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.     

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.     

Muonic Molecules: Beyond the Coulomb Model

We report the latest numerical results for the binding energy of the weakly bound states of the muonic molecules (ddμ)₁₁ and (dtμ)₁₁ obtained with account of the leading QED, relativistic and nuclear structure effects, as well as of the interactions within the molecular complexes. The uncertainty of the theoretical value of the binding energy of (ddμ)₁₁ does not exceed 0.1 meV. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon-catalyzed fusion theory

Some topics in muon-catalyzed fusion theory are discussed: Resonant formation ofddμ molecules appears to be well understood, with good agreement so far between theory and experiment. The situation for resonantdtμ formation is much less clear, because of the more complicated kinetics, the apparent three-body effect, and the evident need to treat thermalization and molecular formation together to compare theory and experiment. Recent theoretical progress inpdμ fusion by Friar et al. has resolved a serious discrepancy in the Wolfenstein-Gershtein effect, i.e., the increase inpdμ fusion yield with increased deuterium fraction.     

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.     

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.     

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.     

Monte Carlo simulations of the <Emphasis Type="Italic">μ</Emphasis>CF processes kinetics in deuterium gas

The kinetics of muon-catalyzed-fusion processes (μCF) in pure D₂ gas have been studied by means of Monte Carlo simulations for various target temperatures and densities. In particular, the role of resonant and non-resonant ddμ formation in μCF has been investigated. It has been shown that non-resonant formation can be directly observed at very short times in the neutron time spectra from μCF for low-density D₂ targets. The time spectra of neutrons from the low-temperature ortho-D₂ and para-D₂ gas targets have been calculated. These spectra display a strong ortho-para effect, which agrees with experimental results for the dilute-gas D₂ targets.     

Observation of the Molecular Quenching of μp(2S) Atoms

Kinetic energy distributions of muonic hydrogen atoms μp(1S) have been obtained by means of a time-of-flight technique for hydrogen gas pressures between 4 and 64 hPa. A high energy component of ∼900 eV observed in the data is interpreted as the signature of long-lived μp(2S) atoms, which are quenched in a non-radiative process leading to the observed high energy: the collision of a thermalized μp(2S) atom with a hydrogen molecule H₂ results in the resonant formation of a {[(ppμ)⁺]^*pee}^* molecule. Then the (ppμ)⁺ complex undergoes Coulomb de-excitation and the ∼1.9 keV excitation energy is shared between a μp(1S) atom and one proton. The preliminary analysis of the time spectra gives a long-lived μp(2S) population of ∼1% of all stopped muons, and a quenching rate of ∼4⋅10¹¹ s⁻¹. This revised version was published online in August 2006 with corrections to the Cover Date.     

Generation of the Ultracold Muonic Hydrogen Flux

We present the study of μp atom scattering in solid hydrogen. Anomalously large emission of E _pμ≤1.9 meV μp's from a solid H₂ layer was observed for the first time. This three times greater μp atom yield is due to non-elastic phonon scattering. As a result, it becomes possible to generate an ultracold flux of μp atoms. The recent calculations of the total and differential cross sections agree with all experimental results of μp atom scattering in solid H₂. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

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.     

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.     

Existence and transition properties of the three-deuteron muonic molecule (3d,2e -,μ-)

We calculated the energy and the size of the three-deuteron muonic molecule (3d,2e ^-,μ^-) = D₃μ. It turns out that this system possesses two equilibrium positions, one at distances typical for muonic molecules, the second one at the usual molecular size. We show, moreover, that the fusion probability of the three deuterons is considerably enhanced due to the existence of a ⁶Li^* threshold resonance. Our estimates indicate that this probability is considerably higher than the decay rate of the competing Auger transition. 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.     

Diffusion radius of muonic hydrogen atoms in H-D gas

The diffusion radius of the 1S muonic hydrogen atoms in gaseous H₂ targets with various deuterium admixtures has been determined for temperatures T=30 and 300 K. The Monte Carlo calculations have been performed using the partial differential cross sections for pμ and dμ atom scattering from the molecules H₂, HD and D₂. These cross sections include hyperfine transitions in the muonic atoms, the muon exchange between the nuclei p and d, and rotational-vibrational transitions in the target molecules. The Monte Carlo results have been used for preparing the time-projection chamber for the high-precision measurement of the nuclear μ^- capture in the ground-state pμ atom, which is now underway at the Paul Scherrer Institute.     

Measurement of the temperature dependence of the ddμ molecule formation rate in dense deuterium at temperatures of 85–790 K

Muon catalyzed fusion (MCF) in deuterium was studied by the MCF collaboration on the Joint Institute for Nuclear Research Phasotron. The measurements were carried out with a high-pressure deuterium target in the temperature range 85–790 K at densities of about 0.5 and 0.8 of the liquid hydrogen density. The first experimental results for the ddμ molecule formation rate λ _ddμ in the temperature range 400–790 K with a deuterium density of about 0.5 of the liquid hydrogen density are presented.     

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.     

Results for the tμ+D<Subscript>2</Subscript> Reaction by the Methods of Quantum Reactive Scattering

In a recent paper [1], we applied the methods of quantum reactive scattering to the key resonant reaction in the muon catalyzed fusion (MCF) cycle that leads to the formation of a dtμ muonic molecular ion, in which fusion takes place very rapidly. We calculated reaction probabilities for tμ + D₂ scattering for incident kinetic energies less than 0.6 eV in the centre of mass frame and total angular momentum J _tot=0, using the APH (adiabatically adjusting, principal axes hyperspherical) formalism of Pack and Parker [2], which had previously been applied to simple chemical reactions. This was the first successful application of the above methods to the tμ + D₂ reaction. In this paper, we examine a significant discrepancy between our values for the back decay partial width for the resonances we consider and the results that have been obtained using previous methods. This revised version was published online in August 2006 with corrections to the Cover Date.     

Measurement of helium-3 and deuterium stopping power ratio for negative muons

The measurement method and results measuring of the stopping power ratio of helium-3 and deuterium atoms for muons slowed down in the D/³He mixture are presented. Measurements were performed at four values of pure ³He gas target densities, ϕ_He = 0.0337, 0.0355, 0.0359, 0.0363 (normalized to the liquid hydrogen density) and at a density 0.0585 of the D/³He mixture. The experiment was carried out at PSI muon beam μE4 with the momentum Pμ= 34.0 MeV/c. The measured value of the mean stopping ratio S$_{3^He/D}$ is 1.66±0.04.