Long-Range Interactions of Hydrogen Atoms in Excited States. II. Hyperfine-Resolved 2S-2S Systems

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 \u3c 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

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

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

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

Precision Measurement of the Hydrogen-Deuterium 1S-2S Isotope Shift

Measuring the hydrogen-deuterium isotope shift via two-photon spectroscopy of the 1S-2S transition, we obtain 670994334606(15) Hz. This is a 10-times improvement over the previous best measurement confirming its frequency value. a calculation of the difference of the mean square charge radii of deuterium and hydrogen results in r2d-r2 p=3.82007(65)fm2, a more than twofold improvement compared to the former value

Hydrogen-Deuterium Isotope Shift: From the 1S-2s-Transition Frequency to the Proton-Deuteron Charge-Radius Difference

We analyze and review the theory of the hydrogen-deuterium isotope shift for the 1S-2S transition, which is one of the most accurately measured isotope shifts in any atomic system, in view of a recently improved experiment. A tabulation of all physical effects that contribute to the isotope shift is given. These include the Dirac binding energy, quantum electrodynamic effects, including recoil corrections, and the nuclear-size effect, including the pertaining relativistic and radiative corrections. From a comparison of the theoretical result Δfth=670999566.90(66)(60)kHz (exclusive of the nonrelativistic nuclear-finite-size correction) and the experimental result Δfexpt=670994334605(15) Hz, we infer the deuteron-proton charge-radius difference (r2)d- (r2)p=3.82007(65) fm2 and the deuteron structure radius rstr=1.97507(78) fm

Feasibility of Coherent xuv Spectroscopy on the 1S-2S Transition in Singly Ionized Helium

The 1S-2S two-photon transition in singly ionized helium is a highly interesting candidate for precision tests of bound-state quantum electrodynamics (QED). With the recent advent of extreme ultraviolet frequency combs, highly coherent quasi-continuous-wave light sources at 61 nm have become available, and precision spectroscopy of this transition now comes into reach for the first time. We discuss quantitatively the feasibility of such an experiment by analyzing excitation and ionization rates, propose an experimental scheme, and explore the potential for QED tests

Optical trapping of antihydrogen towards an atomic anti-clock

The unprecedented flux of low energy antiprotons delivered by the Extra Low ENergy Antiprotons (ELENA) ring, being under commissioning at CERN, will open a new era for precision tests with antimatter including laser and microwave spectroscopy and tests ofits gravitational behaviour. Here we present an alternative to magnetic trapping to perform ultra-high precision laser spectroscopy of antihydrogen. The proposed scheme is to load the ultra cold anti-hydrogen atoms produced by the GBAR experiment in an optical trap tuned at the magicwavelength of the 1S–2S transition in order to measure this interval at a level comparable or even better than its matter counter part. This will provide a very accurate test of Lorentz/CPT violating effects which can be parametrised in the framework of the Standard Model Extension. © Springer Nature 2018ISSN:0304-3843ISSN:0304-3834ISSN:1572-954