The μCF Experiments at PSI – A Conclusive Review

During 25 years pioneering μCF experiments were performed at PSI. After initial study of the Wolfenstein–Gershtein effect in H/D, an intense research program on dμd fusion led to the early discovery of resonant dμd formation at low temperature and to the first direct observation of μd spin flip. With the Gatchina ionisation chamber absolute precisions of ∼1% on the determination of dμd formation and spin flip rates were recently obtained in good agreement with the theory. In a very large effort the highly resonant dμt fusion cycle was investigated. Record cycle rates up to 2×10⁸ s⁻¹ and yields up to 124 fusions per muon were measured. By slope analysis and by direct observation, effective sticking ω _s = (0.505 ± 0.029)% is the final PSI result. Clear experimental evidence of large epithermal resonances in D/T and H/D/T mixtures was found. This revised version was published online in August 2006 with corrections to the Cover Date.     

Insights on d μ t sticking from d μ d stripping and μ,3He capture

Data from the recent PSI high statistics experiment on d μ d fusion are used to measure the stripping process in d μ d→ n+μ,³He and test current calculations of the stripping process. The PSI results in μ³He capture are also used to remove a troubling background from this measurement. Combination of these results with the old dμ t sticking analysis slightly raise and improve that result to ω_s= (0.58± 0.04)% and indicate that theory and experiment can meet if theoretical stripping is increased only at the beginning of the track. This conclusion is in accord with the new stripping calculations where excited state stripping is increased significantly. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon catalyzed fusion in deuterium gas

We present the results of an experiment performed at PSI to investigate muon catalyzed fusion in pure deuterium gas of 5% density (LHD) at temperatures ranging from 28 K to 350 K. Using a new high pressure ionization chamber the reactions dd → n + ³He and dd → p+t were observed with 100% detection efficiency. The rates of dμd formation were measured with the absolute precision of 1% and the μd spin-flip rates with 0.5%. The temperature dependence of molecular formation and spin-flip rates display pronounced resonance structures. A preliminary fit based on the Vesman mechanism of resonant muonic molecule formation was carried out yielding a dd fusion rate of 3.5·10⁸ s^-1 and a hfs splitting energy of 24.3 meV, both in good agreement with the theory. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon catalyzed fusion and muon to 3He transfer in solid T2 studied by X-ray and neutron detection

X-ray and neutron measurements were carried out for muon catalyzed fusion and related phenomena in solid T₂. The X-ray originated from the μ^- to α sticking in muon catalyzed fusion; t + t + μ ^- → (μ ^- α) + 2n was measured for the first time, yielding K _α X-ray intensity of (μα) atom and the intensity ratio of K _β to K _α . Utilizing the phenomena of ³He accumulation in solid T₂, the X-ray in the μ^- transfer process from (tμ) to ³He was detected, providing a formation rate and radiative decay branching-ratio of (t ³Heμ) molecule. From fusion neutron measurements, estimated values were obtained for (ttμ) molecular formation rate as well as sticking probability ω_t in ttμ fusion. A possible new insight in t + t fusion reaction process at a low energy limit is also obtained. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muonic Molecule Formation in Condensed Deuterium

Resonant formation of the muonic molecule ddμ in dμ atom scattering in condensed deuterium is considered. In particular, ddμ formation in D₂ solid targets containing different ortho-D₂ concentration is discussed, and the respective time spectra of the dd fusion products are shown. The results of the first calculation of the resonant ddμ formation rate in liquid deuterium are presented. At large momentum transfers the ddμ formation rate takes the Doppler form, similar to that obtained for a dilute gas target. A condition of validity of this approximation is also discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Study of μ-catalyzed fusion in H-D mixtures

Muon-catalyzed fusion was first observed in the pdμ system, and remains a good test of our understanding of the underlying molecular and nuclear processes. In contrast to the ddμ and dtμ systems, no resonant behavior is expected, which considerably simplifies the dynamics. We will discuss data taken with solid H-D mixtures of 0.05%, 2%, 15% and 75% D₂. In these measurements we observed simultaneously muons from pdμ→μ+ ³He and γs from pdμ→μ ³He + γ. A simulation code incorporating the relevant physics processes has been developed for the analysis of this data. Preliminary results are presented for the fusion and molecular formation rates. This new data stringently tests the currently-accepted fusion scheme. A new value of the astrophysical S-factor is derived. This revised version was published online in August 2006 with corrections to the Cover Date.     

Total and transport elastic cross-sections for excited muonic and pionic hydrogen atoms

The results of an experiment on muon catalyzed dd-fussion in HD gas are presented. The experiment was performed at the muon beam of PSI using a high-pressure ionization chamber filled with pure HD-gas of low D₂ concentration on the level 1%, at temperatures 50, 150 and 300 K. The non-resonant character of ddμ-molecule formation on HD molecules was confirmed by measuring the ratio of yields of the two ddμ-fusion channels, R=Y(³He,n)/Y(³H,p), which proved to be close to unity. The ddμ formation rate was found to vary from λ_ddμ-HD=0.05· 10⁶ s^-1 at T=50 K to λ_ddμ-HD=0.12· 10⁶ s^-1 at T=300 K, in agreement with the theoretical prediction. A prominent peak at t<60 ns was observed in the time spectrum of fusion neutrons indicating a resonant contribution of ddμ formation from epithermal dμ atoms. This revised version was published online in August 2006 with corrections to the Cover Date.     

Experimental investigation of muon-catalyzed t + t fusion

The muon-catalyzed fusion (μCF) process in tritium was studied by the μCF collaboration on the muon beam of the JINR Phasotron. The measurements were carried out with a liquid tritium target at the temperature 22 K and density approximately 1.25 of the liquid hydrogen density (LHD). Parameters of the μCF cycle were determined: the ttμ muonic molecule formation rate λ _ttμ = 2.84(0.32) μs⁻¹, the ttμ fusion reaction rate λ _f = 15.6(2.0) μs⁻¹, and the probability of muon sticking to helium ω _tt = 13.9(1.5)%. The results agree with those obtained earlier by other groups, but better accuracy was achieved due to our unique experimental method. The article is published in the original.     

Weak neutral currents in the U3(W)-gauge theory of weak and electromagnetic interactions

A discussion is given of the implications of the recently proposed U₃(W)-gauge theory of weak and electromagnetic interactions (Pandit 1976) for some phenomena resulting from its weak neutral currents: (1) neutrino-electron scattering, (2) neutrino-nucleon elastic and inelastic scattering, (3) coherent neutrino-nucleus scattering (4) weak interaction effects ine ⁺ e ⁻→μ⁺μ⁻ and (5) parity-violation in atomic physics. The theory agrees quite well with the available experimental results on neutrino processes. We find the coherent neutrino-nucleus cross-section for Fe⁵⁶ to be about 6 times larger than that in the WS-GIM theory giving some hope of accounting for supernova explosion by the resulting neutrino-radiation pressure.     

Measurement of the Temperature Dependence of the ddμ-Molecule Formation Rate in Dense Deuterium at Temperatures 300–800 K

Muon catalyzed fusion in deuterium was studied by the MCF collaboration at JINR phasotron. The measurements were carried out with a high-pressure deuterium target at the JINR phasotron in the temperature range 300–800 K at densities ≃0.5 LHD. The first experimental results for ddμ-molecule formation rate λ _ddμ in the temperature range 400–800 K with deuterium density 0.5 LHD are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Measurement of the fusion rate in μd3He

Many atomic and molecular processes may occur after a muon has been stopped in a mixture of hydrogen and helium isotopes. In particular, the muonic molecule μd³He can be formed. This molecule either decays or undergoes muon catalyzed fusion. Theory predicts a fusion rate much lower than the decay rate; moreover, the various theoretical predictions differ from each other by several orders of magnitude. With the experiment presented here we intend to measure the effective fusion rate via the detection of the 14.7 MeV fusion proton. A new target and gas mixing system, designed at JINR, were used in a ten-day test run at PSI. The fusion protons and products from other transfer and background reactions were measured with several different detectors (plastic scintillators, BGO, Germanium, neutron, and Silicon detectors). The formation rate of the μd ³He molecule and an upper limit for the effective fusion rate have been measured and are presented here. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muons in type-II superconductors: μ+ diffusion in ultra-pure niobiumdiffusion in ultra-pure niobium

The diffusivityD _μ of positive muons (μ⁺) in the mixed state of superconducting high-purity, high-perfection niobium single crystals is investigated by measurements of the relaxation of the transverse muon spin polarization (μ⁺SR). The method makes use of the strong magnetic field gradients existing in the mixed state of Type-II superconductors and monitorsD _μ through the variation of the magnetic field felt by the μ⁺ during their diffusion through the crystals. For μ⁺ near the centres of the flux lines inNb it givesD _μ(4.6 K)=(8±2)·10⁻¹¹m²S⁻¹. The positive temperature coefficient ofD _μ indicates that at liquid-helium temperatures the diffusivity of μ⁺ inNb is mainly due to phonon-assisted tunnelling processes.     

Experimental Results on Muon Catalyzed dt Fusion in H/D/T Mixture

Experimental study on muon catalyzed dt fusion in a triple mixture of hydrogen isotopes (H/D/T) was carried out at the JINR phasotron. The measurements have been performed at various temperatures and densities with liquid and gaseous H/D/T mixtures. Results are presented for the main characteristics of the dtμ cycle. A reduction of the number of dt fusions is observed when hydrogen is added to the D/T mixture, This is mainly due to muon loss to the pt and pd cycles, which have a high sticking probability. We also observe an increase of the cycle rate when the temperature of the H/D/T mixture rises. This confirms the theoretical prediction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Investigation of the Parameters of Muon-Catalyzed Fusion in Double D/T Mixture at High Temperature and Density

Experiments on the study of the muon catalyzed fusion (μCF) process in a double D/T mixture of hydrogen isotopes in the temperature range 300–800 K at densities 0.3–0.5 LHD are performed at the JINR phasotron. The values of the effective μCF parameters (cycling rate λ _c , neutron yield Y _n , muon losses w) are obtained. Tentative dtμ-molecule formation rates on D₂ and DT molecules (λ _dtμ−d and λ _dtμ−t ) are obtained for different mixture temperatures and densities. The results obtained show that λ _dtμ−t increases with temperature, but its value is smaller than theoretical predictions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hadron production near threshold

Final state interaction effects inpp→ pΛK ⁺ andpd →³Heη reactions are explored near threshold to study the sensitivity of the cross-sections to thepΛ potential and theηN scattering matrix. The final state scattering wave functions between Λ andp andη and³He are described rigorously. The Λ production is described by the exchange of one pion and aK-meson between two protons in the incident channel. Theη production is described by a two-step model, where in the first step a pion is produced. This pion then produces anη by interacting with another nucleon     

Influence of the Epithermal Effects on the MCF Steady State

This work is devoted to the correct interpretation of the steady state parameters of the muon catalyzed fusion (MCF) process in a D/T mixture. Previously the influence of the epithermal effects dtμ-molecule formation by ‘hot,’ non-thermalyzed tμ-atoms) on the steady state parameters was studied only for measurements with a low-density target (density φ = 0.01 relative to the liquid hydrogen density). We suggest a new method allowing direct determination of the necessary corrections to the MCF cycling rate for high-density data (φ ≥ 0.4).     

Precise Measurement of Muon Capture on the Proton

The aim of the μCap experiment is a 1% measurement of the singlet capture rate Λ _S for the basic electro-weak reaction μ + p → n + ν_μ. This observable is sensitive to the weak form-factors of the nucleon, in particular to the induced pseudoscalar coupling constant g _P . It will provide a rigorous test of theoretical predictions based on the Standard Model and effective theories of QCD. The present method is based on high precision lifetime measurements of μ⁻ in hydrogen gas and the comparison with the free μ⁺ lifetime. The μ⁻ experiment will be performed in ultra-clean, deuterium-depleted H₂ gas at 10 bar. Low density compared to liquid H₂ is chosen to avoid uncertainties due to ppμ formation. A time projection chamber acts as a pure hydrogen active target. It defines the muon stop position in 3D and detects rare background reactions. Decay electrons are tracked in cylindrical wire-chambers and a scintillator array covering 75% of 4π. This revised version was published online in August 2006 with corrections to the Cover Date.     

He accumulation effect in solid and liquid D-T mixture

This article reports the accumulation effect of the ³He originating from tritium β decay; ³He created in solid remains in it, while one in liquid diffuses and goes out to the vapor gas. We observed this effect through the neutron detection from muon catalyzed fusion phenomenon (μCF), and gave it qualitative understanding, by which the muon transfer rate from (dμ) and (tμ) to helium was derived. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetics of muon catalyzed fusion processes in solid H/D mixture

This paper presents the final results of an experimental study of the kinetics of the muon catalysed fusion (MCF) in solid hydrogen-deuterium mixtures (H/D) at a temperature of 3 K. The experiment E742 was carried out on a TRIUMF meson facility in Canada. Four exposures were performed at different deuterium concentrations in the H/D mixture: c_d = 0.0005, 0.02, 0.15 and 0.75. A simultaneous analysis of the measured time distributions of the 5.5 MeV γ-quanta and the 5.3 MeV conversion muons obtained from nuclear fusion in the pdμ molecule allowed to extract the values of MCF chain parameters in the H/D mixture: the fusion partial rates for different nuclear spin states of the pdμ molecule, and the pdμ molecule formation rate. The experimental data fitting procedure was conducted in two ways: using solely the analytical formulae describing the kinetics of the MCF processes in the H/D mixture, and the detailed Monte Carlo simulation of the entire experiment. The results obtained by these two methods are consistent with each other and confirm the existence of the Wolfenstein-Gerstein effect.     

Search for muon catalyzed d 3He-fusion

We report on the results of an experiment aimed at observing muon-catalyzed d ³He-fusion with a setup previously used for studies of the muon-catalyzed dd-fusion. The basic element of the setup is a high pressure ionization chamber operating as an active target. In this experiment the chamber was filled with an HD + ³He (5.6%) gas mixture at 13.2 bar pressure and 50 K temperature. These conditions were chosen as optimal for formation of the ³Heμd-molecules with a low level of background from the d-μ-d fusion. The chamber was exposed to the negative muon beam at PSI. During a 3-week data-taking period, 9.7 × 10⁸ muon stops have been selected. The analysis of the data was able to determine a new upper limit for the d ³He-fusion rate in the ³Heμd-molecule (λ_f≤ 6× 10⁴ s^-1), which is more than three orders of magnitude lower than the previously existed limit. This revised version was published online in August 2006 with corrections to the Cover Date.