Electroweak tests with τ leptons at LEP

We report on two sensitive tests of lepton universality carried out by the 4 LEP experiments at the Z⁰ pole. From measurements of the τ polarization in e⁺ e^?→τ ⁺ τ ^?, the ratios of the vector and axial vector coupling constants of the electron and the tau lepton to the weak neutral current are obtained to beg _{v e} /g _{a e} =0.066±0.015 andg _{V τ} /g _{A τ} =0.070±0.009 respectively. From measurement of the τ lifetime and the τ leptonic branching ratios, the ratio of the coupling constants describing weak leptonic decays of the τ and the μ is measured to beG _τ /G _μ =0.996±0.008.     

Standard<Emphasis Type="Italic">SU</Emphasis>(5) supergravity grand unification model and predictions

A review is given of the StandardSU(5) supergravity model. This model has passed an important check regarding unification of the electro-weak and the strong couplings using high precision LEP data. It is shown that for a significant domain of the parameter space the model also satisfies constraints on the SUSY spectrum from CDF and LEP, as well as proton stability and cosmological relic density constraints.     

Synthesis, crystal structure, and properties of MnNCN, the first carbodiimide of a magnetic transition metal

Synthesis, single-crystal structure determination, and magnetic properties are reported for manganese carbodiimide, MnNCN. The presumably unstable but inert phase adopts the trigonal system (R3m) with a = 3.3583(4) A, c = 14.347(2) A, V = 140.13(3) A3, and Z = 3. Divalent manganese is octahedrally coordinated by nitrogen atoms at 2.26 A, and the NCN(2-) unit adopts the linear [N=C=N](2-) carbodiimide shape with two C=N double bonds of 1.23 A. MnNCN contains high-spin Mn(II) with five unpaired electrons and behaves like an antiferromagnet with an ordering temperature below 30 K.     

Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem

The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations, or even exact expressions, for the Fukui function for electron attachment.