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. 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

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

Hadrons in Matter: From Pions to D-Mesons and Charmonia

The jet fragmentation function of inclusive jets with transverse momentum pT above 100 GeV/c in PbPb collisions has been measured using reconstructed charged particles with pT above 1 GeV/c in a cone of radius 0.3 around the jet axis. A data sample of PbPb collisions collected in 2011 at a nucleon-nucleon center-of-mass energy of √ sNN = 2.76 TeV corresponding to an integrated luminosity of 150 μb−1 is used. The results for PbPb collisions as a function of collision centrality and jet transverse momentum are compared to reference distributions based on pp data collected at the same center-of-mass energy in 2013, with an integrated luminosity of 5.3 pb−1. A centrality-dependent modification of the fragmentation function is found. For the most central collisions, a significant enhancement is observed in the PbPb/pp fragmentation function ratio for charged particles with pT less than 3 GeV/c. This enhancement is observed for all jet pT bins studied

Search for the lepton flavor violating τ → 3_μ decay in proton-proton collisions at √s=13 TeV

A search for the lepton flavor violating tau -> 3 mu decay is performed using proton-proton collision events at a center-of-mass energy of 13 TeV collected by the CMS experiment at the LHC in 2017-2018, corresponding to an integrated luminosity of 97.7 fb(-1). Tau leptons produced in both heavy-flavor hadron and W boson decays are exploited in the analysis. No evidence for the decay is observed. The results of this search are combined with an earlier null result based on data collected in 2016 to obtain a total integrated luminosity of 131 fb(-1). The observed (expected) upper limits on the branching fraction.( tau -> 3 mu) at confidence levels of 90 and 95% are 2.9 x 10(-8) (2.4 x 10(-8)) and 3.6 x 10(-8) (3.0 x 10(-8)), respectively.LPHE-L

Measurement of simplified template cross sections of the Higgs boson produced in association with W or Z bosons in the H → bb decay channel in proton-proton collisions at √s=13 TeV

Differential cross sections are measured for the standard model Higgs boson produced in association with vector bosons (W, Z) and decaying to a pair of b quarks. Measurements are performed within the framework of the simplified template cross sections. The analysis relies on the leptonic decays of theW and Z bosons, resulting in final states with 0, 1, or 2 electrons or muons. The Higgs boson candidates are either reconstructed from pairs of resolved b-tagged jets, or from single large-radius jets containing the particles arising from two b quarks. Proton-proton collision data at root s = 13 TeV, collected by the CMS experiment in 2016-2018 and corresponding to a total integrated luminosity of 138 fb(-1), are analyzed. The inclusive signal strength, defined as the product of the observed production cross section and branching fraction relative to the standard model expectation, combining all analysis categories, is found to be mu = 1.15(-0.20)(+0.22). This corresponds to an observed (expected) significance of 6.3 (5.6) standard deviations.LPHE-L