Hyperfine structure effects in the collisions of the 2s metastable muonic hydrogen with hydrogen atoms

Cross sections for elastic and spin-flip scattering of metastable 2s muonic hydrogen on hydrogen atoms are calculated for the symmetric systems pμ+p, dμ+d and tμ+t. The calculations are performed in the two-level approximation of the adiabatic method with inclusion of the Lamb shift and electron screening. Due to the large polarizability of the 2s state, the obtained cross sections significantly exceed their counterparts for the ground-state muonic hydrogen.     

Hyperfine structure in hydrogen and helium ion

QED theory of the hyperfine splitting of the 1s and 2s state in hydrogen isotopes and helium-3 ion is considered. We develop an accurate theory of a specific difference 8E_HFS(2s)−E_HFS(1s). We take into account higher-order QED and nuclear structure effects. In particular, we found the vacuum polarization contribution in order α(Zα)³E_F and examined the recoil contribution in order (Zα)³m/M and thus completed a calculation of the fourth order QED corrections. The higher-order nuclear structure contributions were also analysed. The theoretical predictions reported here are now of a higher accuracy than the experiment. The study of the difference provides the most accurate test (at a level of a part in 10⁸) of the QED theory of ns HFS up to date. The theory agrees with most of the experimental data.     

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.     

The contribution of pseudoscalar mesons to hyperfine structure of muonic hydrogen

In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of pseudoscalar mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The parametrization of the transition form factor of two photons into π,η mesons, based on the experimental data on the transition form factors and QCD asymptotics is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented.     

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.     

Hyperfine interaction parameters and ground-state wavefunctions of vanadyl ion complexes

Using crystal field approach a theoretical estimate of the ground-state wavefunctions of vanadyl ion doped in various crystals have been made using ESR data and is found to bed _xy in our coordinate system with slight admixture of the excited states ,d _xz andd _yz. The hyperfine interaction parameterP and Fermi contact coupling parameterK have also been estimated for these vanadyl-doped crystals. Results agree with similar studies made earlier.     

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).     

Hyperfine structure of the ground state muonic <Superscript>3</Superscript>He atom

On the basis of the perturbation theory in the fine structure constant α and the ratio of the electron to muon masses we calculate one-loop vacuum polarisation and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of the muonic helium atom (μ e ³ ₂He). We obtain total results for the ground state hyperfine splitting Δ ν ^hfs = 4166.648 MHz which improves the previous calculation of Lakdawala and Mohr due to new corrections of orders α ⁵ and α ⁶. The remaining differences between our theoretical result and experimental value of the hyperfine splitting lie in the range of theoretical and experimental errors and require the subsequent investigation of higher order corrections.     

Correlation between muonic levels and nuclear structure in muonic atoms

A method that deals with the nucleons and the muon unitedly is employed to investigate the muonic lead, with which the correlation between the muon and nucleus can be studied distinctly. A “kink” appears in the muonic isotope shift at a neutron magic number where the nuclear shell structure plays a key role. This behavior may have very important implications for the experimentally probing the shell structure of the nuclei far away from the β-stable line. We investigate the variations of the nuclear structure due to the interaction with the muon in the muonic atom and find that the nuclear structure remains basically unaltered. Therefore, the muon is a clean and reliable probe for studying the nuclear structure. In addition, a correction that the muon-induced slight change in the proton density distribution in turn shifts the muonic levels is investigated. This correction to muonic level is as important as the Lamb shift and high order vacuum polarization correction, but is larger than anomalous magnetic moment and electron shielding correction.     

Electron screening of the elastic scattering of muonic hydrogen on hydrogen

The electron screening effect is shown to be important in the calculation of scattering lengths for scattering of muonic hydrogen on an isotopic pure hydrogen target.     

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.     

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.     

Transport cross sections for excited muonic hydrogen

Transport cross sections for scattering of excited muonic hydrogen on hydrogen are calculated in the quasi-classic approximation in the energy range 0.01–50 eV.     

Angular distributions of scattered excited muonic hydrogen atoms

Coulomb deexcitation differential cross sections of excited muonic hydrogen in collisions with the hydrogen atom are studied for the first time. In the fully quantum-mechanical close-coupling approach, both the differential cross sections for the nl → n′l′ transitions and l-averaged differential cross sections have been calculated for the initial exotic atom states with n = 2–6 at kinetic energies of E _cm = 0.01–15 eV and for scattering angles of ϑ_cm = 0°–180°. The vacuum polarization shifts of the ns states are taken into account. The differential cross sections of the elastic and Stark scattering obtained in the same approach are also presented. The main features of the calculated differential cross sections are discussed, and a strong anisotropy of Coulomb deexcitation cross sections is predicted. The text was submitted by the authors in English.     

Production of slow muonic hydrogen isotopes in vacuum

Muonic hydrogen isotopes (μ⁻ p, μ⁻ d, and μ⁻t) are simple quantum mechanical systems ideally suited for studies of numerous fundamental phenomena in electroweak and strong interactions as well as in applied areas such as muon chemistry or muon catalyzed fusion. Emission of muonic hydrogen isotopes into vacuum helps to overcome the limitations which are normally imposed on conventional investigations with gaseous and liquid targets. A proof of principle experiment for this new technique was performed at TRIUMF last year. Negative muons with 30 MeV/c momentum were stopped in a thin film of solid hydrogen and produced very low energy μ⁻d in vacuum. The distribution center of the normal velocity components of emitted μ⁻d atoms was measured to be ∼1 cm/μs. The yield of μ⁻d in vacuum is an increasing function of H₂ film thickness δ up to a value of δ≥1 mm.     

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.     

Low energy muonic hydrogen reactions with heavy atoms

Average s-wave cross-sections appropriate for liquid hydrogen temperatures are calculated with the aid of an in-coming wave boundary condition for the muon transfer process μ^-p + Z → (μ^-Z)¹ + p on heavy atoms. The surface-correlated nature of the heavy atom X-rays is emphasized.     

Low-energy scattering of muonic hydrogen on hydrogen molecules: a semi-classical approach

We present results of PAC measurements in heavy-fermion compound Yb₄As₃. The quadrupole hyperfine interaction has been investigated over the temperature range 78–850 K. The interpretation of the experimental data yields a microscopic proof of the existence of a charge-ordered state with periodic arrangement of Yb²⁺ and Yb³⁺ ions in the low temperature phase. In the high temperature phase all Yb ions are in a valence fluctuating state.