Weak convergence in Hilbert space and weak uncertainty relations in quantum theory

A suitable weak topology is considered on the Hilbert phase space of a quantum-mechanical system. It is then shown that if two bounded observables of the system have no common eigenvector, the sum of their variances in any state is always greater than some positive constant. Consequences of this result on some observables of simple physical systems are examined. First of all, the case of the position and momentum of the elementary particle in one dimension is studied and a comparation with Heisenberg's indeterminacy principle is carried out. Then, the case of angular variables is also examined, with special emphasis on spin 1/2. An experiment with neutrons is finally suggested and analysed with the help of the theory developed.     

19F NMR analysis of the fluorides of perfluorocyclohexane-sulphonic acid and of 3-trifluoromethylperfluorocyclopentane-1-sulphonic acid

From the electrochemical fluorination of the chloride and the fluoride of benzenesulphonic acid, in addition to the main product C₆F₁₁SO₂F, the side products C₅F₈(CF₃)SO₂F, a structural isomer of the main product and C₆F₁₀Cl? SO₂F are also obtained. The NMR analysis of these products was performed. Chemical shift and coupling constant values were obtained for all the compounds. The NMR parameters of the main product are compared with those of perfluoromethylcyclohexane according to the data of Jolley, Sutcliffe and Walker. From the NMR parameters of C₅F₈(CF₃)SO₂F it was possible to demonstrate that substitution on the ring for —SO₂F and CF₃— is of the 1,3 and not the 1,2 type.     

Contributions from higher twist effects to the quark fragmentation functions in neutrino data

Quark fragmentation functions are studied with ≈3500 charged current events induced in the bubble chamber Gargamelle by neutrinos of the SPS wide band beam, with 〈E_ν〉 ≈ 25 GeV. The Q² and W² regions covered by this experiment are Q² ≈ 0–40 GeV² and W² ≈ 1–100 GeV², the mean values being 〈Q²〉 = 6.5 GeV², 〈W²〉 = 22GeV². A correlation between the variables $\text{z =}\text{E}{}_{\mathrm{\pi }}\text{E}{}_{\mathrm{<mtext>H</mtext>}}$ and $\text{y =}\text{E}{}_{\mathrm{<mtext>H</mtext>}}\text{E}{}_{\mathrm{v}}$ is found in the data in the region Q² = 1–10 GeV², which can be explained in terms of higher twist effects. These effects reproduce the Q² evolution of the non-singlet moments of the fragmentation function without any need for logarithmic terms.     

Post-collision interactions in the (e,e′ Auger) coincidence spectra

Summary The argon LMM Auger energy spectra measured in a recent (e,e′ Auger) coincidence experiment are compared with the predictions of a semiclassical model of this post-collision interactions (PCI). The model satisfactorily reproduces both the measured shift towards higher energy and the observed lineshapes of the experimental spectra.     

Strange particle production by antineutrinos

Cross sections are presented for antineutrino production of Λ, Σ⁰ and K⁰ in strangeness changing reactions. Associated production reactions (ΔS = 0) have been observed in the charged and the neutral current channels. For the elastic reaction $\text{v}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{Λ}$, estimates have been made of the axial transition form factor.     

Chloride interference in the determination of bromate in drinking water by reagent free ion chromatography with mass spectrometry detection

Bromate, a well known by-product of the ozonation of drinking water, has been included among the substances which have to be monitored in the drinking water according to the last EC Directive 251/98 on potable water with a regulated limit of 10 microg l(-1). The need of performing routine analysis at this limit is a driving force for the developing of new simple and sensitive methods of detection, which should be also able to overcome the effect of matrix composition. This work explored the use of mass spectrometry detection with electrospray ionisation hyphenated to a reagent free ion chromatograph with hydroxide gradient elution for the determination of bromate in drinking water. The use of a high capacity hydroxide selective column operated in gradient mode allowed to avoid the interference by carbonate peak, which moved to longer retention times. The effect of increasing chloride concentrations from 0 to 250 mg l(-1), which is the guideline limit for drinking water in Directive 251/98/EC, was to decrease absolute mass spectrometric response and chromatographic efficiency and, on the consequence, to increase the effective detection limits. The effect of the chloride concentration on the detection of bromate is discussed.