Hyperfine structure of S-states in muonic deuterium

On the basis of quasipotential method in quantum electrodynamics we calculate corrections of order $\alpha^5$ and $\alpha^6$ to hyperfine structure of S-wave energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $\Delta E^{hfs}(1S)=50.2814$ meV (1S state) and $\Delta E^{hfs}(2S)=6.2804$ meV (2S state) represent reliable estimate for a comparison with forthcoming experimental data of CREMA collaboration. The hyperfine structure interval $\Delta_{12}=8\Delta E^{hfs}(2S)-\Delta E^{hfs}(1S)=-0.0379$ meV can be used for precision check of quantum electrodynamics predictions for muonic deterium.Comment: 18 pages, 7 figure

Artificial intelligence for heart rate variability analyzing with arrhythmias

Introduction. Existing standards of Heart Rate Variability (HRV) technology limit its use to sinus rhythm. A small number of extrasystoles is allowed, if the device used has special procedures for the detection and replacement of ectopic complexes. However, it is important to expand the indicated limits of the applicability of the HRV technology. This specially regards the cases when the HRV technology looks promising in the diagnostics, as, for example, in atrial fibrillation and atrial flutter. Materials and Methods. All ECG measurements were performed on XAI-MEDICA® equipment and software. Processing of the obtained RR Series was carried out using the software Kubios® HRV Standard. All recommended HRV characteristics for Time-Domain, Frequency-Domain and Nonlinear were calculated. The purpose of the work. The article presents an artificial intelligence (AI) procedure for detecting episodes of arrhythmias and reconstruction of core patient’s rhythm, and demonstrates the efficacy of its use for the HRV analysis in patients with varying degrees of arrhythmias. The results of the study. It was shown efficiency of developed artificial intelligence procedure for HRV analyzing of patients with different level of arrhythmias. These were demonstrated for Time-Domain, Frequency-Domain and Nonlinear methods. The direct inclusion into review of Arrhythmia Episodes and the use of the initial RR Series leads to a significant distortion of the results of the HRV analysis for the whole set of methods and for all considered options for arrhythmia. Conclusion. High efficacy of operation of the procedure AI core rhythm extraction from initial RR Series for patients with arrhythmia was reported in all cases

Self-energy correction to the bound-electron g factor in H-like ions

The one-loop self-energy correction to the 1s electron g factor is evaluated to all orders in Z\alpha with an accuracy, which is essentially better than that of previous calculations of this correction. As a result, the uncertainty of the theoretical prediction for the bound-electron g factor in H-like carbon is reduced by a factor of 3. This improves the total accuracy of the recent electron-mass determination [Beier et al. Phys. Rev. Lett. 88, 011603 (2002)]. The new value of the electron mass is found to be m_e = 0.000 548 579 909 3(3) u

Radiative nonrecoil nuclear finite size corrections of order α(Zα)5\alpha(Z\alpha)^5 to the hyperfine splitting of S-states in muonic hydrogen

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $\alpha(Z\alpha)^5$ to the hyperfine structure of S-wave energy levels in muonic hydrogen and muonic deuterium. For the construction of the particle interaction operator we employ the projection operators on the particle bound states with definite spins. The calculation is performed in the infrared safe Fried-Yennie gauge. Modern experimental data on the electromagnetic form factors of the proton and deuteron are used.Comment: 8 pages, 1 figur

Muonic hydrogen ground state hyperfine splitting

Corrections of orders alpha^5, alpha^6 are calculated in the hyperfine splitting of the muonic hydrogen ground state. The nuclear structure effects are taken into account in the one- and two-loop Feynman amplitudes by means of the proton electromagnetic form factors. The modification of the hyperfine splitting part of the Breit potential due to the electron vacuum polarization is considered. Total numerical value of the 1S state hyperfine splitting 182.638 meV in the (mu p) can play the role of proper estimation for the corresponding experiment with the accuracy 30 ppm.Comment: 18 pages, Talk presented at the 11th Lomonosov Conference on Elementary Particle Physics, Moscow State University, August 200

Theory of muonic hydrogen - muonic deuterium isotope shift

We calculate the corrections of orders alpha^3, alpha^4 and alpha^5 to the Lamb shift of the 1S and 2S energy levels of muonic hydrogen (mu p) and muonic deuterium (mu d). The nuclear structure effects are taken into account in terms of the proton r_p and deuteron r_d charge radii for the one-photon interaction and by means of the proton and deuteron electromagnetic form factors in the case of one-loop amplitudes. The obtained numerical value of the isotope shift (mu d) - (mu p) for the splitting (1S-2S) 101003.3495 meV can be considered as a reliable estimation for corresponding experiment with the accuracy 10^{-6}. The fine structure interval E(1S)-8E(2S) in muonic hydrogen and muonic deuterium are calculated.Comment: 22 pages, 7 figure

Lamb shift in muonic deuterium atom

We present new investigation of the Lamb shift (2P_{1/2}-2S_{1/2}) in muonic deuterium (mu d) atom using the three-dimensional quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear structure and recoil effects are calculated with the account of contributions of orders alpha^3, alpha^4, alpha^5 and alpha^6. The results are compared with earlier performed calculations. The obtained numerical value of the Lamb shift 202.4139 meV can be considered as a reliable estimate for the comparison with forthcoming experimental data.Comment: 24 pages, 11 figures. arXiv admin note: text overlap with arXiv:hep-ph/061229

Hyperfine Structure of S-States in Muonic Helium Ion

Corrections of orders alpha^5 and alpha^6 are calculated in the hyperfine splittings of 1S and 2S - energy levels in the ion of muonic helium. The electron vacuum polarization effects, the nuclear structure corrections and recoil corrections are taken into account. The obtained numerical values of the hyperfine splittings -1334.56 meV (1S state), -166.62 meV (2S state) can be considered as a reliable estimate for the comparison with the future experimental data. The hyperfine splitting interval Delta_{12}=(8 Delta E^{hfs}(2S)- Delta E^{hfs}(1S)) = 1.64 meV can be used for the check of quantum electrodynamics.Comment: 14 pages, 5 figure

Nuclear structure corrections in the energy spectra of electronic and muonic deuterium

The one-loop nuclear structure corrections of order (Z alpha)^5 to the Lamb shift and hyperfine splitting of the deuterium are calculated. The contribution of the deuteron structure effects to the isotope shift (ep)-(ed), (mu p)-(mu d) in the interval (1S - 2S) is obtained on the basis of modern experimental data on the deuteron electromagnetic form factors. The comparison with the similar contributions to the Lamb shift for electronic and muonic hydrogen shows, that the relative contribution due to the nucleus structure increases when passing from the hydrogen to the deuterium.Comment: Talk presented at the Conference "Physics of Fundamental Interactions" of the Nuclear Physics Section of the Physics Department of RAS, ITEP, Moscow, 2-6 December, 2002; 8 pages, REVTE