q\bar q pair creation in a flux tube with confinement

We calculate the effect of radial confinement on the Schwinger pair production rate by solving the Dirac equation in a flux-tube cylinder containing a constant chromoelectric field in the longitudinal direction. We show how the Dirac equation separates into radial and longitudinal equations for a mass term which has an arbitrary radial dependence and introduce radial confinement by having a finite mass inside the cylinder and an infinitely large mass outside. The resulting boundary conditions are equivalent to the MIT boundary condition. The equations are solved analytically for a constant quark mass inside the flux-tube, which acts like a waveguide. The discretization of the transverse wave vector which has a continuous spectrum in the non-confined case leads to a large suppression of the Schwinger pair-production rate for small radii. The minimal radius where pairs are created decreases with increasing field strength. The suppression turns out to be larger for heavier quarks than for light quarks.     

New light on Hensel''s lemma

The historical development of Hensel's lemma is briefly discussed (Section 1). Using Newton polygons, a simple proof of a general Hensel's lemma for separable polynomials over Henselian fields is given (Section 3). For polynomials over algebraically closed, valued fields, best possible results on continuity of roots (Section 4) and continuity of factors (Section 6) are demonstrated. Using this and a general Krasner's lemma (Section 7), we give a short proof of a general Hensel's lemma and show that it is, in a certain sense, best possible (Section 8). All valuations here are non-Archimedean and of arbitrary rank. The article is practically self-contained.     

Principles and recent developments in ultrasound contrast agents

The behaviour of gas bubbles and gas encapsulated spheres as echographic contrast agents is reviewed. Compared with rigid spheres, gas bubbles are superior scattering agents and they offer a number of useful properties which can be exploited in a variety of ways. The analysis of their velocity of sound, back-scatter intensity, second harmonic emission and resonant frequency opens up new perspectives in the development of contrast agents for echocardiographic research with potential clinical applications.     

Z/E-photoisomerizations of olefins with 4npi- or (4n + 2)pi-electron substituents: zigzag variations in olefin properties along the T(1) state energy surfaces

[Figure: see text]. A quantum chemical study has been performed to assess changes in aromaticity along the T1 state Z/E-isomerization pathways of annulenyl-substituted olefins. It is argued that the point on the T1 energy surface with highest substituent aromaticity corresponds to the minimum. According to Baird (J. Am. Chem. Soc. 1972, 94, 4941), aromaticity and antiaromaticity are interchanged when going from S0 to T1. Thus, olefins with S0 aromatic substituents (set A olefins) will be partially antiaromatic in T1 and vice versa for olefins with S0 antiaromatic substituents (set B olefins). Twist of the C=C bond to a structure with a perpendicular orientation of the 2p(C) orbitals (3p*) in T1 should lead to regaining substituent aromaticity in set A and loss of aromaticity in set B olefins. This hypothesis is verified through quantum chemical calculations of T1 energies, geometries (bond lengths and harmonic oscillator measure of aromaticity), spin densities, and nucleus independent chemical shifts whose differences along the T1 PES display zigzag dependencies on the number of -electrons in the annulenyl substituent of the olefin. Aromaticity changes are reflected in the profiles of the T1 potential energy surfaces (T1 PESs) for Z/E-isomerizations because olefins in set A have minima at 3p* whereas those in set B have maxima at such structures. The proper combination (fusion) of the substituents of set A and B olefins could allow for design of novel optical switch compounds that isomerize adiabatically with high isomerization quantum yields.     

5,15-二(对-取代苯基)八烷基卟啉及其金属配合物的合成

本文报道了五种5,15-二(对-取代苯基)-2,8,12,18-四乙基-3,7,13,17-四甲基卟啉(Ⅱa—Ⅱe)和五种5,15-二(对-取代苯基)-2,3,7,8,12,13,17,18-八甲基卟啉(Ⅰa—Ⅰe)以及它们的铜、铁、镍金属配合物的合成。这些化合物的结构均经元素分析、UV、~1HNMR和MS鉴定。芳环上不同取代基对卟啉成环反应有一定影响,拉电子基团有利于反应。其顺序如下:NO_2>H>CH_3>OCH_3>N(CH_3)_2。     

Group ib organometallic chemistry : XXXIV. Thermal behaviour and chemical reactivity of tetranuclear Me2N-substituted diarypropenylcopper-copper anion (Vi2Cu4X2) and mixed diarylpropenyl/organocopper (Vi2Cu4R2) compounds

Thermal decomposition of configurationally pure 1,2-diarylpropenylcopper compounds Z-Vi₂CU₄Br₂ and Z-Vi₂Cu₄R₂ [Vi  (2-Me₂NC₆H₄)CC(Me)-(C₆H₄Me-4), R  2-Me₂NC₆H₄ or 4-MeC₆H₄CC] predominantly results in the formation of ViH. In contrast, only dimers (ViVi) were formed on thermolysis of (Z-ViCu₂OTf)_η which is a further illustration of the influence of the counter anion on the reactivity of organocopper cluster compounds. However, in both cases partial inversion of configuration, giving mixtures of isomers, was observed. The thermolysis of (Z-ViCu₂OTf)_η is discussed in terms of OTf-enhanced intraaggregate electron-transfer processes. The formation of incipient vinyl cations which are η²-coordinated to the copper cluster can explain the observed isomerization.Also in the hydrolysis reaction of Z-Vi₂Cu₄Br₂ mixtures of isomeric ViH compounds were obtained, the E/Z ratio being dependent on the type of reagent used. Mixtures of isomeric ViX compounds (X  Br, Cl, I) were formed in the reaction of Z-Vi₂Cu₄Br₂ with I₂ and CuCl₂. An explanation for the occurrence of isomerization is presented.Dimers (ViVi) were almost absent in the product mixture resulting from the reaction of Z-Vi₂Cu₄Br₂ with CuCl₂. In contrast, ViVi is obtained in about 50% yield from the reaction of ViLi with CuCl₂ which is in accord with earlier observations for the reaction of aryllithium compounds with cupric halides.Highly selective E-ViBr formation was observed in the reaction of E-ViLi with AgBr. This reaction probably proceeds via a thermally unstable Z-ViAg₂Br intermediate.