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.     

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.     

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     

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.     

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 formation measurements of dt\mu via time of flight

Solid hydrogen in the form of an inhomogeneous layered target offers several experimental advantages when compared with liquid or gas. Beams of non-thermalized muonic hydrogen atoms allow us to explore resonant molecular ion formation processes near eV kinetic energies. Isotopically specific layers make it possible to separate competing and confusing interactions and to employ the time of flight for comparison with predictions based on theoretical energy dependences. Unambiguous charged fusion product detection simplifies absolute intensity measurements. The systematic uncertainties encountered in resonant molecular ion formation measurements, using solid hydrogen target layers, are being investigated with simulations which use the many calculated energy-dependent rates and cross-sections which are now available. The importance of the rates for processes such as muon transfer and elastic scattering are discussed, and results of some recent analyses are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Charge exchange and Coulomb de-excitation of muonic atoms in low energy collisions

The muon transfer and Coulomb de-excitation rates at the collisions of (pμ) _n , (dμ) _n and (tμ) _n muonic atoms in excited states n = 3, 4, 5 with hydrogen isotopes p, d, t are calculated for all possible combinations of hydrogen isotopes. The advanced adiabatic approach (AAA) [1–3] is adapted and used to the specific case of muonic atom collisions. 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.     

The study of prompt and delayed muon induced fission

Mass yield and total kinetic energy release (TKE) distributions of fragments from prompt and delayed muon induced fission, separately, have been measured for the isotopes²³⁵U,²³⁸U,²³⁷Np and²⁴²Pu. The distributions from prompt muon induced fission are compared with the corresponding distributions from hadronic reactions and from spontaneous fission (s.f.). The distributions from the delayed muonic fission processes are compared to the distributions for neutron and proton-induced fission. No mass distributions measured in the prompt muonic fission process show any signature, which can be attributed to the presence of the muon. Differences observed between the TKE distributions of prompt muon induced and hadron induced fission can be explained by the screening effect of the negative charge of the muon bound in the orbit of one of the fission fragments. The observed yield of symmetric muon induced fission was found to be defined merely by the value of the excitation energy.     

On the Use of a H2–O2 Gas Target in Muonic Hydrogen Atom Hyperfine Splitting Experiments

We propose a substantial improvement of the experimental method for the measurement of the hyperfine splitting of the ground state of muonic hydrogen described in earlier papers [1,2]. By further developing the idea to use the diffusion of the muon hydrogen atoms as a signature of laser-induced hyperfine transitions, we suggest a technique based on the energy dependence of the rate of muon transfer to oxygen in the thermal region, and demonstrate its efficiency and significant practical advantages. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Fission of muonic 232Th and 239Pu

The neutron emission is studied following the formation of muonic atoms of ²³²Th and ²³⁹Pu. Energy and time distributions are measured. Various processes which contribute to the measured spectra are considered. A collective resonance model of the muon capture is used to calculate the nuclear excitation function. The probability of the radiationless nuclear excitations and the influence of the presence of the bound atomic muon on the fission barrier are discussed. The existing data for the $\text{Γ}{}_{\mathrm{n}}\text{Γ}{}_{\mathrm{f}}$, are analysed. As a result of the analysis the rates of the prompt and delayed fission events (due to the radiationless mu-atomic transitions and the nuclear muon capture, respectively) are deduced from the experimental data to be 0.006/muon and 0.045/muon for ²³²Th and 0.10/muon and 0.49/muon for ²³⁹Pu, respectively. The increase of the fission barrier for muonic atoms is confirmed. The experimental neutron rates can be consistently explained only if it is assumed that in both nucleides the K_α radiationless transitions do not induce fission. The increase of the fission barrier for ²³⁹Pu is hence deduced to be not less than 1.2 MeV. The fate of the atomic muon after the nuclear fission is briefly discussed. Its influence on the interpretation of the present results is found to be small.     

Temperature dependence of the formation rates of hydrogen-helium mesic molecules in collisions of slow hydrogen atoms with helium

The rates of molecular muon transfer from the ground-state muonic hydrogen to helium isotopes are calculated in an improved adiabatic approximation. The results obtained by us at various temperatures are compared with the available experimental data.     

Muon transfer from hot muonic hydrogen atoms to neon

A negative muon beam has been directed on adjacent solid layers of hydrogen and neon. Three targets differing by their deuterium concentration were investigated. Muonic hydrogen atoms can drift to the neon layer where the muon is immediately transferred. The time structure of the muonic neon X-rays follows the exponential law with a disappearance rate corresponding to the one of ^–p atoms in each target. The rates _pp and _pd can be extracted     

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 transfer from excited states of muonic hydrogen atoms studied by X-ray measurement

Muon transfer from proton to deuteron was examined with muonic X-rays. The parameter q _1s was determined directly and the time spectra of the X-rays were analyzed for effects of the muon transfer reaction. This revised version was published online in August 2006 with corrections to the Cover Date.     

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).     

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.     

Charge transfer from the ground state of muonic hydrogen to at room temperature

The present status of research of muon transfer from the ground state of muonic protium to ⁴He is reviewed. The analysis of a recent measurement in a triple gas mixture of H₂+⁴He+Ne at 15 bar and room temperature is presented and the result is compared to the existing experimental and theoretical rates. The average muon transfer rate from protium to ⁴He determined from all lifetime measurements is . Received: 22 January 1998 / Revised: 4 March 1998 / Accepted: 31 March 1998     

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.