Muon transfer from the excited mesic hydrogen in the metastable 2s-state to helium nuclei

The rate of the molecular charge exchange of the excited muonic hydrogen in the 2s-state on helium nuclei is calculated. Resonance muon transfer is shown to occur with the formation of the intermediate excited complex ([(H μ)*He²⁺]2e)*. The resulting rates prove that the muon transfer from the 2s-state alone can not account for the experimental data on the muon transfer frompμ-atoms to⁴He nuclei.     

Muon transfer induced by collisional excitation of helium muonide Heμ+ after muon catalyzed fusionafter muon catalyzed fusion

Possibility of negative muon transfer from helium muonide He⁺ to T /or D/ through collisional excitation after muon catalyzed fusion has been pointed out. The transfer process depends on the efficiency of collisional excitation of He⁺ in the medium of tritium or deuterium. It is argued that tritium has larger nuclear stopping power and better excitation efficiency than deuterium. This effect is in the same direction as the tritium concentration dependence of muon loss probability in recent experimental work.     

A role of the hyperfine interaction of the negative muon and an electron shell in formingP-odd correlations in the muonic ion μ20 Ne

The weak interaction of neutral currents of the negative muon and nucleons results in arisingP-odd correlations in the radiative 2s→ 1s muon-ion transition. At the present paper we consider how the hyperfine muon-electron interaction influences forming these correlations in the muonic ion μ²⁰ Ne with oneK-electron. It is shown that the general form of expressions describing aP-odd asymmetry of an angular distribution of the quanta and their circular polarization does not depend on electron configurations. On the other hand such dependence takes place for expressions describing an angular correlation between the momenta of the quantum and the hard electron emitted in the μ-decay process at the 1s-orbit. Therefore we think that measuring theP-odd asymmetry of the angular distribution is the preferable experiment for studying the neutral currents interaction. The spin polarization of the muon at the 2s-orbit can be obtained by measuring the circular polarization of the quanta in the same experiment.     

Level energies and infrared radiative lifetimes of the muonic molecule Heμ+

Energies and radiative lifetimes are calculated for all bound and quasibound levels of the positive muon molecular ion Heμ⁺, together with the tunneling predissociation lifetimes of its quasibound levels. The radiative lifetimes obtained are much longer than the positive muon decay lifetime, so spontaneous (“infrared”) emission will not be a useful diagnostic for the presence of Heμ⁺ or the analogous molecular ions formed by the heavier inert gas atoms.     

Muon Spin Rotation/Resonance (μSR) for Studying Radical Reactivity of Unsaturated Organophosphorus Compounds

The positive muon (μ⁺) can be regarded as a light isotope of proton and has been an important tool to study radical reactions of organic compounds. Recently, muons have been applied to produce short-lived paramagnetic species from the heavier unsaturated organic molecules including the p-block elements. This article overviews recent muon spin rotation/resonance (μSR) studies on the phosphorus analogs of alkenes, anthracenes, and cyclobutane-1,3-diyls together with the fundamentals of μSR. The acyclic phosphaalkene of P=C and phosphasilenes of P=Si can accept muonium (Mu=[μ⁺e⁻]) at the heavier double bonds, and the corresponding radicals have been characterized. The phosphorus atom in 9-phosphaanthracene, whose P=C double bond is stabilized by the peri-substituted CF₃ groups, predominantly captures muonium to provide the corresponding paramagnetic fused heterocyclic system. The peri-trifluoromethyl groups are functional to promote the unprecedented light isotope effect of muon providing the planar three-cyclic molecular structure to consume the increased zero-point energy. The formally open-shell singlet 1,3-diphosphacyclobutane-2,4-diyl unit can accept muonium at the (ylidic) phosphorus or the skeletal radicalic carbon, and the corresponding paramagnetic phosphorus heterocycles can be characterized by μSR. The findings on these muoniation processes to the unsaturated phosphorus-containing compounds will contribute not only to development of novel paramagnetic functional species but also to progress on muon science.     

Muonic hydrogen and deuterium in H-D mixture and muon transfer in excited states

The deexcitation of µp and µd atoms in hydrogen-deuterium mixtures has been studied with a new kinetics model that takes the energy dependence of the cascade processes into account. The X-ray yields, the populations of atomic states, and the muon transfer from hydrogen to deuterium during the cascade have been calculated as functions of density and isotope fractions. The evolution of the kinetic energy distribution during the cascade is shown to play an important role in the transfer kinetics. The atomic energy distribution in the ground state is significantly changed by the transfer. The calculated X-ray yields and the muon transfer probabilities are in fair agreement with experimental data provided the current theoretical transfer rates are reduced by a factor of about 2.     

Collisional processes in muon catalyzed fusion as studied by the classical collision theory

Collisional processes involving a negative muon in the deuterium and tritium system were studied using the classical binary encounter theory. The time needed for slowing down of a 10 keV muon was found to be of the order of 10^–8s to 10^–12s, depending on the density of the system. The Sticking Probabilities for the d-t and d-d fusions were obtained to be 0.48% and 10.2%, respectively. The usefulness of the classical model for understanding fundamental processes in muon catalyzed fusion is suggested.     

Inversion of 1JCC correlations in 1,n‐ADEQUATE spectra

ADEQUATE experiments provide an alternative to the more commonly employed GHMBC experiment for the establishment of long‐range heteronuclear connectivities. The 1,1‐ADEQUATE experiment allows the unequivocal identification of both protonated and non‐protonated carbon resonances adjacent to a protonated carbon. The 1,n‐ADEQUATE experiment establishes correlations via an initial ¹J_CH heteronuclear transfer followed by an ⁿJ_CC out‐and‐back transfer, most typically, via three carbon–carbon bonds. Hence, the 1,n‐ADEQUATE experiment allows the equivalent of ⁴J_CH heteronuclear correlations to be probed when they are not observed in a GHMBC spectrum. Aside from the lower sensitivity of the 1,n‐ADEQUATE experiment relative to GHMBC experiments, the interpretation of the former is also complicated by the ‘leakage’ of ¹J_CC correlations into the spectrum that must be identified. A method for the inversion of ¹J_CC correlations to facilitate the interpretation of 1,n‐ADEQUATE spectra is presented that allows a single experiment to be performed to access ¹J_CC and ⁿJ_CC correlation information. Copyright © 2012 John Wiley & Sons, Ltd.     

The photon-electron directional correlation and the weak neutral current in muonic boron

Precise determination of the four coupling constants describing the parity-odd neutral current interaction between muon and nucleons would provide a critical test of the standard model. The directional correlation between the photon emitted in the transition between 2S- and 1S-states and the decay electron provides a suitable observable. The two isotopes of boron constitute a unique system for a complete determination of the coupling constants. Completeness requires that the hyperfine components of the initial or final state of the photon transition be distinguished. An elegant method of measuring the directional correlations in the hyperfine components of the final state is the Fourier analysis of the muon spin precession in correlation with the emitted photon radiation. The purpose of this paper is to derive the relationship between the directional correlations and the coupling constants, determine optimal energy and angular intervals for a measurement, and discuss the experimental issues which must be resolved in preparation of an experiment.     

Correlation analysis of reactivity in the addition of substituted benzylamines to ethyl α-cyanocinnamate

The kinetics of addition of a number of ortho-, meta-, and para-substituted benzylamines to ethyl α-cyanocinnamate (ECC) in acetonitrile have been studied. The reaction is first-order with respect to the amine and ECC. The rates of reaction of meta- and para-substituted benzylamines showed excellent correlations with Taft's σ₁ and σ_R⁰, and with σ₁ and σ_R^BA values, respectively. The reaction of the ortho-compounds showed a very good correlation with Charton's triparametric equation. The reaction is subject to steric hindrance by the ortho-substituents. A mechanism involving formation of a zwitterionic intermediate in a slow step followed by a fast proton transfer has been proposed. © 1996 John Wiley & Sons, Inc.     

On the electron transfer in low-energy collisions of the fully-ionized muonic boron with helium atoms

In connection with recent experiments on the observation of the metastable 2s state of muonic boron (μB)⁴⁺ formed in helium with a small admixture of diborane (B₂H₆) we estimated the cross-section of the electron transfer from helium to the muonic ion. The collisions energy T was considered to lie between the thermal energy and 1 a. u. The muonic ion (μB)⁴⁺ was treated as a heavy beryllium isotope Be4+. It was found that the main reaction responsible for the electron transfer at the energies specified above was: Be⁴⁺ + He → Be³⁺(1s) + He²⁺ + e^-. . Its mechanism is the Auger effect in the two-electron quasi-molecule (Be-He)⁴⁺. In our estimation of its cross-section we used adiabatic quasi-molecular terms obtained by diagonalizing the electronic Hamiltonian on a basis of several diabatic states constructed from two-centre orbitals. The electronic wavefunctions built with this way were employed to calculate Auger effect rates. The outgoing electron was treated to be free. The relative motion of the nuclei was considered classically. It was found that in the region 0.001 ≤ T ≤ 0.01 (in atomic units) the cross-section was a decreasing function of T and it was small (～ 10^-2 Ų). Then it starts to increase and mounts to typical atomic values (1 Ų) at T = 1 ÷ 2. The comparison of the reaction rate constant estimated on the basis of the obtained cross-section with experimental results establishes the upper limit of the energy of muonic boron during the 2s state lifetime (≈ 40 ns). It proves to be about 25 eV. This limit is in agreement with the typical value of 1 eV resulting from the energy transfer in the muon capture by the diborane molecule and the recoil energy acquired in the cascade. However, it does not exclude the possibility of an additional acceleration of muonic boron during its formation in the molecule.     

Doubly excited1 P 0 resonances in He

Doubly excited¹ P ⁰ autoionizating states in He below then=2 threshold of He⁺ ions are calculated by use of a method of complex-coordinate rotation. Hylleraas type wave functions are used to calculate resonance parameters for intrashell states (the two electrons occupy the same shell), and products of Slater-orbitals are used for intershell states (the two electrons occupy different shells). A total of 15 resonances below then=2 He⁺ thresholds are reported in this work. This includes six members in the 2snp ₊ (2≦n≦7) series, five members in the 2snp _? (3≦n≦7) series, and four members in the 2pnd (3≦n≦6) series. Comparisons are made with other theoretical calculations and with experimental observations.     

Muonium diffusion in ice

Muonium (Mu, μ⁺e⁻) is generally regarded as a light isotope of hydrogen. The procession signals of muonium in single crystals of H₂O and D₂O ice have been studied from 8 to 263 K using the muon spin rotation (μSR) technique. Transverse spin relaxation rates have been extracted and interpreted in terms of modulation of the dipolar interaction between muonium and the protons/deuterons in the lattice by translational diffusion of muonium. In contrast to the situation for H and a previous claim for Mu, muonium is found to be diffusing at temperatures as low as 8 K. An activation energy of 40 meV is obtained by fitting the highest temperature data to an Arrhenius expression. At low temperature muonium is thought to diffuse by quantum tunnelling.     

Study on the pressure induced charge transfer phase transition in (C5H11)4N(FeFe(C2O2S2)3) by means of μSR spectroscopy

We have investigated the magnetic properties of iron mixed-valence complexes, (n-C_nH_2n+1)₄N[Fe^IIFe^III(dto)₃] (dto = C₂O₂S₂, n = 3, 5), in which not only a ferromagnetic transition but also a novel charge transfer phase transition (CTPT) take place [1]. This CTPT can be observed under ambient pressure for n = 3, while it appears abruptly above 0.5 GPa for n = 5 [2]. Recently, we have measured the muon spin relaxation (μSR) for the CTPT of n = 3, which revealed the dynamical process of electron-transfer between Fe^II and Fe^III and its frequency was estimated at about 0.1 MHz [3]. To investigate the pressure induced CTPT for n = 5, we carried out the μSR measurement for n = 5 at 150 K between 0.30 and 0.64 GPa with the ⁴He gas-operated pressure system. The asymmetry of the muon spin relaxation for n = 5 with Cu-Be pressure cell was almost constant up to 0.55 GPa, while it rapidly decreased with increasing pressure above 0.60 GPa. This result shows that the applied pressure causes the spin fluctuation due to the CTPT, which induces the decrease of the asymmetry of muon spin relaxation. This experiment can correctly decide the phase transition pressure from the absence to the appearance of the CTPT for n = 5.     

Photoionization of lanthanum and its ions in the region of the “giant” resonance

The photoionization cross sections of outer and intermediate shells including 4d of La and its ions are calculated in the region of the “giant” resonance. The prominent effects of both intershell correlational effects and rearrangement are demonstrated.     

Mechanism of the molecular hysteresis

The redox behavior in acetone solution of (1,5-dithiacyclooctane 1-oxide)bis(pentaammineruthenium(II)) has been characterized, where the concept of “molecular hysteresis” is presented. Detailed thermodynamics for the complex are studied, in which intramolecular electron transfer rates for Ru³⁺OS/Ru²⁺→Ru²⁺SO/Ru³⁺ were determined as 0.12 sec^?1 and 0.055 sec^?1. The molecular hysteresis consists of two important factors: isomerizations for the sulfoxideruthenium complexes and the slow intramolecular electron transfer in the complex; both are examined. Isomerization rates for Ru³⁺S→O and Ru²⁺O→S determined range from 0.4 to 5000 sec^?1 and from 0.7 to 16 sec^?1, respectively, for [Ru(NH₃)₅(sulfoxide)]^2+/3+. A mechanism for the slow electron transfer in the complex is also presented. Features of molecular hysteresis are discussed.     

Calculation of the ground‐state energy and studies of other properties of exotic helium atoms with the use of boundary conditions of wave function

The minimum energy and average distance between particles of doubly muonic helium atoms Heμμ (He²⁺ + 2μ ), are calculated with the use of a wave function that satisfies boundary conditions such as the behavior of the wave function when two particles are close to each other or far away from each other. In this wave function, the muon–muon correlation in doubly muonic helium atoms is described to arrive at the correct behavior for r₁₂ tending to zero and infinity. It is shown that the obtained results are very close to the values calculated by others. Finally, to confirm the method and results, calculated values are compared with a similar electronic system, and it is shown that the small differences in the energies of Heμμ and He are due to the reduced masses, as expected. In addition to being very simple, the proposed wave function provides relatively accurate values for the energy and expectation values of r²ⁿ, emphasizing the importance of the local properties of the wave functions. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Understanding solvent effects on hyperfine coupling constants of cyclohexadienyl radicals

Quantum chemical calculations have been carried out to understand better solvent effects on the isotropic muon and proton hyperfine coupling constants in the C₆H₆Mu^• radical. Both polarizable continuum solvent models and explicit inclusion of water molecules into supermolecular complexes were used. Changes in the hyperfine couplings of in-plane hydrogen atoms are very small and difficult to discuss, partly due to relatively large experimental error bars. In contrast, the out-of-plane proton and muon hyperfine couplings exhibit more pronounced changes. These are partly due to structural changes of the radical and partly due to direct electronic polarization effects. Polarizable continuum solvent models agree well with experimental changes for benzene but overshoot the enhancement of the hyperfine couplings for water. Explicit inclusion of water molecules reduces this overestimated spin density increase and thereby tends to bring theory and experiment into closer agreement. The enhancement of the spin density on the out-of-plane hydrogen or muon atoms by the solvent environment is mainly due to an increased polarization of the singly occupied MO towards this side. Electronic Supplementary Material: Supplementary material is available in the online version of this article at dx.doi.org/10.1007/s00214-005-0680-x     

Some internal background processes impeding the observation ofP-odd effects in the one-photon 2s→1s transition of muonic neon

The weak interaction of neutral currents of the negative muon and nucleons leads to the appearance of observableP-odd correlations in the one-photon 2s→1s transition of light μ-atoms. Muonic neon was found to be one of promising μ-atoms for observing these correlations. It must be prepared under specific conditions so that its electron shell contains noL-electrons during the 2s- orbit lifetime (～0.1 ns). The presence ofK-electrons is permissible. Here we have considered three processes impeding the observation of the one-photon 2s→1s transition for such a situation. They are other decay channels of the same 2s-state. The first is the cascade of the radiative 2s→2pj (j=1/2, 3/2) and 2pj→1s transitions of the muon. The second is the radiation of one photon in the 2s→1s transition accompanied by exciting the electron shell. The third is also the one photon radiation but it is accompanied by ionizing the shell. The energies of photons radiated in these processes are close to the 2s→1s transition energy. Moreover, they actually carry no information on the weak interaction. Thus, the given photons form the internal background in observing the one-photon transition. We have calculated the intensities of these photons, their circular polarization and angular correlations between the momenta of one of them and a hard electron emitted in the μ-decay at the 1s-orbit. The results obtained show theP-odd effects in the angular distribution and circular polarization of the photons of the 2s→1s transition appear to be more preferable for measuring than the ones in angular photon-electron correlations.     

μSR studies of magnetic superconductors based on the BETS molecule

Muon spin rotation and relaxation measurements have been made on the molecular magnetic superconductors κ-BETS₂FeCl₄ and κ-BETS₂FeBr₄ and the non-magnetic molecular metals κ-BETS₂GaCl₄ and λ-BETS₂GaCl₄. In the magnetic materials, zero field muon spin relaxation signals show the formation of static antiferromagnetically ordered states and multiple precession frequencies are observed, corresponding to muon sites situated both within the anion layers and within the BETS layers. Studies of the relaxation behavior in the FeCl₄ salt have previously shown significant changes around its superconducting transition and the FeBr₄ salt reveals similar changes in the region of its superconducting transition, whose onset is around 1.5 K. In the non-magnetic GaCl₄ salts the formation of a superconducting vortex lattice was observed and the penetration depth λ was derived from the transverse field muon relaxation. When the BETS superconductors are compared with the ET-based superconductors that we have already studied using μSR, a striking correlation was observed between T_c and λ⁻³.