Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

A stochastic model of the influence of buffer gas collisions on Mollow spectra

In this paper, using the idea introduced in (K. Wódkiewicz, Noise in strong laser-atom interaction, Proceedings of the VI International School of Coherent Optics, Ustron, Poland, September (1985) 19–26) and developed in (Cao Long Van, Stochastic Models of Isolated Collisions: Applications to Optical Phenomena, paper presented in LAMP Conference’89, Trieste, Italy (1989) II) we consider the influence of collisional fluctuations on the Mollow spectra of resonance fluorescence (RF). The fluctuations are taken into account by a simple shift of the constant detuning, involved in a set of optical Bloch equations by collision frequency noise which is modelled by a two-step random telegraph signal (RTS). We consider in detail the Mollow spectra for RF in the case of an arbitrary detuning of the laser frequency, where the emitter is a member of a statistical ensemble in thermodynamic equilibrium with the buffer gas at temperature T which is treated as a colored environment, and velocity v is distributed with the Maxwell-Boltzmann density.     

Plasmonic enhancement of blue emission from ZnO nanorods grown on the anodic aluminum oxide (AAO) template

Luminescent properties of ZnO nanorods covered with Ag nanoparticles are examined. Nanorods were synthesized on AAO templates using Atomic Layer Deposition (ALD) technique. Two types of the samples were prepared with different arrangement of ZnO nanorods and doping conditions. Nanorods of the second type were codoped with Al, to stimulate defect-related emissions. The ZnO material fills heterogeneously the interior of the AAO nanopores and has hexagonal, wurtzite structure. Both types of structures exhibit a broad defect-related emission at about 440 nm, most probably related to recombination at zinc interstitial (Zn_i) defects. This emission in samples with a random distribution of ZnO:Al nanorods and finer Ag nanoparticles is enhanced by factor of ～2.5 upon Ag deposition. The so-obtained material is interesting from the point of view of its application in blue range emitting diodes.     

On collinear Griffiths points

J. Tabov has proved [1] that four Griffiths points are collinear if the vertices of a given quadrangle are on a circle. In this article we prove some generalization of this result in a very simple geometrical way (based on Desargues theorem). Received 9 July 1999; revised 13 December 1999.     

On stochastic processes with linear conditional moments

In the paper, we show that a stochastic process with linear regression and linear conditional variance must be either a Gaussian process or a Poisson-type process. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

MCSCF calculation of response properties of Argon

Summary Analytic equations of the multiconfigurational SCF (MCSCF) response theory are combined with the finite-field (FF) approach to compute static and frequency dependent electric and magnetic properties of the Argon atom. A complete active space (CAS SCF) function including the 3s, 3p, 3d, 4s and 4p orbitals in the active space and a large (17s 13p 7d 5f 3g) basis set are employed. This permits an accurate determination of various linear and non-linear response properties such as e.g. electric dipole polarisability and second hyperpolarisability, Verdet constant, magnetisability and second hyperpolarisability. The results, both for the static values and for the frequency dependence of these properties, compare well with other most recent experimental and theoretical data.Dedicated to Jan Linderberg on the occasion of his 60th birthday     

On the structure of random plane-oriented recursive trees and their branches

This paper is an investigation of the structural properties of random plane-oriented recursive trees and their branches. We begin by an enumeration of these trees and some general properties related to the outdegrees of nodes. Using generalized Pólya urn models we study the exact and limiting distributions of the size and the number of leaves in the branches of the tree. The exact distribution for the leaves in the branches is given by formulas involving second-order Eulerian numbers. A martingale central limit theorem for a linear combination of the number of leaves and the number of internal nodes is derived. The distribution of that linear combination is a mixture of normals with a beta distribution as its mixing density. The martingale central limit theorem allows easy determination of the limit laws governing the leaves in the branches. Furthermore, the asymptotic joint distribution of the number of nodes of outdegree 0, 1 and 2 is shown to be trivariate normal. © 1993 John Wiley & Sons, Inc.     

Investigation of muonic hydrogen isotopes scattering from H2 molecule

Hyperfine Interactions - Knowledge of the cross sections for scattering of µp, µd and µt on molecules of hydrogen isotopes is necessary not only for checking the algorithmic solution...     

Influence of substituent length in dichroic dye molecules on the orientational properties of guest-host liquid crystal mixtures

The polarized absorption spectra of eight dichroic dyes, alkyl derivatives of 4-amino-(N-ethylnaphthalimide) dissolved in the nematic liquid crystals 5CB and 6CHBT have been measured as a function of temperature. On the basis of these spectra, the guest order parameter has been evaluated. The influence of the alkyl chain length of the dye molecule on the molecular orientation has been examined. Moreover, the nematic-isotropic transition temperatures for the dye-liquid crystal mixtures have been determined. The experimental results have been compared in some detail with calculations made on the basis of the mean field theory for binary mixtures.     

Acid-catalyzed Hydrolysis of the cis-[Cr(1,10-phenanthroline)2(O2CO)]+ Ion Studied by the u.v.–vis Stopped Flow Method

The cis-[Cr(phen)₂(O₂CO)]⁺ ion was prepared through the displacement of two molecules of water from the cis-[Cr(phen)₂(OH₂)₂]³⁺ by the bidentate carbonate anion. It underwent two-phase hydrolysis reactions under acidic conditions (0.1 < [H⁺] < 2.7 m) at 5, 10, 15, 20 and 25 °C. Via slow carbonato chelate ring opening (first step k₁^slow) and a second fast decarboxylation(k₂^fast value). The first step was preceded by protonation of the coordinate bidentate carbonate ligand. The second step exhibited no pH dependence, while k₁^slow values increased with acid concentration that suggested the presence of both protonated and deprotonated reactant species. Based on these observations we have proposed a hydrolysis mechanism featuring H₂O-induced ring-opening of the coordinate CO₃²⁻ group in the first step k₁^slow followed by loss of CO₃²⁻ from two intermediates, [Cr(phen)₂(O₂COH)]²⁺ (k₁^slow) and [Cr(phen)₂(OH₂)(O₂COH)]²⁺ (k₂^fast).