The First Observation of the Temperature-Dependent Phenomenon of Muon Catalyzed Fusion in Solid D–T Mixtures

A systematic study on muon catalyzed fusion (μCF) was conducted in solid deuterium and tritium (D–T) mixture. A variety of experimental conditions were investigated, i.e., tritium concentrations from 20 to 70%, temperatures from 5 to 16 K. A preliminary analysis result suggests a steep decrease in the dtμ-molecule formation rate with decreasing temperature, and also an increase in the probability for a muon reactivation after an α-sticking phenomenon. This revised version was published online in August 2006 with corrections to the Cover Date.     

Facility for preparation of gas mixture in muon catalyzed fusion experiments

A facility is described that allows safe handling of high tritium gas activity as dozens kilocuries in a regular laboratory environment. It is used to make and deliver into the target a mixture of specific isotopic composition with the contamination requirement of 10^-7 v.f. for Z>1 elements, and recover it upon completion of operation. With this facility, efforts have been accomplished to investigate into the muon catalyzed fusion on two targets – liquid tritium and high-pressure tritium types. Also, the operation range was 0.1–120 MPa for pressure and 20–800 K for temperature and the amount of tritium used was about 100 kCi. The facility showed reliability in operation without indications of radiation beyond the safety level. 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.     

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.     

μCF based 14 MeV intense neutron source

Results of a design study for an advanced scheme of a μCF based 14 MeV intense neutron source for test material irradiation including the liquid lithium primary target and a low temperature liquid deuterium-tritium (D–T) mixture as a secondary target are presented. According to this scheme negative pions are produced inside a 150-cm-long 0.75-cm-radius lithium target. Pions and muons resulting from the pion decay in flight are collected in the backward direction and stopped in the D–T mixture. The fusion chamber has the shape of a 10-cm-radius sphere surrounded by two 0.03-cm-thickness titanium shells. Assuming 100 fusions per muon in this scheme one can produce 14-MeV neutrons with a source strength up to 10¹⁷ n/s. A neutron flux of up to 10¹⁴ n/cm²/s can be achieved in a test volume of about 2.5 l and on the surface of about 350 cm². The results of the thermophysical and thermomechanical analysis show that the technological limits are not exceeded. This source has the advantage of producing the original 14 MeV fusion spectrum without tails, isotropically into a 4π solid angle, contrary to the d-Li stripping neutron source. This revised version was published online in August 2006 with corrections to the Cover Date.     

Review of Muon Catalyzed Fusion Experiments – Activities after EXAT98 and Future Perspectives

Since EXAT98 at Ascona, significant progress has been marked for experimental investigations of the fundamental understanding of muon catalyzed fusion (μCF) phenomena in D–T, D₂ and other hydrogen systems. Future progress in the μCF studies is now guaranteed due to the successful launching of advanced accelerator projects such as JAERI-KEK Joint Proton Accelerator project and RI Beam Factory project at RIKEN. Also, the start of the next-phase thermal nuclear fusion project of ITER becomes promising so that some future contributions from ITER to μCF or vice-versa can be expected for various physical or technological aspects of fusion research. The future progress of μCF studies will also be promoted because of the growth of various other scientific research using muons. The essence of all these subjects is reviewed. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Theory of muon spin depolarization in crystalline phases of 3He

As is obvious from the energetic point of view, positive muons must form the molecular ion ( He_2μ)⁺ in condensed phases of helium. A theory of positive muon spin depolarization in crystalline phase of ³He in this model is devised. The theory explains experimental results. It is shown that the abrupt temperature dependence of the muon spin depolarization rate at T < 2 K which is observed in experiments is explained by spin–phonon interaction. This interaction mechanism arises due to a modulation of the exchange interaction between host atoms of the ³He‐lattice. This revised version was published online in August 2006 with corrections to the Cover Date.     

Anomalous frequency shift of negative muon spin precession in n‐type silicon

The dependence of the residual polarization of negative muons in n‐type Si with impurity concentration (1.6\pm 0.2)\times 10¹³\ cm^-3 on temperature in the 10–300 K range has been investigated. Measurements were carried out in external magnetic field of 0.08 T transverse to the muon spin. Muon spin relaxation and frequency shift were observed at temperatures below 30 K. The relaxation rate at 30 K is equal to 0.25\pm 0.08\,μ s^-1. The frequency shift at 20 K is equal to 7\times 10^-3. Both the relaxation rate and the frequency shift grow with decrease of temperature. Below 30 K the relaxation rate is well described by the dependence \varLambda=bT^-q, where q=2.8. An analysis of present and earlier published data on behavior of negative muon polarization in silicon is given. A possible mechanism of relaxation and frequency shift of muon spin precession in silicon is considered. This revised version was published online in August 2006 with corrections to the Cover Date.     

Implications of the recent D–T μCF experiments at RIKEN-RAL and near-future directions

The paper describes physics implications obtained through the recent experimental results on D–T μCF at RIKEN-RAL. Smaller sticking and larger cycling rates in solid/liquid D–T mixture than the theoretical predictions were observed, suggesting needs of further theoretical understandings. Some possible future directions in D–T μCF experiments are also described. This revised version was published online in August 2006 with corrections to the Cover Date.     

Negative muon spin precession in ferromagnetic iron and the hyperfine anomaly

The hyperfine field (B _μ ^hf ) at the negative muon μ⁻ in ferromagnetic iron was investigated by means of the zero-field μ⁻ spin precession technique. In the temperature range 320–690 K,B _μ ^hf for μ⁻ Fe departs from the magnetization curve of pure iron in the same way as the hyperfine field seen by a⁵⁵Mn impurity in dilute MnFe measured by NMR. The hyperfine anomaly for μ⁻ Fe relative to dilute (1.5 at.%)⁵⁵Mn in iron is found to be −0.9(3)% and temperature independent over the temperature range investigated.     

Theory of muon spin depolarization in condensed phases of hydrogen isotopes

A theory of muon spin depolarization in the molecular ion ( H₂μ)⁺(( D_2μ)) formed in a crystalline phase of hydrogen isotopes is presented. It is shown that the molecular ion ( H_2μ)⁺ has no time to thermalize during the muon lifetime, but after \tau\ll \tau_μ has time to transit to the lowest energy levels of the vibration‐rotation spectrum. The depolarization of the muon spin is determined by the interaction of the ion’s electric dipole moment with the lattice and by spin‐rotation interactions V_LS in the ion. This mechanism is analogous to that of “muonium”, replacing the hyperfine interaction by V_LS. The results can explain the experimental data and in particular the absence of a strong isotopic effect. This revised version was published online in August 2006 with corrections to the Cover Date.     

Excited states of muonic helium hydride ions and their possible impact on muon reactivation

Several previously unknown resonances of the μtμ helium hydride ion have been identified using a variational procedure. It is suggested that these resonances may form in αμ(1s)-TD(T₂) scattering, for centre of mass collision energies in the range 8–10 keV. If the molecular complex [(αtμ)*dee]* is formed in a dissociative state (with respect to the α tμ-d coordinate), the dissociation energy may in part be transferred to the muonic degrees of freedom, opening the exit channel [(αtμ)*dee]* → tμ + α e + T, effectively amounting to muon transfer from α to t. We present a theoretical formulation of this novel and hypothetical mechanism for muon reactivation together with a numerical calculation of its cross-section for a special case. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Muonic Hydrogen Lamb Shift Experiment at PSI

A measurement of the 2S Lamb shift in muonic hydrogen (μ⁻p) is being prepared at the Paul Scherrer Institute (PSI). The goal of the experiment is to measure the energy difference ΔE(2⁵ P _3/2−2³ S _1/2) by laser spectroscopy (λ≈6μm) to a precision of 30 ppm and to deduce the root mean square (rms) proton charge radius with 10⁻³ relative accuracy, 20 times more precise than presently known. An important prerequisite to this experiment is the availability of long-lived μp_2S -atoms. A 2S-lifetime of ∼1 μs – sufficiently long to perform the laser experiment – at H₂ gas pressures of 1–2 hPa was deduced from recent measurements of the collisional 2S-quenching rate. A new low-energy negative muon beam yields an order of magnitude more muon stops in a small low-density gas volume than a conventional cloud muon beam. A stack of ultra-thin carbon foils is the key element of a fast detector for keV-muons. The development of a 2 keV X-ray detector and a 3-stage laser system providing 0.5 mJ laser pulses at 6 μm is on the way. This revised version was published online in August 2006 with corrections to the Cover Date.     

Time‐differential radio‐frequency muon spin resonance (TD‐RFμSR) technique at a pulsed muon beam

Longitudinal‐field μSR methods, e.g., radio‐frequency μ⁺ spin resonance (RFμSR), are well suited to investigate dynamic processes that destroy the phase coherence of the muon spin ensemble. Additional information on relaxation processes of the muon species under investigation is obtained from time‐differential (TD) data acquisition. In this paper we describe the set‐up of a TD‐RFμSR spectrometer installed at the ISIS pulsed muon facility at the Rutherford Appleton Laboratory (RAL, Chilton, UK). As an example, results of TD‐RFμSR measurements on muons in diamagnetic environment μ^d in a boron‐doped silicon sample under illumination at 55 K are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Surface muon production in medium energy heavy ion reaction at RIKEN

A new type of beam transport system for secondary light charged particles (“Large Ω” Beam Course) has been constructed and used to transport surface muons from the decay of pions produced in heavy-ion reactions at RIKEN Ring Cyclotron (RRC). In an experiment carried out using a¹⁴N beam of 135 MeV/u and a carbon target of 0.9 g/cm² thickness, the surface muon intensity obtained in 5×5 cm² sample was around 100 1/s for 500 nA of the primary beam. This number may be increased by two orders if the energy were doubled.     

Emission of muonic tritium into vacuum: An atomic beam for muon experiments

The emission of muonic tritium atoms from a thin film of hydrogen isotopes into vacuum was observed. The time and position of the muon decays were measured by tracking the decay electron trajectory. The observations are useful both for testing the theoretical cross sections for muonic atomic interactions, and producing an atomic beam of slow μ^-t with a controllable energy. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Temperature dependence of the muon and proton hyperfine constants of an \alpha‐muonium‐substituted methyl radical

Muon hyperfine constants A_μ have been measured by transverse field μSR for (CH₃)₃Si\mbox\.CHMu in hexane from 167 K to 332 K. In addition, avoided level‐crossing resonance was used to determine \alpha‐proton coupling constants A_p over a similar range of temperatures. The two hyperfine constants can be described by a common temperature dependence, d|A_i|/ dT=1.4\times 10^-3 MHz\,K^-1, where A_i represents A_p or the reduced muon constant A^\prime_μ=0.3141A_μ. There is a small isotope effect (A^\prime_μ is 2.2 % larger than A_p) consistent with zero‐point motion in the anharmonic C–H bond stretch. The common temperature dependence is tentatively attributed to a coupled deviation of the C–H and C–Mu bonds out of the nodal plane of the p orbital containing the unpaired electron. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon spin relaxation in CeCu2Si2 and muon knight shift in various heavy-fermion systems

Positive muon spin precession has been observed in various heavy-fermion systems in the transverse external magnetic field. In the superconductor CeCu_2.1Si₂, the relaxation rate of muon spins increases rapidly with decreasing temperature below T_C. This is interpreted as the results of the inhomogeneous fields due to the imperfect penetration of the external field into the type-II superconducting state. The magnetic-field penetration depth λ is derived from the observed muon spin relaxation rate. λ is about 1200 ∢ at T∼0.5T_C, and the temperature dependence of λ is consistent with the relation expected for a BCS superconductor. We have also measured the muon Knight shift K_μ in the normal (or paramagnetic) state of various heavy-fermion systems. K_μ is large and negative (about −1000∼−3000 ppm at T=10 K) for CeCu₂Si₂, UPt₃ and CeAl₃, while more complicated signals are measured in CePb₃ and CeB₆. The negative muon Knight shift in the non-magnetic heavy-fermion systems is discussed in terms of the Kondo-coupling between the conduction- and f-electrons.