Observation of magnetic order of Cu-moment aroundx=0.12 in La2−x Ba x CuO4 and La2−x sr x CuO4 by μ+SR

Zero field positive muon spin rotation method ( ⁺SR) is applied on La_2–x Sr _x CuO₄ around forx=0.12 at which the high-T _c superconductivity (SC) is suppressed. The magnetically ordered state of Cu-moments, which is not a spin glass state but an antiferromagnetic like state, appears below 15 K for 0.105x0.120. The magnetic phase boundary is very similar to the one of the La_2–x Ba _x CuO₄ in which the structural transition from the low temperature orthorhombic (LTO) phase to the low temperature tetragonal (LTT) phase is observed aroundx=0.12. The present study suggests that there is no big difference of the electronic state of the CuO₂ plane between the La-Ba system and the La-Sr system and that the magnetic ordering of Cu-moments plays an important role for the suppression of the high-T _c SC aroundx=0.12 in both of the systems, although the LTO-LTT structural transition has not been observed yet in the La-Sr system.     

Positive muons in [Co(NH3)6]Cl3 and [Co(ND3)6]Cl3

We have carried out SR experiments on [Co(NH₃)₆]Cl₃ and [Co(ND₃)₆]Cl₃. At 293 K, all the muons implanted into the complexes were in the diamagnetic state. The observed Gaussian-type muon spin relaxation function proved that the internal magnetic field was caused by nuclear dipole moments of the atoms in the complexes. In addition, another exponential-type muon spin relaxation function was observed in [Co(ND₃)₆]Cl₃ below 50 K.     

Relaxed excited states and anomalous hyperfine structure of muonium centers in KBr

We report on the luminescence induced by positive muons implanted (with 4 MeV) into KBr crystal, which evidences a long-lived (lifetime=13.3 s excited state produced by muon radiolysis. The temperature dependence of the luminescence yield has a strong correlation with the amplitude of an anomalous muonium center: both are observed only below 50 K. This correlation strongly suggests that the muonium center is perturbed by the muon-induced excitons to cause the anomalous hyperfine structure. Moreover, the luminescence energy and decay time indicate that the observed luminescence is not associated with the intrinsic or impurity-related self-trapped excitons, but with a relaxed excited state specific to the muon(ium)-KBr system.     

The theorem for semisimple Hopf algebras

We give an algebraic version of a result of G. I. Kac, showing that a semisimple Hopf algebra of dimension , where is a prime and , over an algebraically closed field of characteristic 0 contains a non-trivial central group-like. As an application we prove that, if , is isomorphic to a group algebra.

     

Fan-type theorem for path-connectivity

A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg _G ^x , deg _G ^y }k for every pair of verticesx,y withd _G (x,y)=2 in a 2-connected graphG, whered _G (x,y) is the distance betweenx andy inG, thenG isk-path-connected.     

Synthesis of Six-Membered Compounds by Environmentally Friendly Cyclization Using Indirect Electrolysis

[Ni(cyclam)](ClO(4))(2)-catalyzed indirect electroreduction of olefinic bromides produced six-membered compounds in low to high yields. The synthetic intermediate 49 of Ipecac and Corynanthe alkaloids was obtained in 88% yield in a highly stereoselective manner. Lactam 66, the synthetic precursor of tacamonine, was prepared in 49% yield as a mixture of two diastereoisomers. The electrolysis of the bromoacetates gave the debrominated compounds in good yields.     

Spin dynamics in a site diluted finite spin cluster system probed by positive muons

The site diluted finite spin cluster system Rb₂CO _x Mg_1–x F₄ (x=0.15, 0.4, 0.5) has been investigated by the ⁺SR technique. Muon spin relaxation was observed in these diluted magnetic systems in a weak longitudinal field of 100 G. By reducing temperature below 100 K, the experimental data show features of slowing down phenomena of the Co electron moments in the finite spin clusters.     

Ultra-slow muon facility for surface HFI studies

A concept, a design, a construction and an account of commissioning experiments are given for the recently completed ultra-slow muon facility at the pulsed muon facility of UT-MSL/KEK. The intense (more than 10³/s) slow ⁺ beam with an extremely narrow phase-space volume (0.2 eV×(3 cm)²) to be produced in this facility will open a new muon science including surface physics and chemistry and fundamental atomic physics.Post-doctoral fellow of Swiss National Science Foundation.