Modelling hydrogen in silicate materials

The expectation that the hydroxyl analogue state of positive muons implanted in quartz should be stabilized by a suitable charge compensation centre is supported by preliminary data. The diamagnetic fraction correlates with aluminium content over the narrow range investigated. This revised version was published online in August 2006 with corrections to the Cover Date.     

New spectroscopy solves an old puzzle: the Kondo scale in heavy fermions

Resonant inelastic x-ray scattering (RIXS) yields clear evidence of spectroscopic Kondo scales in heavy fermions. In YbInCu4 and YbAgCu4 RIXS probes the Yb2+ component of the hybrid ground state and the temperature dependence of the Yb 4f occupation. We report a sudden valence change at a phase transition in YbInCu4, but a continuous temperature dependence in YbAgCu4, consistent with the predictions of the Anderson impurity model, for a Kondo temperature T(K) = 70 K. These results solve a long-standing controversy and establish RIXS as a quantitative probe of the electronic structure of strongly correlated electron systems.     

Search for lepton-flavor-violating decays of the neutral kaon

The Fermilab KTeV experiment has searched for lepton-flavor-violating decays of the K(L) meson in three decay modes. We observe no events in the signal region for any of the modes studied, and we set the following upper limits for their branching ratios at the 90% C.L.: BR(K(L) --> pi(0) micro(+/-) e(-/+)) <7.6 x 10(-11); BR(K(L) --> pi(0)pi(0) micro(+/-) e(-/+)) <1.7 x 10(-10); BR(pi(0) --> micro(+/-) e(-/+)) <3.6 x 10(-10). This result represents a factor of 82 improvement in the branching ratio limit for K(L) --> pi(0) micro(+/-) e(-/+) and is the first reported limit for K(L) --> pi(0)pi(0) micro(+/-) e(-/+).     

On a class of martingale inequalities

Let Z = {Z₀, Z₁, Z₂,…} be a martingale, with difference sequence X₀ = Z₀, X_i = Z_i ? Z_{i ? 1}, i ≥ 1. The principal purpose of this paper is to prove that the best constant in the inequality λP(sup_i |X_i| ≥ λ) ≤ C sup_iE |Z_i|, for λ > 0, is C = (log 2)^?1. If Z is finite of length n, it is proved that the best constant is $\text{C}{}_{\mathrm{n}}\text{= [n(2}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}\text{? 1)]}{}^{\mathrm{?1}}$. The analogous best constant C_n(z) when Z₀ ≡ z is also determined. For these finite cases, examples of martingales attaining equality are constructed. The results follow from an explicit determination of the quantity G_n(z, E) = sup_zP(max_i=1,…,n |X_i| ≥ 1), the supremum being taken over all martingales Z with Z₀ ≡ z and E|Z_n| = E. The expression for G_n(z,E) is derived by induction, using methods from the theory of moments.     

Base‐dependent selectivity of an SNAr reaction

A detailed kinetic analysis and computational study of an S_NAr reaction between 2,5,6‐trifluoronicotinonitrile, 2 , and the ambident 3‐isopropoxy‐1H‐pyrazol‐5‐amine, 3 , is presented. The selectivity with respect to the reaction at the primary amino group of 2 , to give the desired product, 2,5‐difluoro‐6‐[(3‐isopropoxy‐1H‐pyrazol‐5‐yl)amino]nicotinonitrile, 1 , is strongly dependent upon reaction conditions. Reaction is found to proceed via both uncatalysed and base catalysed routes, and selectivity towards 1 is strongly enhanced in the presence of the base diazabicyclo[2,2,2]octane (DABCO). Computational studies in tetrahydrofuran solution at the B3LYP/6‐31G* level of theory have provided valuable insight into alternative kinetically indistinguishable reaction pathways. The results suggest that for reaction at the primary amino group, proton removal by DABCO accompanying amine addition allows avoidance of a high‐energy, zwitterionic Meisenheimer intermediate. Reactions at the alternative pyrazole nitrogen atoms are less sensitive to the presence of base because of stabilisation of the Meisenheimer zwitterions by intramolecular hydrogen bonding. Copyright © 2010 John Wiley & Sons, Ltd.     

Longitudinal relaxation of muonium in Ge and GaAs

Longitudinal-field muon-spin depolarization rates in high-purityGe and semiinsulatingGaAs are reported and compared to similar data for intrinsicSi. Depolarization onset temperatures provide a comparison of charge carrier concentrations leading to rapid charge exchange and a shift in the onset, for n-typeGaAs verifies anelectron process. The temperature dependence of the low-field rate constants imply more complicated dynamics inGe than observed earlier inSi. Features near 750K inGaAsTe appear consistent with dissociation of aMu-Te pair.This work was supported by the US National Science Foundation (DMR-8917639 [TLE, BH]), the Science and Engineering Research Council of the UK (EAD, AS, SFJC), the Robert A. Welch Foundation (D-1053 [RLL], and C-1048 [TLE]), and a NATO Collaborative Research Grant (RLL, SFJC, RCD, CS). We wish to thank D.A. Vanderwater of Hewlett Packard for providing theGaAsTe sample.