New results in the theory of muonic atom formation in molecular hydrogen

Muonic atom formation in molecular hydrogen proceeds in two stages. In the first stage, the mu-molecular complex (abµe)^* is formed due to Coulomb capture of a muon by a hydrogen molecule (abee), and, in the second stage, the decay of the complex leads to exotic-atom formation. We consider various channels for the decay of the complex. The main competition channels are direct dissociation and Auger decay. The primary distribution of muonic atoms over quantum states and kinetic energy has been obtained taking into account the competition of the decay channels.     

Time-of-flight measurement of resonant molecular formation in muon-catalyzed dt fusion

Preliminary results are reported for an experiment at TRIUMF where a time-of-flight technique was tested for measuring the energy dependence of the rate for muon-catalyzed dt fusion. Muonic tritium atoms were created following transfer of negative muons from muonic protium in a layer of solid hydrogen (protium) containing a small fraction of tritium. The atoms escaped from the solid layer via the Ramsauer-Townsend mechanism, traversed a drift region of 18 mm, and then struck an adjacent layer of deuterium, where the muonic atom could form a molecular system. The time of detection of a fusion product (neutron or alpha) following muon arrival is dependent upon the energy of the muonic tritium atom as it traverses the drift region. By comparison of the time distribution of fusion events with a prediction based on the theoretical energy dependence of the rate, the strength of resonant formation can in principle be determined. The results extracted so far are discussed and the limitations of the method are examined.     

Observation of long-lived muonic hydrogen in the 2S state

The kinetic energy distribution of ground state muonic hydrogen atoms mup(1S) is determined from time-of-flight spectra measured at 4, 16, and 64 hPa H2 room-temperature gas. A 0.9 keV component is discovered and attributed to radiationless deexcitation of long-lived mu p(2S) atoms in collisions with H2 molecules. The analysis reveals a relative population of about 1%, and a pressure-dependent lifetime (e.g., 30.4 +21.4/-9.7 ns at 64 hPa) of the long-lived mu p(2S) population, equivalent to a 2S quench rate in mu p(2S)+H2 collisions of 4.4 +2.1/-1.8 x 10(11) s(-1) at liquid-hydrogen density.     

Muonic atoms and muon-catalyzed fusion in inhomogeneous mixtures of hydrogen isotopes

The emission of µd and µt atoms from multilayer solid targets consisting of the mixtures of hydrogen isotopes has been investigated with a kinetics model. The methods to study the elastic scattering of muonic atoms, muon transfer, and molecular formation reactions with µ-atomic beams are discussed.     

Muon transfer to light atoms

Several experiments performed by our group in recent years have put into evidence the complex structure of the time distributions of the muonic X-rays following transfer from muonic hydrogen isotopes to heavier elements. Simulations have shown that a substantial fraction of the µp atoms in the ground state have epithermal energies. Therefore, an energy dependence of the transfer rate seems a reasonable assumption for the explanation of the complex time structure.     

High-velocity components in exotic atoms,their origin and effects

The evolution of the kinetic energy distribution during the cascade is shown to play an important role for pionic and muonic atoms in hydrogen and deuterium. The kinetics of muon transfer in excited states is studied with a new cascade code and the results are compared with recent experimental data.     

Cascade Processes in Muonic Hydrogen Atoms

The QCMC scheme created earlier for cascade calculations in heavy hadronic atoms of hydrogen isotopes has been modified and applied to the study of cascade processes in the μp muonic hydrogen atoms. The distribution of μp atoms over kinetic energies has been obtained and the yields of K-series X-rays per one stopped muon have been calculated. Comparison with experimental data indicated directly that for muonic and pionic atoms new types of non-radiative transitions are essential, while they are negligible for heavy (kaonic, antiprotonic, etc.) atoms. These processes have been considered and their probabilities have been estimated. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Statistical study of the muon catalyzed d-t fusion cycle

In this paper we discuss the statistics of the main branch species of the muon catalyzed d-t fusion. From a master equation we derive and numerically solve kinetic equations for the average density and the covariances of a system composed of muons, muonic deuterium and muonic tritium atoms, muon molecular d-t ions, muonic helium, helium and neutrons. The system consists of an initial fixed amount of muons in a 50–50% D₂ + T₂ mixture without any external muon source. It is known that the probability distribution function of the population species with the exception of the neutron and helium follow a multinomial distribution function.     

Quadrupole corrections to matrix elements of transitions in resonant reactions of muonic molecule formation

The calculated resonant formation rates of the muonic molecules ddµ and dtµ are presented. The approach developed earlier for calculating the transition matrix elements in the dipole approximation has been extended to include the quadrupole terms in the multipole expansion of the interaction operator. The calculated dependence of the dtµ formation rates on the energies of the incident tµ muonic atoms shows that the effect of including the quadrupole correction is to reduce the magnitude of the peak rates by about 20–30% at the different temperatures, compared to those calculated in the dipole approximation. The dependence on temperature for the ddµ formation rates is obtained with the differences between the presented and previous calculations being less than 5%.     

Experiments with energetic μd and μt emitted from solid hydrogen

A set of experiments is reviewed which makes use of the emission of muonic deuterium from the surface of a layer of solid hydrogen. The behaviour of muons in a solid target system has been studied via detection of muon decay electrons, muonic X-rays, and fusion products (neutrons and charged particles). The emission of muonic deuterium is understood to result from the Ramsauer-Townsend scattering minimum. The energy distribution of the emitted atoms ranges from tenths of eV to about 10 eV, and can be controlled to some extent. A proposal is described to use muonic tritium emission to measure the energy dependence of muonic molecular formation.     

Nonradiative transition to the ground state and superelastic scattering of exited atoms upon impact on the surface of wide-bandgap dielectrics

The impact of excited cesium atoms on sapphire and glass surfaces have been experimentally studied. It is established that the probability of electron excitation quenching upon impact of an atom on the dielectric surface is close to unity. The velocity distribution of unexcited atoms upon scattering from the surface has been determined using the time-of-flight technique. The kinetic energies of most of these atoms are several tens of times greater than the energy of thermal motion of the excited atoms impinging on the surface. Conversion of the internal energy of atoms into their kinetic energy is explained in terms of nonradiative electron transitions with simultaneous excitation of lattice vibrations in the dielectric crystal. This mechanism of atomic excitation quenching near the dielectric surface explains the significant difference between the energies of atoms upon superelastic scattering and upon photodesorption from an adsorbed state.     

Ramsauer–Townsend Effect in Solid Hydrogen

The TRIUMF E742 experiment has measured 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. The experimental setup permits the creation of muonic atom (μd or μt) beams. The multilayered target system gives the possibility to choose the type of interactions to study and to isolate a particular interaction. The scattering of μd or μt beams on H₂ is analyzed via the muon transfer reaction to neon. The time-of-flight method is used to measure the scattering cross section as a function of the energy of the muonic atom beam. The results are compared, using Monte Carlo simulations, with theoretical calculations which have been recently performed with high accuracy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon molecular formation and transfer rate in solid hydrogen-deuterium mixtures

In an experiment at TRIUMF to study muon-catalyzed fusion and associated atomic and molecular effects, negative muons were stopped in a solid protium hydrogen layer containing a small amount of deuterium. Most of the resulting µp atoms disappeared by formation of ppµ molecules or by muon transfer to a deuteron. The µd can drift almost freely through the hydrogen layer due to the Ramsauer-Townsend effect and may even leave the layer. If a thin neon layer is frozen atop the hydrogen, the exiting muonic atoms will very rapidly release their muon to a neon atom. The analysis of the time structure of the neon X-rays is used to determine the rates of the slower processes involved in the evolution of the µp. This analysis has been performed with the help of Monte Carlo calculations, which simulate the kinetics of both µp and µd atoms in the hydrogen mixtures.     

Resonant Scattering of Muonic Hydrogen Atoms and Dynamics of the Muonic Molecular Complex

Resonant scattering of muonic hydrogen atoms via back decay of the molecular complex, a key process in the understanding of epithermal muonic molecular formation, is analyzed. The limitations of the effective rate approximation are discussed and the importance of the explicit treatment of the back decay is stressed. An expression of the energy distribution for the back-decayed atoms is given. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Muonic Atom Deexcitation via Formation of Metastable Molecular States, in Light of Experimental Verification

In a recent experiment performed at PSI, a peak in the time-of-flight distribution of pμ(1s) atoms could be identified with decay of ppμ^* molecular ions situated below the 2s threshold, providing 900 eV of kinetic energy to the pμ atom. This finding may be interpreted in terms of the side path model which suggests that metastable muonic molecules may form with high probability in resonant collisions between muonic hydrogen in the 2s state and hydrogen molecules, e.g. $$p\mu (2s) + {\text{H}}_{\text{2}} \to [(pp\mu ^* )_{vJ}^{pq} - pee]_{vK} \to [(pp\mu ^* )_{v'J'}^{p'q'} - pe]^ + + e^ - .$$ The Coulombic decay of the Auger stabilised ppμ^* molecular ion then leads to the formation of highly energetic pμ(1s) atoms. In the present paper calculations of resonant formation rates in pure hydrogen are presented and compared to the quenching rate of pμ(2s) atoms measured at low hydrogen density.     

Study of muonic hydrogen transport in TRIUMF experiment 742 by the Monte Carlo method

A technique of neutral muonic atom beams is proposed in the TRIUMF E742 experiment for measuring the scattering cross sections of muonic hydrogen isotopes in solid hydrogen. We present the results of Monte Carlo modeling of pµ and dµ atoms transport under the conditions of this experiment, taking into account the main physical as well as the geometrical aspects. The optimization of set-up parameters is performed in order to choose the most sensitive experimental conditions.     

Emission of muonic tritium into vacuum: An atomic beam for muon experiments

The emission of muonic tritium atoms from a thin film of hydrogen isotopes into vacuum was observed. The time and position of the muon decays were measured by tracking the decay electron trajectory. The observations are useful both for testing the theoretical cross sections for muonic atomic interactions, and producing an atomic beam of slow μ^-t with a controllable energy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Resonances in the dtµ molecular ion between tµ(n=2) and dµ(n=2) thresholds

Elastic and inelastic cross sections in collisions of a tµ atom in 2s and 2p states on deuteron have been obtained within the framework of a four-channel adiabatic approximation for the case of total orbital angular momentumJ=0. The calculated data has been applied to verify the existence of resonance in the dtµ molecular ion at 0.8 eV above the tµ(n=2) threshold. It appears that the second and third resonant states (at 0.8 eV and at 7 eV above the tµ threshold) in a series converging to the dµ(n=2) threshold do not produce any resonant structure in the energy spectrum. The higher vibrational states are visible in the spectrum, however their widths are about 0.1 eV and therefore their life-times are about 10^–15 s which allows to conclude that these states could not play an important role in the µCF cycle as well as in processes of diffusion of muonic atoms.