Thermal spikes from stopped muons and density effects in muon-catalyzed fusion

Local hot regions caused by energy deposition from stopped muons can significantly influence the cycle rate of muon catalyzed fusion. The observed nonlinear density dependence of molecular formation rates is explained as a result of the temperature dependence since muonic deuterium-tritium molecules are formed at a high effective temperature that increases roughly linearly with density.     

The kinetics of muon-catalyzed dt fusion

A main source of information about the muon-catalyzed fusion cycle in D-T mixtures are the cycling rates _c, which are characteristic for the kinetic equilibrium of states attained rapidly in dense targets. The measurement, analysis and interpretation of these rates will be discussed, concentrating on the extensive set of rates observed at PSI over the last decade in gaseous, liquid and solid targets.Invited talk presented by Peter Kammel.     

Experimental results on muon-catalyzed dt fusion

A comprehensive experimental study of the kinetics of muon-catalyzed dt fusion has been conducted at PSI, based on the measurement of the 14 MeV neutrons from the fusion process. The target conditions included densities from 1–150% of the atomic density of liquid hydrogen, relative tritium concentrations of 2–95%, and temperatures of 13–300 K. Information about the dt cycle has been obtained from the measured neutron time distributions by different methods: Monte Carlo simulations primarily aimed at investigating epithermal effects in molecular formation and the determination and interpretation of cycling rates describing the steady state regime.     

Techniques for measuring initial sticking in d-t fusion

Monte Carlo simulations are used to compare experimental techniques for the direct measurement of the initial sticking coefficient _s ⁰ in muon-catalyzed d-t fusion. Three methods based on observing alpha-neutron coincidences from fusions in a low-density D₂-T₂ gas target are investigated. The experimental systems use either a surface barrier detector or a thin plastic scintillator to detect the and , and mylar windows or a thin coating of aluminium oxide to protect this detector from the tritium activity in the target.     

The PSI experiments on muon-catalyzed pt fusion

The experiments on pt fusion performed at Paul Scherrer Institut, Villigen, Switzerland, are described. Liquid triple mixtures of protium, deuterium and tritium with low concentrations on deuterium and tritium were used. Gamma rays, X-rays, neutrons and, for the first time, conversion muons, were measured. Preliminary results are: Rate for spin flip from the triplet to the singlet state of t(1s), ₁₀=(1.0±0.2) × 10³s^–1; rate for muon-catalyzed pt fusion from the (I=1) nuclear-spin state, _pt ^f (I=1)=0.07±0.01s^–1; and the molecular formation rate, _pt ^m =(7.5±1.3)s^–1 (all normalized to liquid hydrogen density).     

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.     

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.     

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.     

Method of determination of muon-catalyzed fusion parameters in H-T mixture

A method for measurement of the muon-catalyzed fusion (μCF) parameters in an H-T mixture is proposed. The kinetics of the μ-atomic and μ-molecular processes preceding the pt reaction in the ptμ molecule is described. Analytical expressions are obtained for the yields and time distributions of γ quanta and conversion muons formed in nuclear fusion reactions in ptμ molecules. It is shown that information on the desired parameters μCF can be found from the joint analysis of the time distributions of γ quanta and conversion muons to be obtained in experiments with the H-T mixture at three (or more) appreciably different atomic concentrations of tritium. The experiments with the H-T mixture at the meson facility PSI (Switzerland) were optimized to gain precise information about the desired μCF parameters.     

Experimental investigation of muon-catalyzed dt fusion at cryogenic temperatures

An experimental investigation of muon-catalyzed fusion (μCF) in gaseous, liquid and solid mixtures of deuterium and tritium was performed. The target conditions included the range of densities of 0.03 ≲ φ ≲ 1.5, tritium concentrations of 2% ≲ c_t ≲ 90% and temperatures of 13 ≲ T ≲ 40K. The study was based on the analysis of observed cycling rates extracted from the measured time distributions of the fusion neutrons. For the first time, the density dependence of the rates λ_(dtμ)d⁰ for the dtμ molecule formation in collisions of tμ atoms in the lower (F=0) hyperfine state with D₂ molecules was determined experimentally. Evidence for the proposed effects of below-threshold resonances on molecular formation was found. Measurements at low temperatures in mixtures of different molecular compositions revealed a clear predominance of the λ_(dtμ)d⁰ formation rate. The probability q_1s for dμ atoms to reach the ground state was determined as a function of density and tritium concentration.     

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.     

Discovery of temperature-dependent phenomena of muon-catalyzed fusion in solid deuterium and tritium mixtures

A systematic experimental study on muon-catalyzed fusion was conducted using a series of solid deuterium and tritium mixtures. A variety of conditions were investigated, i.e., tritium concentrations from 20% to 70%, and temperatures from 5 to 16 K. With decreasing temperature, we observed an unexpected decrease in the muon cycling rate (lambda(c)) and an increase in the muon loss probability (W). The origins of these observed changes were interpreted by the temperature-dependence in the dt mu formation process for lambda(c) and that in the muon reactivation process after muon-to-alpha sticking for W.     

Measuring sticking and stripping in muon-catalyzed dt fusion with multilayer thin films

We propose a direct measurement of muon sticking to alpha particles in muon-catalyzed dt fusion at a high density. Exploiting the features of a multilayer thin-film target developed at TRIUMF, the sticking is determined directly by detection of charged fusion products. Experimental separation of initial sticking and stripping may become possible for the first time. Monte Carlo simulations, as well as preliminary results of test measurements are described.     

Relativistic and QED contributions to the coulomb three-body system in muon-catalyzed fusion

Energy shifts in the shallowest level of the muonic moleculedtμ are estimated by using an accurate wave function of the point-charge three-body system which gives ε ₁₁ ⁰ = ?660.3 meV. Contributions of nuclear finite size, vacuum polarization, relativistic effect and internuclear interaction are evaluated to be +10.4 meV, +17.2 meV, +0.9 meV and ～ +10^?4 meV, respectively. These corrections to ε ₁₁ ⁰ amount to 28.5 meV, which is significantly different from the corresponding value 20.6 meV of the Soviet group, with serious dependence on the dtμ, formation rate.     

New insights in muon-catalyzed dd fusion by using ortho-para controlled solid deuterium

For the first time, we observed the dependence of the ddmu formation rate and the dmu hyperfine-transition rate on the ortho-para state in muon-catalyzed fusion in the solid D2 state, and found that the effect is even opposite to a recent theoretical prediction. We also determined the back-decay rate and the hyperfine-transition rate via scattering in solid state by using the ortho-para dependence. A theory to describe properly our experimental result is called for to understand the nature of muon-catalyzed fusion in the solid state.     

Experimental investigation of muon-catalyzed dt fusion in wide ranges of D/T mixture conditions

A vast program of the experimental investigation of muon-catalyzed dt fusion was performed on the Joint Institute for Nuclear Research phasotron. Parameters of the dt cycle were obtained in a wide range of the D/T mixture conditions: temperatures of 20–800 K, densities of 0.2–1.2 of the liquid hydrogen density (LHD), and tritium concentrations of 15–86%. In this paper, the results obtained are summarized.     

X-ray measurement on muon to alpha sticking in muon catalyzed d-t fusion; present and future

Among a series of X-ray experiments on the muon catalyzed fusion (CF) carried out by using pulsed muons at UTMSL/KEK, a direct knowledge of -sticking probability ( _s) in CF of high density D-T mixture with high T concentration has been obtained by measuring a characteristic muonic X-ray from the () atoms (central energy of 8.2 keV with a correct Doppler broadening). Combining with the recent X-ray measurements in (d) to³He and⁴He impurities, new insight is now obtained for the detailed background structure in the X-ray spectrum, suggesting the future direction for the X-ray measurements.