Search Results (13 total)

The differential cross sections for muonic atom scattering from hydrogenic molecules have been calculated using the Morse potential of the internuclear interaction in these molecules. Numerical calculations have been performed for the scattering dμ+H₂ and tμ+H₂ at collision energies of ε≤30  eV. Our calculations are fully quantum mechanical. The obtained differential cross sections are necessary for a proper description of muonic atom scattering and diffusion over a wide energy range.

The differential cross sections for low-energy muonic hydrogen atom scattering in solid molecular H₂, D₂, and T₂ targets under low pressure have been calculated for various temperatures. The polycrystalline fcc and hcp structure of the solid hydrogenic targets are considered. The Bragg and phonon scattering processes are described using the Debye model of a solid. The calculated cross sections are used for Monte Carlo simulations of the muonic atom slowing down in these targets. They have been successfully applied for a description of the production of the muonic atom beams in the multilayer hydrogenic crystals.

The differential cross sections for low-energy muonic hydrogen atom scattering from hydrogenic molecules are directly expressed by the corresponding amplitudes for muonic atom scattering from hydrogen-isotope nuclei. The energy and angular dependence of these three-body amplitudes is thus taken naturally into account in scattering from molecules, without involving any pseudopotentials. Effects of the internal motion of nuclei inside the target molecules are included for every initial rotational-vibrational state. These effects are very significant as the considered three-body amplitudes often vary strongly within the energy interval ≲0.1  eV. The differential cross sections, calculated using the presented method, have been successfully used for planning and interpreting many experiments in low-energy muon physics. Studies of μ⁻ nuclear capture in pμ and the measurement of the Lamb shift in pμ atoms created in H₂ gaseous targets are recent examples.

We present the final results of an experimental study of μd and μt atom scattering in solid hydrogen cooled to 3  K. Strong effects resulting from the Ramsauer-Townsend effect have been observed in the TRIUMF experiment E742 where muons were stopped in thin frozen layers of hydrogen. The measured Ramsauer-Townsend minimum energy for both μd and μt atoms and the minimum cross section are in agreement with theory.

Resonant formation of the muonic molecule dtμ in tμ atom collision with condensed H-D-T targets is considered. A specific resonance correlation function, which is a generalization of the Van Hove single-particle correlation function, is introduced to calculate the resonant-formation rate in such targets. This function is derived in the case of a polycrystalline harmonic solid. Also, a general asymptotic form of the resonance correlation function for high momentum transfers is found, which is valid for any solid or dense-fluid hydrogen-isotope target. Numerical calculations of the rates are performed for solid hydrogen isotopes at zero pressure, using the isotropic Debye model of a solid. It is shown that condensed-matter effects in resonant formation are strong, which explains some unexpected experimental results. In particular, the resonance profiles are affected by large zero-point vibrations of the hydrogen-isotope molecules bound in the considered crystals, even for high (∼1  eV) collision energies. This is important for explaining the time-of-flight measurements of the dtμ-formation rate, carried out at TRIUMF. The calculated mean values of the formation rate in solid D-T targets, for fixed target temperatures and steady-state conditions, are in good agreement with the PSI and RIKEN-RAL experiments.

We present the results of experimental and theoretical study of the scattering of low-energy pμ atoms in solid hydrogen cooled to 3 K. Strong effects resulting from the solid state interactions have been observed in the TRIUMF experiment E742 where muons were stopped in thin frozen layers of hydrogen. The resulting emission of low-energy pμ atoms from the hydrogen layer into the adjacent vacuum was much higher than that predicted by calculations which ignored the solid nature of the hydrogen. New differential scattering cross sections have been calculated for the collisions of pμ atoms on solid hydrogen to account for its quantum crystalline nature. Analysis of the experimental data performed using such cross sections shows the important role of the coherent scattering in pμ atom diffusion. For pμ energies lower than the Bragg cutoff limit (≈2 meV) the elastic Bragg scattering vanishes which makes the total scattering cross section fall by several orders of magnitude, and thus the hydrogen target becomes transparent allowing the emission of cold pμ atoms to occur.

The rate of ddμ muonic-molecule resonant formation in dμ atom collisions with a condensed deuterium target is expressed in terms of a single-particle response function. In particular, ddμ formation in solid deuterium at low pressures is considered. Numerical calculations of the rate in the case of fcc polycrystalline deuterium at 3 K have been performed using the isotropic Debye model of a solid. It is shown that the energy-dependent ddμ formation rates in the solid differ strongly from those obtained for D₂ gaseous targets, even at high dμ kinetic energies. Monte Carlo neutron spectra from dd fusion in ddμ molecules have been obtained for solid targets with different concentrations of orthodeuterium and paradeuterium. The recent experimental results performed in low-pressure solid targets (statistical mixture of ortho-D₂ and para-D₂) are explained by the presence of strong recoil-less resonance peaks in the vicinity of 2 meV and very slow deceleration of dμ atoms below 10 meV. Good agreement between the calculated and experimental spectra is achieved when a broadening of D₂ rotational and vibrational levels in solid deuterium is taken into account. It has been shown that resonant ddμ formation with simultaneous phonon creation in the solid gives only about 10% contribution to the fusion neutron yield. The neutron time spectra calculated for pure ortho-D₂ and para-D₂ targets are very similar. A practically constant value of the mean ddμ formation rate, observed for different experimental conditions, is ascribed to the fact that all the recent measurements have been performed at temperatures T≲19 K, much lower than the target Debye temperature Θ_D≈110 K. In result, the formation rate, obtained in the limit T/Θ_D≪1, depends weakly on the temperature.

Measurements of muon-catalyzed dt fusion ( dμt→⁴He+n+μ^-) in solid HD have been performed. The theory describing the energy dependent resonant molecular formation rate for the reaction μt+HD→[(dμt)pee]^* is compared to experimental results in a pure solid HD target. Constraints on the rates are inferred through the use of a Monte Carlo model developed specifically for the experiment. From the time-of-flight analysis of fusion events in 16 and 37 μġcm^-2 targets, an average formation rate consistent with 0.897±(0.046)_stat±(0.166)_syst times the theoretical prediction was obtained.

Resonant formation of dμt molecules in collisions of muonic tritium ( μt) on D₂ was investigated using a beam of μt atoms, demonstrating a new direct approach in muon catalyzed fusion studies. Strong epithermal resonances in dμt formation were directly revealed for the first time. From the time-of-flight analysis of 2036±116 dt fusion events, a formation rate consistent with 0.73±(0.16)_meas±(0.09)_model times the theoretical prediction was obtained. For the largest peak at a resonance energy of 0.423±0.037 eV, this corresponds to a rate of (7.1±1.8)×10⁹ s^-1, more than an order of magnitude larger than those at low energies.

Muon catalyzed fusion in deuterium traditionally has been studied in gaseous and liquid targets. The TRIUMF solid-hydrogen-layer target system has been used to study the fusion reaction rates in the solid phase of D₂ at a target temperature of 3 K. Products of two distinct branches of the reaction were observed: neutrons by a liquid organic scintillator and protons by a silicon detector located inside the target system. The effective molecular formation rate from the upper hyperfine state of μd and the hyperfine transition rate have been measured: λ̃_{3 / 2}=2.71(7)_stat(32)_systμs^-1 and λ̃_{3 / 21 / 2}=34.2(8)_stat(1)_systμs^-1. The molecular formation rate is consistent with other recent measurements, but not with the theory for isolated molecules. The discrepancy may be due to incomplete thermalization, an effect that was investigated by Monte Carlo calculations. Information on branching ratio parameters for the s and p wave d+d nuclear interaction has been extracted.

Recent experimental results on the muon exchange from muonic hydrogen to argon show that the reaction rate is energy dependent near 0.1 eV. A muonic hydrogen atom, formed by muon capture in H₂ gas at 15 bars, is thermalized in a few hundreds of nanoseconds. If the muon transfer reaction occurs before that time, the rate is shown to be slightly lower compared to thermalized muonic atoms [λ_pAr=(1.63±0.09)×10¹¹fs^-1]. As an indirect consequence, the muon transfer rate from μp to helium, determined by our group [R. Jacot-Guillarmod and co-workers, Phys. Rev. A 38, 6151 (1988)] is lowered by about 40%. The present value λ_pHe=(0.51±0.19)×10⁸fs^-1 is in good agreement with other experiments. The transfer rate from muonic deuterium to argon shows also an energy dependence. The muon transfer rate to argon from the deuteron is λ_dAr=(0.86±0.04)×10¹¹fs^-1 at room temperature. The intensity patterns of the muonic Lyman series of argon obtained by muon transfer from both hydrogen isotopes are determined and compared with theoretical predictions.

Diffusion of muonic deuterium μd and muonic hydrogen μp atoms produced following the stopping of negative muons in D₂ or H₂ at 300 K was studied at pressures of 47–750 mbar (H₂) and 94–1520 mbar (D₂) in two distinct target geometries. Time intervals were recorded between entry of negative muons into the gas and arrival of each resulting μd or μp atom at one of 50 foils immersed in the gas, and spaced regularly along the muon beam axis. The results of such measurements were fitted to time distributions generated by Monte Carlo methods, using theoretical scattering predictions and empirically chosen forms for the initial energy distributions of the muonic atoms in the 1S state. Results indicate muonic atom energy distributions which (a) are different for μd and μp and (b) vary with pressure. The best-fit energy distributions have mean energies ranging from 1.5 eV for μd at 94 mbar to ≥9 eV for μp at 750 mbar. The data are also sensitive to scattering cross sections for μd and μp, and are consistent with current theoretical calculations for the μd+D₂ cross sections. In the case of μp+H₂ scattering, the experimental data suggest discrepancies with the theoretical predictions.