Investigation of muonic hydrogen isotopes scattering from H2 molecule

Hyperfine Interactions - Knowledge of the cross sections for scattering of µp, µd and µt on molecules of hydrogen isotopes is necessary not only for checking the algorithmic solution...     

Coulomb deexcitation and nonresonant charge exchange of muonic hydrogen in mixtures of hydrogen isotopes

The process of inelastic collisions of excited muonic hydrogen has been considered in the framework of the asymptotic theory of nonadiabatic transitions. The Coulomb deexcitation and chargetransfer rates are calculated in the energy range 0.001–100 eV taking into account the electron-screening effect for excited states in the range n = 3–10 for various isotopic configurations. The text was submitted by the authors in English.     

Production of slow protonium in vacuum

We descrbe how protonium, the quasi-stable antiproton-proton bound system, has been synthesized following the interaction of antiprotons with the molecular ion in a nested Penning trap environment. From a careful analysis of the spatial distributions of antiproton annihilation events in the ATHENA experiment, evidence is presented for protonium production with sub-eV kinetic energies in states around n = 70, with low angular momenta. This work provides a new two-body system for studies using laser spectroscopic techniques.      

Hadronic vacuum polarization contribution to the Lamb shift in muonic hydrogen

We report on the accuracy of the measurement of the total cross section of the process e⁺e^– ZH and of the Higgs boson mass that would be achieved in a linear collider operating at a centre-of-mass energy of 350 GeV, assuming an integrated luminosity of 500 fb^–1. For that we have exploited the recoil mass off the Z using its leptonic decays into electron and muon pairs. The Higgs mass is determined with 150 MeV accuracy, the recoil mass resolution is about 1.5 GeV and the cross section is obtained with a statistical error of 3%.     

Thermalization of muonic hydrogen in hydrogen targets

The thermalization of pµ atoms in protium and dµ atoms in deuterium is considered. Monte Carlo calculations are performed for gaseous (300 K) and solid (3 K) protium and deuterium targets. Complete sets of the total and differential cross sections for the scattering of pµ on protium targets and dµ on deuterium targets are used as an input to the Monte Carlo simulations. At 300 K, muonic atom scattering from single molecules of H₂ and D₂ is considered. In the case of solid hydrogen the correlation effects from all molecules of the sample are taken into account. In particular, the Bragg and phonon scattering cross sections are calculated. The spin states and average energy of the muonic atoms are shown as functions of time. It is shown that at energies below about 0.01 eV the solid-state effects influence strongly the calculated cross sections, and therefore the deceleration processes in the solids are much slower than in the gaseous targets. It is shown that the neutron spectrum due to ddµ formation and subsequent dd fusion is significantly affected by slow dµ thermalization in solid deuterium.     

Evidence for the production of slow antiprotonic hydrogen in vacuum

We present evidence showing how antiprotonic hydrogen, the quasistable antiproton (p)-proton bound system, has been synthesized following the interaction of antiprotons with the molecular ion H2+ in a nested Penning trap environment. From a careful analysis of the spatial distributions of antiproton annihilation events, evidence is presented for antiprotonic hydrogen production with sub-eV kinetic energies in states around n=70, and with low angular momenta. The slow antiprotonic hydrogen may be studied using laser spectroscopic techniques.     

Production of polarized molecules of hydrogen isotopes

The possibility of producing polarized molecules of hydrogen isotopes by their spin separation in the inhomogeneous field of superconducting magnets has been demonstrated. This method proposed in our previous works has been implemented with a source of polarized atoms developed at the Budker Institute for Nuclear Physics. The measured flux of polarized molecules is compared with the simulation results. The possibility of developing a more intense source of polarized molecules is discussed.     

Effects of vacuum polarization and of proton polarizability in the Lamb shift of muonic hydrogen

The contributions to the Lamb shift in muonic hydrogen from hadronic vacuum polarization and from the correction associated with electron vacuum polarization and with the proton polarizability are calculated by using present-day experimental data on the cross section for e ⁺ e ⁻ annihilation into hadrons and on structure functions for deep-inelastic ep scattering. The numerical value of the total contribution to the (2P-2S) shift in muonic hydrogen is found to be 10.95 μeV. __________ Translated from Yadernaya Fizika, Vol. 64, No. 7, 2001, pp. 1358–1363. Original Russian Text Copyright ? 2001 by Martynenko, Faustov.     

Hadronic vacuum polarization correction in muonic atoms

The contribution of hadronic vacuum polarization to the energy levels of muonic atoms is reevaluated using an improved parametrization of the total cross section for e⁺ e^?→hadrons. The numerical results can be simply related to the correction due to muonic vacuum polarization.     

Muonium/muonic hydrogen formation in atomic hydrogen

The muonium/muonic hydrogen atom formation in μ^±−H collisions is investigated, using a two-state approximation in a time dependent formalism. It is found that muonium cross-section results are similar to the cross-section results obtained for positronium formation in e⁺-H collision. Muonic hydrogen atom formation cross-sections in μ^--H collision are found to be significant in a narrow range of energy (5 eV–25 eV).     

The semiclassical treatment of slow muonic collisions

This paper exposes some of the problems which occur when muons replace electrons in heavy ion collisions. It focusses on the coupling between the heavy particle and muonic motion in the semiclassical treatment of the collision and shows how an energy conserving classical path can be defined. An example, which shows some of the effects of this path, is discussed.     

Scattering of muonic hydrogen atoms

Our measurement compares the energy dependence of the scattering cross-sections of muonic deuterium and tritium on hydrogen molecules for collisions in the energy range 0.1–45 eV. A time-of-flight method was used to measure the scattering cross-section as a function of the muonic atom beam energy and shows clearly the Ramsauer–Townsend effect. The results are compared with theoretical calculations by using Monte Carlo simulations. The molecular pdμ and ptμ formation creates background processes. We measure the formation rates in solid hydrogen by detecting the 5.5 MeV (pdμ) and 19.8 MeV (ptμ) γ-rays emitted during the subsequent nuclear fusion processes. This revised version was published online in August 2006 with corrections to the Cover Date.     

Charge distributions of barium isotopes from muonic X-rays

The results of a muonic X-ray study of the charge radii of stable barium isotopes are presented and compared with optical isotope shifts. The isotope shifts Δ〈r²〉 of a wide range of barium isotopes are found to be in good agreement with the droplet model and with IBA calculations.     

Hyperfine ground-state structure of muonic hydrogen

Corrections of orders α⁵ and α⁶ to the superfine ground-state structure of the muonic hydrogen atom were calculated. The calculations took into account the effects of the structure of the nucleus on one-and two-loop Feynman amplitudes with the help of the electromagnetic form factors of the proton and the modification of the superfine part of the Breit potential caused by the electronic polarization of the vacuum. The total splitting of the 1S state is 182.725 meV; this value can be used as a reliable estimate in conducting a corresponding experiment with an accuracy of 30 ppm.     

Spin-flip cross sections in muonic hydrogen scattering on hydrogen molecules

The results of calculations of the total cross sections of spin-flip processes in low energy muonic hydrogen scattering on hydrogen molecules are presented. These calculations are based on the respective set of cross sections for muonic hydrogen scattering on hydrogen nuclei, obtained within the framework of the multichannel adiabatic method. All combinations of the three hydrogen isotopes are considered. Molecular binding effects are described in terms of the Fermi pseudopotential method. Electron screening effects are calculated in the distorted wave Born approximation. Rotational and vibrational transitions of the molecules, due to collisions with muonic hydrogen atoms, are taken into account. The molecular and electron screening corrections do not exceed a few tens per cent for lowest collision energies.     

Deceleration of muonic hydrogen atoms in solid hydrogens

Results of recent calculations of cross-sections for muonic hydrogen atom scattering in solid hydrogen isotope targets are presented. The coherent parts of these cross-sections, namely, the elastic Bragg scattering and phonon coherent scattering, are calculated accurately for the first time. A fine structure of Bragg peaks is obtained in the case of Bravais fcc structure of hydrogen targets frozen rapidly at 3 K. The one-phonon coherent cross-section is estimated using the Debye approximation. The calculated differential cross-sections are used for Monte Carlo simulations of muonic atom diffusion and slowing down in solid hydrogens. Also is calculated the energy-dependent rate of resonant ddμ molecule formation in 3 K solid deuterium quantum crystal, using the Debye model and Van Hove's formalism of the response function. This rate is very different from that obtained for the 3 K gas model. The influence of dμ atom slowing down on the average ddμ formation rate is considered. It is shown that very slow dμ deceleration below 10 meV is important for explanation of experimental results. This revised version was published online in August 2006 with corrections to the Cover Date.     

Critical discussion of the vacuum polarization measurements in muonic atoms

Recent disagreement between theoretical and experimental values of transition energies for outer states in muonic atoms is discussed in the range of 150–440 keV. A brief review of the present status of calculation of the theoretical contributions is given. A rigorous theoretical framework for the electron-muon system is considered. A set of self-consistent equations is derived. Several mechanisms for the explanation of the discrepancy are discussed. No explanation within the frame of standard quantum electrodynamics is found.     

Differential cross sections for muonic hydrogen scattering on hydrogen molecules

The results of first calculations of the differential cross sections for muonic hydrogen scattering on hydrogen molecules are presented. They are functions of the initial and final kinetic energy of the system and the scattering angle. These calculations are based on the respective set of cross sections for muonic hydrogen scattering on hydrogen nuclei, obtained within the framework of the adiabatic method. The Fermi pseudopotential method is used to estimate the molecular binding effects. The influence of electrons on the cross sections under consideration is described in terms of the effective screening potential. Rotational and vibrational transitions are taken into account. The calculated molecular differential cross sections show a strong angular dependence. This effect is very significant for the electronic contributions to the cross sections, e.g. for collision energies above approximately 0.1 eV only the cross sections of small scattering angles are influenced considerably by the screening. Since these differential cross sections give detailed information about the final energies and complicated angular distributions of the scattered muonic atoms they are the proper basis for calculations concerning the deceleration of muonic hydrogen atoms in molecular hydrogen targets and for Monte Carlo simulations of different experiments in muonic physics.