manifestly covariant formulation the probability for a transition from a one-photon state to a position eigenvector is the first order Glauber correlation function, bridging the gap between photon counting and the sensitivity of light detectors to electromagnetic energy density. The position eigenvalues are identified as the spatial parameters in the canonical quantum field operators and the position basis describes an array of localized devices that instantaneously absorb and re-emit bosons.