Influence of ion-molecular reactions on μ-capture in hydrogen and on fusion in 3Hedμ muonic molecule

The de-excitation processes (J=1)→ (J=0) in muonic molecular ions (ppμ)⁺ and (³Hedμ)⁺ are studied. It is shown that the rate of such transitions substantially depends on the chain of ion-molecular reactions initiated by positively charged muonic ions. The probabilities of ortho-para transition in the [(ppμ)⁺H₂] and [(ppμ)⁺e] complexes formed as a result of chemical reactions in the pure hydrogen were estimated. Taking into account the ion-molecular processes in D₂ + He mixtures, the evaluation of the observed rate λ_f of nuclear fusion in the ³Hedμ muonic molecules was performed. The expected yield of fusion reactions per muon at the mixture density φ=0.1 and concentration C _He =0.05 was obtained to be equal to . This revised version was published online in August 2006 with corrections to the Cover Date.     

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%.     

Measurement of the resonant d(mu)t molecular formation rate in solid HD

Measurements of muon-catalyzed dt fusion ( d(mu)t-->4He + n + mu(-)) in solid HD have been performed. The theory describing the energy dependent resonant molecular formation rate for the reaction (mu)t + HD-->[(d(mu)t)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 microg x cm(-2) targets, an average formation rate consistent with 0.897+/-(0.046)(stat)+/-(0.166)(syst) times the theoretical prediction was obtained.     

High precision study of muon catalyzed fusion in D2 and HD gas

Muon catalyzed dd fusion in D₂ and HD gases in the temperature range from 28 to 350 K was investigated in a series of experiments based on a time-projection ionization chamber operating with pure hydrogen. All main observables in this reaction chain were measured with high absolute precision including the resonant and non-resonant ddμ formation rates, the rate for hyperfine transitions in dμ atoms, the branching ratio of the two charge symmetric fusion channels ³He + n and t + p and the muon sticking probability. The report presents the final analysis of the data together with a comprehensive comparison with calculations based on recent μCF theories. The energy of the loosely bound ddμ state with quantum numbers J = 1, ν = 1, which is central to the mechanism of resonant molecule formation, is extracted with precision ?₁₁(fit) = ?1.9651(7) eV. in impressive agreement with the latest theoretical results ?₁₁(theory) = ?1.9646 eV.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.     

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.