Atomic capture ratios of negative muons in gaseous mixtures of hydrogen,nitrogen, neon and argon

The yields of muonic x rays of the Lyman series of nitrogen, neon and argon have been analysed to determine capture ratios A(Z₁,Z₂) in about thirty gaseous mixtures under different experimental conditions. In addition, capture ratios A(Z,H) have been determined in hydrogen mixtures by taking into account transfer processes from muonic hydrogen to elements Z. The influence of the spectral flux density of the muons on capture ratios has been analysed. Our per-atom ratios form a coherent set and confirm the value A(Ar,Ne) = 1. 262(10).     

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.     

Dynamics of muonic atom cascade in hydrogen-helium mixtures

The deexcitation of excited muonic protium and deuterium in the mixture of hydrogen and helium isotopes is considered. Methods of experimental determination of the probability of direct atomic muon capture by hydrogen and muon transfer rates from excited muonic hydrogen to helium are proposed. Theoretical results for the population of the muonic atoms in the ground state, , are compared with the existing experimental data. Results obtained for mixtures are of interest for investigation of nuclear fusion in muonic molecules. Received: 6 August 1998 / Revised: 1st October 1998 / Accepted: 2 October 1998     

Present status of the investigation on muon transfer in gaseous mixtures of hydrogen and oxygen

To investigate the energy dependence of muon transfer to oxygen, we performed measurements in gaseous mixtures of hydrogen and oxygen. The time distributions of the muonic oxygen X-rays showed the same structure as the one observed earlier in H₂+SO₂ mixtures. In the delayed part of these distributions, one can distinguish a short-time and a long-time component. From the latter, we deduced the transfer rates from thermalized muonic protium, respectively deuterium, to oxygen. The short-time component can be interpreted as being due to muon transfer from epithermal muonic hydrogen atoms. The time parameters are characteristic for the deceleration process as well as for energy-dependent transfer rates. With results of recent research on the formation and the thermalization of muonic hydrogen, we performed Monte Carlo simulations in order to test the hypothesis of an energy-dependent transfer rate.     

Formation of fast exotic atoms by radiative Coulomb capture

Interesting surprises in some exotic atom kinetics have been reported recently. These involve muonic atom transfer cross sections, nuclear pion capture and theq 1s effect in CF. These can be explained if the exotic atom population contains a contributing fast component. Such fast atoms can be formed by radiative continuum to bound transitions of fast (keV) muons or pions. Cross sections for formation of such fast pionic and muonic atoms and their velocity distributions are reported. The possibility of these processes competing with the thermalisation channels and contributing effectively to the exotic atom population is discussed.     

Ephemeral and/or coloured nuonic hydrogen atoms

The unexpected and, in conventional terms, yet unexplained experimental results, obtained in systematic measurements of muon transfer from muonic hydrogen to sulphur and oxygen of sulphur dioxide, seem to violate the principle of reproducibility of muon transfer data. With the hypothesis of ephemeral muonic hydrogen atoms, the number of different hydrogen atoms can be reduced from four to two. This hypothesis does, however, not help to interpret the transfer data to helium, neon and argon, where the muonic hydrogen atoms seem to wear colours.     

First measurement of the temperature dependence of muon transfer rate from muonic hydrogen atoms to oxygen

We report the first measurement of the temperature dependence of muon transfer rate from muonic hydrogen atoms to oxygen between 100 and 300 K. Data were obtained from the X-ray spectra of delayed events in a gaseous target, made of a H₂/O₂ mixture, exposed to a muon beam. This work sets constraints on theoretical models of muon transfer and is of fundamental importance for the measurement of the hyperfine splitting of muonic hydrogen ground state as proposed by the FAMU collaboration.     

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.     

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.     

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.     

Recent experiments on muon transfer in gas mixtures

The experimental muon transfer rates from muonic protium and deuterium to heavier elements show a complexZ dependence. Instead of the expected monotonicZ dependence considerable variations between neighboring elements are observed. Transfer to neon has a specially small rate. Furthermore, the time distribution of the muonic X-rays shows in a number of molecules a complex structure, and depends in the case of a H₂ + CH₄ gas mixture also on the total pressure.     

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.     

Transfer of negative muons from hydrogen to oxygen

Negative muons were trapped in gaseous mixtures of hydrogen and oxygen. The time distributions of the muonic oxygen X-rays showed a clear deviation from a single exponential structure. From these time distributions we evaluated the transfer rate from thermalized muonic hydrogen atoms to oxygen. In order to test the hypothesis of an energy-dependent transfer rate to oxygen we performed Monte Carlo simulations of the thermalization and the transfer process. We report on the present status of our investigations.     

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.     

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.     

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.     

Lamb shift in muonic hydrogen—II. Analysis of the discrepancy of theory and experiment

Currently, both the g factor measurement of the muon as well as the Lamb shift 2S–2P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. We find that a virtual millicharged particle which could explain the muonic Lamb shift discrepancy alters theoretical predictions for the muon anomalous magnetic moment by many standard deviations and therefore is in conflict with experiment. Also, we find no parameterizations of an unstable virtual vector boson which could simultaneously explain both “muonic” discrepancies without significantly altering theoretical predictions for electronic hydrogen, where theory and experiment currently are in excellent agreement. A process-dependent correction involving electron screening is evaluated to have the right sign and order-of-magnitude to explain the observed effect in muonic hydrogen. Additional experimental evidence from light muonic atoms and ions is needed in order to reach further clarification.     

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.     

Radiative corrections to the light muonic atoms decay rate

Radiative corrections to the decay rate in low-Z hydrogen-like muonic atoms are considered. The correction is due to the Uehling potential and it has the relative order of α. The numerical results are reported for the 2p → 1s transition for atoms with nuclear charge up to Z = 10.