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.     

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.     

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.     

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.     

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.     

Resonances in Muon Transfer from Muonic Hydrogen to Oxygen and Neon

The influence of resonances on the muon transfer processes from muonic hydrogen to oxygen and neon (pμ)_1s + O⁸⁺ → p + (μO)_nl⁷⁺ and (pμ)_1s + Ne¹⁰⁺ → p + (μNe)_nl⁹⁺ is considered using the Smith lifetime matrix formalism. It is shown that the existence of a long lived resonance in the case of Ne induces a stronger dependence on collision energy of the muon transfer cross-section for this system. Present address: Chemistry Department, Vancouver University, Vancouver, BC V6T 1Z3, Canada     

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.     

237Np Mössbauer Investigations of (U1−x Np x )2Rh2Sn

Surprisingly, Np₂Rh₂Sn does not order magnetically whereas the uranium counterpart U₂Rh₂Sn orders antiferromagnetically at 24 K with a 5f moment μ _U ≈0.38μ _B . We have investigated the magnetic and electronic properties of (U_1−x Np _x )₂Rh₂Sn solid solutions. For x=0.25 and 0.5, the ordering temperature decreases to 11 K whereas the Np-rich compound (x=0.75) shows the onset of magnetic order around T≈6 K. The average Np magnetic moment amounts to 0.84 μ _B ,0.83μ _B and 0.25 μ _B respectively. The isomer shift slightly decreases, from −9.6 mm/s to −10.4 mm/s (versus NpAl₂) as x increases. The values of the quadrupole interaction parameter in the ordered and paramagnetic state suggest that Np moments are parallel to c for x=0.25 and then rotate to the basal plane for higher x. This revised version was published online in September 2006 with corrections to the Cover Date.     

Unparticles in gauge theory

A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle (“ungluon”). The model is formulated in terms of Lagrangian which features the source field S(x) which becomes a local pseudo-Goldstone field of conformal symmetry — the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by B _μ(x) ∼ ∂_μ S(x). Because the conformal sector is strongly coupled, the mode S(x) may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the “ungluon” exchange pattern — the “ungluon” propagator.     

Quantum deformation of lorentz group

A one parameter quantum deformationS _μ L(2,ℂ) ofSL(2,ℂ) is introduced and investigated. An analog of the Iwasawa decomposition is proved. The compact part of this decomposition coincides withS _μ U(2), whereas the solvable part is identified as a Pontryagin dual ofS _μ U(2). It shows thatS _μ L(2,ℂ) is the result of the dual version of Drinfeld's double group construction applied toS _μ U(2). The same construction applied to any compact quantum groupG _c is discussed in detail. In particular the explicit formulae for the Haar measures on the Pontryagin dualG _d ofG _c and on the double groupG are given. We show that there exists remarkable 1-1 correspondence between representations ofG and bicovariant bimodules (“tensor bundles”) overG _c . The theory of smooth representations ofS _μ L(2,ℂ) is the same as that ofSL(2,ℂ) (Clebsh-Gordon coefficients are however modified). The corresponding “tame” bicovariant bimodules onS _μ U(2) are classified. An application to 4D ₊ differential calculus is presented. The nonsmooth case is also discussed.     

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.     

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.     

Synchrotron and annihilation channels for axion production in an external electromagnetic field

We consider axion formation processes in the synchrotron (e ⁻→e ⁻ a) and annihilation (e ⁻ e ⁺→a) channels in a constant crossed field F _μν F^μν=Fμν*F ^μν =0, which approximates constant fields of other configurations in the ultrarelativistic asymptotic limit. The probability and intensity of axion emission are obtained, and we analyze the energy and field asymptotics. A comparison with the characteristic neutrino channel yields the constraints on the axion mass and the energy scale for Peccei-Quinn symmetry breaking. Possible astrophysical applications are discussed. Zh. éksp. Teor. Fiz. 112, 25–31 (July 1997)     

Dynamic magnetic permeability of a thin, high-T c superconducting wafer

The field dependence of the vibrational contribution to the dynamic magnetic permeability μ _V(H) is calculated for a thin (of thickness d∼λ) high-T _c superconducting wafer in a magnetic field parallel to the surface. The resulting curves are plotted on the basis of an exact numerical analysis of the vortex structures both for the thermodynamic-equilibrium vortex lattice and in the presence of pinning forces and the Bean-Livingston surface barrier. It is shown that the μ _V(H) curves are highly sensitive to the size factor (d/λ) and exhibit abrupt changes corresponding to a change in the number of vortex rows. The equilibrium μ _V(H) curve is found to be similar in its general behavior and absolute value (obtained with allowance for the distribution of grain sizes and with appropriate values of λ and ϰ) to the experimental μ _V(H) curve plotted at nitrogen temperature for fine-grained YBa₂Cu₃O_x with grain diameters 〈D〉∼λ in an increasing magnetic field. It is established that the main cause of the experimentally observed irreversible behavior of the μ _V(H) curves during cyclic variation of the applied magnetic field is the existence of a surface barrier to the exit of vortices from the superconductor. The lower limit H _min(B) of stability of the mixed state in the presence of an ideal surface barrier in a thin, high-T _c superconducting wafer (d∼λ) is determined, along with the range of the vortex state (H _max-H _min) for a fixed number of vortices in micrometer-size grains of the investigated YBaCuO samples. Fiz. Tverd. Tela (St. Petersburg) 39, 1943–1947 (November 1997)     

Vibrational Feshbach resonances in electron attachment to carbon dioxide clusters

Using a high resolution ( meV) laser photoelectron attachment method, we have studied the formation of (CO ₂) _q ⁻ ions (q = 4−22) in collisions of low energy electrons (1−180 meV) with (CO₂) _N () clusters. The previously reported “zero energy resonance”, observed at much larger electron bandwidths, actually consists of several narrow vibrational Feshbach resonances of the type [(CO ₂) _{N −1}CO which involve a vibrationally-excited molecular constituent ( denotes vibrational mode) and a diffuse electron weakly bound to the cluster by long range forces. The resonances occur at energies below those of the vibrational excitation energies of the neutral clusters [(CO ₂) _{N −1}CO ]; the redshift rises with increasing cluster ion size q by about 12 meV per unit; these findings are recovered by a simple model calculation for the size dependent binding energies. The size distribution in the cluster anion mass spectrum, resulting from attachment of very slow electrons, mainly reflects the amount of overlap of solvation-shifted vibrational resonances with zero energy; the cluster anion size q is identical with or close to that of the attaching neutral cluster. Received 11 January 2000 and Received in final form 10 April 2000     

On the Poisson Limit Theorems of Sinai and Major

Let f(ϕ) be a positive continuous function on 0 ≤ϕ≤Θ, where Θ≤ 2 π, and let ξ be the number of two-dimensional lattice points in the domain Π _R (f) between the curves r=(R+c ₁/R)f(ϕ) and r=(R+c ₂/R)f(ϕ), where c ₁<c ₂ are fixed. Randomizing the function f according to a probability law P, and the parameter R according to the uniform distribution μ _L on the interval [a ₁ L,a ₂ L], Sinai showed that the distribution of ξ under P×μ _L converges to a mixture of the Poisson distributions as L→∞. Later Major showed that for P-almost all f, the distribution of ξ under μ _L converges to a Poisson distribution as L→∞. In this note, we shall give shorter and more transparent proofs to these interesting theorems, at the same time extending the class of P and strengthening the statement of Sinai. Received: 15 June 1999 / Accepted: 11 February 2000     

Cohesion in lead chloride

The Born model is used as a method to assess the ionicity and the extent of covalent contribution to the binding in lead chloride. In the process, the Madelung constant (11·2429 with respect to cube root of unit cell volume) and cohesive energy (W _L) (484 kcal/mole) are evaluated. The theoreticalW _L, when compared with that derived from a thermochemical cycle indicates that PbCl₂ can be considered to be ‘predominantly ionic’.     

Photoproduction of neutral pion pairs from the proton

Double neutral pion photoproduction from the proton has been measured at MAMI for photon energies between threshold and 820 MeV. The reaction was identified by an invariant mass and missing mass analysis. From threshold up to 370 MeV the total cross-section does not exceed 30 nb. For higher energies it shows a smooth rise until it reaches a maximum of about 10 μb at E _γ = 740 MeV. Dalitz plots of m ²(π⁰π⁰) versus m ²(p,π⁰) for seven bins of incident photon energy have been analysed. For E _γ > 610 MeV, a strong contribution of a sequential decay is observed with the Δ(1232)-resonance as intermediate state. A comparison to model calculations shows that these sequential decays presumably originate from the D ₁₃(1520) and also the P ₁₁(1440)-resonance. Received: 6 June 2000 / Accepted: 18 August 2000