Improved (1s)<Superscript>2</Superscript> variational model for helium

The ground-state energy of neutral helium is estimated variationally with a trial wavefunction of the form ϕ≈e ^−γ(rA/a _o)ⁿe^−γ(rB/a _o)ⁿ. This model represents a modification of traditional textbook examinations of this problem via inclusion of the power “n” as a second nonlinear variational parameter in addition to the usual effective nuclear charge γ and leads to an upper-limit on the ground state energy of −2.86107 E _h (E _h =1 hartree) in comparison with the traditional (n=1) result of −2.84766 E _h . This result represents a reduction of the percentage overestimate from the true ground-state energy (−2.90373 E _h ) of from 1.93 to 1.47. In comparison with the maximum accuracy obtainable from an uncorrelated trial wavefunction, −2.86168 E _h , the present trial wavefunction reduces the percentage overestimate from 0.49 (n=1) to 0.021. The optimum values of (n, γ) are determined to be ≈(0.897, 1.825).     

Quality and the development of reference materials, including the role of traceability and comparability

The global recognition that quality is an economic issue is requiring analytical chemists to look at the chemical measurement process in a way that has not been done before. Much work has been done in certifying reference materials, writing measurement protocols, creating measurement networks, developing analytical measurement techniques and other efforts to make good measurements. This article explores the meaning of quality in chemical measurements and discusses quality in terms of credibility, reliability, traceability and comparability. The importance of understanding the contribution of comparability and traceability to quality in chemical measurements and chemical metrology is emphasized.     

Group Theoretic Properties of the Group of Computable Automorphisms of a Countable Dense Linear Order

We compare Aut(Q), the classical automorphism group of a countable dense linear order, with Aut _c (Q), the group of all computable automorphisms of such an order. They have a number of similarities, including the facts that every element of each group is a commutator and each group has exactly three nontrivial normal subgroups. However, the standard proofs of these facts in Aut(Q) do not work for Aut _c (Q). Also, Aut(Q) has three fundamental properties which fail in Aut _c (Q): it is divisible, every element is a commutator of itself with some other element, and two elements are conjugate if and only if they have isomorphic orbital structures.     

Cation transport at 25°c from binary Tl+Mn+ and K+Mn+ nitrate mixtures in a H2OCHCl3H2O liquid membrane system containing a series of macrocyclic polyether carriers

Carrier-mediated cation fluxes were determined using a H₂OCHC1₃H₂O liquid merebrane system for TlNO₃ and for binary mixtures of either TlNO₃ or KNO₃ with alkali metal ions, alkaline earth metal ions, and Pb²⁺ (in the case of TlNO₃). Both macrocyclic polyether and cryptand ligands were used as carriers. In Tl⁺Mⁿ⁺ mixtures, selective transport of Tl⁺ was found over all cations studied, except in the cases of Ag⁺ by 2.2 and of Pb²⁺ by 18C6, DC18C6, ClDKP18C6, and 2.2. Generally, K⁺ was transported selectively from K⁺Mⁿ⁺ mixtures, except in the cases of K⁺Tl⁺ mixtures in which Tl⁺ was transported selectively in all cases. A model relating cation flux to log K(CH₃OH) for Mⁿ⁺—macrocycle interaction and to ion-partitioning between the organic and aqueous phases was successful in rationalizing selective cation transport in most of the systems studied.     

Fermions coupled to autonomous (λΦ 4)3+1 theory

Recent Gaussian-effective-potential results for “autonomous”λΦ ⁴ theory, an apparently nontrivial, positive-λ, 3+1 dimensional theory, are extended to include a Yukawa coupling to fermions. The formerly massless bosons of the symmetric phase acquire a mass.     

The scattering of classical waves from inhomogeneous media

By extending Kato's theory of two Hilbert space scattering, we are able to formulate both optical and accoustical scattering from inhomogeneous media as strictly elliptic problems. We use this formulation to present simple proofs of the existence and completeness of scattering states.