The long range intermolecular potential of H2-H2

Approximately 250 lines of the CaO c ³Σ⁺-a ³Π (0, 0) band have been resolved using sub-Doppler intermodulation spectroscopy and the principal molecular constants of the c ³Σ⁺ (2³Σ⁺) state determined. These results will be of particular value to those wishing to use laser induced fluorescence population diagnostics for all six Ω, e/f components of the a ³Π state. Accurate rotational linestrengths for all branches of the c ³Σ⁺-a ³Π (0,0) transition, computed from eigenvectors of the effective hamiltonians, are presented. Extreme localization of the CaO valence orbitals on either the Ca or the O centre has permitted simple and accurate estimates to be made of fine-structure-determining matrix elements and the locations of unobserved electronic states, including the use of results from CaF to describe the properties of Ca-centred orbitals in CaO. Isoconfigurational second-order spin-orbit arguments, applied to the observed value of the effective spin-spin constant (λ₀) for the c ³Σ⁺ ν = 0 state, lead to confirmed predictions of the previously unknown locations of the E ¹Σ^- (1¹Σ^-) and e ³Σ^- (1³Σ^-) states and of the value of λ₀(e ³Σ^-). Assignments are made of nearly all band features in the CaO orange band spectrum.     

Introduction to 𝒫𝒯-symmetric quantum theory

In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a Hamiltonian, one writes H?=?H ^?, where the symbol ? denotes the usual Dirac Hermitian conjugation; that is, transpose and complex conjugate. In the past few years it has been recognized that the requirement of Hermiticity, which is often stated as an axiom of quantum mechanics, may be replaced by the less mathematical and more physical requirement of space?–?time reflection symmetry (𝒫𝒯 symmetry) without losing any of the essential physical features of quantum mechanics. Theories defined by non-Hermitian 𝒫𝒯-symmetric Hamiltonians exhibit strange and unexpected properties at the classical as well as at the quantum level. This paper explains how the requirement of Hermiticity can be evaded and discusses the properties of some non-Hermitian 𝒫𝒯-symmetric quantum theories.     

Spectroscopy and single-particle structure of the odd- Z heavy elements 255Lr, 251Md and 247Es

The odd-Z isotope ²⁵⁵Lr, its daughter ²⁵¹Md and grand-daughter ²⁴⁷Es were studied in two experiments performed at GANIL and the University of Jyv?skyl?. The ²⁵⁵Lr nuclei were produced using the cold fusion-evaporation reaction ²⁰⁹Bi(⁴⁸Ca, 2n)²⁵⁵Lr at a bombarding energy of 217MeV. The single-particle structure and decay properties were investigated using α, γ and electron spectroscopy. The ground-state spin and parity could be assigned for ²⁵⁵Lr (1/2^-) and ²⁵¹Md (7/2^-). States corresponding to the 7/2⁺[633], 7/2^-[514] and 1/2^-[521] Nilsson orbitals were observed. Results are compared to experimental data obtained in neighbouring isotopes and to Hartree-Fock-Bogoliubov calculations using the Skyrme interaction SLy4 and a density-dependent pairing interaction. The position of the 1/2^-[521] orbital from the spherical 2f _5/2 shell is discussed.     

Synthesis of low polydispersity polybutadiene and polyethylene stars by convergent living anionic polymerization

Star‐shaped polybutadiene stars were synthesized by a convergent coupling of polybutadienyllithium with 4‐(chlorodimethylsilyl)styrene (CDMSS). CDMSS was added slowly and continuously to the living anionic chains until a stoichiometric equivalent was reached. Gel permeation chromatography‐multi‐angle laser light scattering (GPC‐MALLS) was used to determine the molecular weights and molecular weight distribution of the polybutadiene polymers. The number of arms incorporated into the star depended on the molecular weight of the initial chains and the rate of addition of the CDMSS. Low molecular weight polybutadiene arms (M_n = 640 g/mol) resulted in polybutadiene star polymers with an average of 12.6 arms, while higher molecular weight polybutadiene arms (M_n = 16,000 g/mol) resulted in polybutadiene star polymers with an average of 5.3 arms. The polybutadiene star polymers exhibited high 1,4‐polybutadiene microstructure (88.3–93.1%), and narrow molecular weight distributions (M_w/M_n = 1.11–1.20). Polybutadiene stars were subsequently hydrogenated by two methods, heterogeneous catalysis (catalytic hydrogenation using Pd/CaCO₃) or reaction with p‐toluenesulfonhydrazide (TSH), to transform the polybutadiene stars into polyethylene stars. The hydrogenation of the polybutadiene stars was found to be close to quantitative by ¹H NMR and FTIR spectroscopy. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 828–836, 2006     

Calculating the C Operator in PT-symmetric Quantum Mechanics

It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition it is cumbersome to calculate C in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method can be used to calculate the C operator in quantum field theory. The C operator is a new time-independent observable in PT-symmetric quantum field theory.     

Maximal Inequalities for Fractional Lévy and Related Processes

In this article we study processes that are constructed by a convolution of a deterministic kernel with a martingale. A special emphasis is put on the case where the driving martingale is a centred Lévy process, which covers the popular class of fractional Lévy processes. As a main result we show that, under appropriate assumptions on the kernel and the martingale, the maximum process of the corresponding “convoluted martingale” is p-integrable and we derive maximal inequalities in terms of the kernel and of the moments of the driving martingale.     

PREPARATION OF LARGE-PARTICLE-SIZE MONODISPERSE LATEXES IN SPACE: POLYMERIZATION KINETICS AND PROCESS DEVELOPMENT

Monodisperse polystyrene latexes are prepared by seeded emulsion polymerization; however, sizes larger than 2μm are difficult to prepare because of the creaming and settling of the particles, and their sensitivity to mechanical shear. Preparation in space would obviate the creaming and settling, and allow agitation just sufficient for good heat transfer and mixing. Three polymerizations yielding 3-5μm size particles were carried out successfully on the third flight of the “Columbia” launched March 22, 1982; however, four polymerizations yielding sizes up to 10μm on the fourth flight launched June 27, 1982, were incomplete owing to apparatus malfunction. The results of these polymerizations and the prospects of developing a preparative space process are reviewed     

Characterization of SIPOS films by spectroscopic ellipsometry and transmission electron microscopy

The structural and compositional properties of undoped SIPOS thin films have been studied by spectroscopic ellipsometry and transmission electron microscopy. It is shown that in most cases the former method provides fast and reliable results. The growth rate and crystallinity of SIPOS layers are studied as a function of N₂O concentration in the gas phase and annealing temperature.