An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –} , whered is the space dimensionality and>0. It allows for a unified treatment of short-range (=2) and long-range (<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^d–d× ^d subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd, 0d. It is shown that the-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

Interfacial free energies and solute diffusivities from data on Ostwald ripening

Using recent theoretical modifications of the kinetic constants characterizing Ostwald ripening, it is demonstrated that accurate values of the interfacial free energy, , and solute diffusivities, D, can be obtained from experimental data when the kinetics of particle growth are measured in conjunction with independent measurements of either the decrease of the matrix supersaturation or the increase in volume fraction with aging time. The accuracy of is limited only by the assumption that the matrix phase is an ideal solid solution, and is effectively independent of the influence of equilibrium volume fraction, _e, on the kinetics of coarsening. Analyses of the available data on the coarsening of -type (Ni₃X) precipitates in binary Ni–Al, Ni–Si and Ni–Ti alloys yield values of =6.9±0.3, 10.2±3.0 and 13.0 mJ/m², respectively, assuming ideal solution thermodynamics; a more realistic thermodynamic model for the Ni–Al solid solution raises the value of in Ni–Al alloys to 8.1±0.2 mJ/m². Proportional increases probably obtain in the other two alloys. The accuracy with which D can be evaluated from comparable data depends theoretically on _e. However, analyses of the same data yield values of D in very good agreement with the results of conventional diffusion experiments. This is consistent with the absence of an effect of _e on the kinetics of Ostwald ripening in these alloys over the ranges of _e investigated.     

α-Particle Loss from Cylindrical Magnetized DT Plasma

-particles from fusion reactions in a DT magnetized plasma are confined inside the plasma not only by magnetic fields but also by induced electric fields which are due to the different mobilities of -particles and electrons. Criteria are derived for the -confinement in a cylindrical plasma, inertially confined by a heavy liner. It is observed that the suprathermal population in the DT plasma will influence the overall dynamics.     

Theta-point exponent for polymer chain in random media

Using field-theoretic arguments for self-avoiding walks on dilute lattices with site occupation concentrationp, we show that the-point size exponent _p ⁰ of polymer chains remains unchanged for small disorder concentration (p>p _c ). At the percolation thresholdp=p _c , using a Flory-type approximation, we conjecture that _pc ⁰ =5/(d _B +7), whered _B is the percolation backbone dimension. It shows that the upper critical dimensionality for the-point transition atp=p _c shifts to a dimensiond _c >3. We also propose that the-point varies practically linearly withp for 1>pp _c .     

Beta-decay studies of neutron-rich Sc- Cr nuclei

The neutron-rich nuclei ₂₁^{57, 58}Sc, ₂₂^58-60Ti, ₂₃^60-63V, ₂₄^62-66Cr have been produced at Ganil via interactions of a 61.8A MeV ⁷⁶Ge beam with a ⁵⁸Ni target. Beta-decay studies have been performed using combined - and -ray spectroscopy. Half-lives have been determined and -decay schemes are proposed for ⁵⁸Ti, ⁶¹V and ⁶²Cr. From these studies, new hints for the existence of -decaying isomers in ⁶⁰V and in ⁶²Mn are provided. These results are compared to shell model calculations. The role of the f_7/2- f_5/2 proton-neutron interaction is examined through its influence on the lifetime values.     

Alpha-decay of neutron-deficient 200Fr and heavier neighbours

A new measurement of the ²⁰⁰Fr -decay half-life, with improved accuracy compared to previous measurements, has been carried out at the Isolde-CERN on-line mass separator. A half-life of 49(4) ms has been obtained, which is substantially different from earlier literature values. For the ¹⁹⁶At daughter decay, a half-life of 389(54) ms and an branching ratio b = 94(5)% were measured. In addition, the half-lives of ^{201, 203, 205}Fr and ^197,199At are reported.     

Quantum particle-like configurations of the electromagnetic field

We construct explicitly three-dimensional localized solutions of the free Maxwell's equations with a phase expi(k x - t) which move like relativistic particles. The total field energyE of the moving lump is proportional to the frequency and its momentumP is proportional to the wave vectork, withE ² =P ² +M ². Further, if the angular momentum is different from zero, thenE =. These solutions thus model the wave-particle duality of quantum particles.     

On the efficiency of small-angle Čerenkov second harmonic generation in optical waveguides

It is well known that in the non-depleted pump approximation, the efficiency of a second harmonic generation (SHG) of a guided mode in a non-linear optical waveguide increases quadratically with the interaction length (P ₂ L ²), and linearly (P ₂ L) in the erenkov regime. The efficiency of the erenkov SHG in the waveguide with a non-linear substrate and linear guiding layer is known to be strongly peaked at a particular pump wavelength and a particular waveguide thickness, with the erenkov angle approaching zero. The known theory predicts an infinite efficiency value at the peak, however. In this contribution, a simple integral expression for the SHG efficiency in the erenkov regime is derived. For large erenkov angles and interaction lengths it yields the expected P ₂ L dependence, while in the limit of small erenkov angles the dependence is found to have the form of P L ^3/2, possessing also a finite value at the efficiency peak. The condition determining the accurate position of the efficiency peak in the waveguide thickness–pump wavelength plane is given, too.     

Photometric and fluorimetric study of the acid-base behavior of 2,2′-diquinolyl and 2,2′,2″-terpyridyl

A photometric and fluorimetric study of the acid-base behavior of 2,2-diquinolyl and 2,2,2-terpyridyl was performed. In sulfuric acid medium, the doubly charged 2,2-diquinolynium ion undergoes the first dissociation atH ₀=0.20±0.09, as determined by fluorimetry (_ex=336 nm, _em=424 nm). Photometric titration is less accurate because of the overlapping of the absorption spectra. The second dissociation constant of 2,2-diquinolyl was determined by fluorimetric titration (_ex=336 nm, _em=420 nm), obtaining a value of 3.67±0.03. The triply charged 2,2,2-terpyridyl molecule was found to undergo the first dissociation atH ₀=–7.17±0.04, as determined by fluorimetric titration (_ex=316 nm, _em=350 nm), in aqueous sulfuric acid medium. Photometric titration (=335 nm) was performed in the presence of 6.5% ethanol because of the low solubility of the compound in water. In this ethanolicwater medium, a value of the dissociation constant atH ₀=–7.39±0.03 was calculated. The second dissociation constant was determined to be 2.81±0.12 by photometric titration at 285 nm, and values of 4.03±0.26 and 4.16±0.20 were found for the third dissociation constant by photometric titrations at 320 and 295 nm, in 10% ethanol, in close agreement with previously reported values. The fluorimetric titration profile obtained by exciting at 274 nm and measuring the fluorescence emission at 350 nm, in the zone betweenH ₀=–3 and pH=10, is complicated by the several equilibria involved.     

Faceting of Σ3 and Σ9 Grain Boundaries in Copper

Faceting is a well documented phenomenon known both for surfaces and interfaces, particularly, grain boundaries (GBs). Faceting can be considered as a phase transition when the original surface or GB dissociates onto flat segments whose energy is less than that of the original surface or GB. For the investigation of GB faceting a cylindrical Cu bicrystal with an island grain was grown by the Bridgman technique. Grain 1 in this bicrystal is completely surrounded by grain 2. The dissociation 9 3 + 3 proceeds during the growth of the bicrystal. The twins appear instead of {111}₁/{115}₂ or (110)_9CSL facet. GB faceting was studied at 1293 K, 1073 K, and 873 K. The profiles of the GB thermal groove were analysed by atomic force microscopy. Wulff-Herring plots and GB phase diagrams have been constructed for the 3, 9 and 9 + 3 GBs. With increasing temperature the facets with low-density CSL-planes disappear in the GB shape. GB roughening phase transition can be responsible for this phenomenon.     

The correlation function in Wilson's theory of phase transitions: Above and below the transition

The correlation function and the correlation length are discussed in the theoretical framework of the Wilson-Feynman diagram expansion for small =4–d. It is shown explicitly that to order ² the scaling relation = (2–) is satisfied and that the correlation function is a homogeneous function ofk and . The explicit form of the scaled correlation function is exhibited.     

Manifestation of Extracoordination in the Resonance Raman Spectra of Water‐Soluble Cation Co‐Porphyrins

Resonance Raman spectra (RRS) of Co(II) and Co(III)5,10,15,20tetrakis(4Nmethylpyridinium)porphyrin ((Co^II(TmpyP4), and Co^III(TMPyP4)) in aqueous solutions at different pH as well as in organic solvents (methanol, ethanol, DMSO, DMF) are obtained. The increased sensitivity of the oscillation frequencies ₂, ₄, ₈, and ₆ — the markers of the oxidation state of a metal — to the nature of an axial ligand has been revealed. For Co^III(TmpyP4), the shifts of the indicated frequencies in extracoordination have turned out to be twofold larger than those for Co^II(TmpyP4). The spectral effects observed are related to different electron influence of the extraligands on the system of the porphyrin ring. In the case of Co(III)porphyrin, interaction of the d orbitals of the metal and the e _g ^*orbitals of the macrocycle is more efficient since its ionic radius is smaller than for the Co(II)complex. For Co^III(TmpyP4), a linear correlation between the oscillation frequencies ₂, ₄, ₈, and ₆ and the experimental Gutmann parameters characterizing the electronacceptor properties of solvents is found.     

EC and α decays of 235Am

EC and decays of ²³⁵Am have been studied using a gas-jet coupled on-line isotope separator. Excited states in ²³⁵Pu have been established for the first time by means of -ray spectroscopy following the EC decay of ²³⁵Am. The deduced log ft value suggests that the ground state of ²³⁵Am should have the 5/2^-[523] configuration. The - coincidence result has revealed that the 5/2^-[523] state in ²³¹Np populated by the favored transition of ²³⁵Am is located at < 15 keV, which allows us to precisely determine the Q value of ²³⁵Am.     

Measurements of 110Xe and 106Te decay half-lives

The -decays of ¹¹⁰Xe and ¹⁰⁶Te were studied at the GSI on-line mass separator. By using the grow-in and decay of the activity, observed in pulsed-beam measurement, the half-life of ¹¹⁰Xe was found to be T_1/2 = 105⁺³⁵_-25ms. The lifetime of ¹⁰⁶Te was determined to be T_1/2 = 70⁺²⁰_-10s by measuring the time between two successive ¹¹⁰Xe ^{106} Te ^{102} Sn -decays. The newly determined half-lives were used to calculate reduced -decay widths for ¹⁰⁶Te and ¹¹⁰Xe. Universal systematics of reduced widths are proposed to search for the evidence of enhancement of the formation amplitude in the emitters above ¹⁰⁰Sn.     

Optical Pumping of Samarium Atoms in a Bichromatic Laser Field in the Presence of Velocity-Changing Collisions

Dark resonances in the ¹⁵⁴Sm -system 4f ⁶6s ²(⁷ F ₀) 4f ⁶6s6p(⁹ F ₁ ⁰) 4f ⁶ s ²(⁷ F ₁) are observed alongside the velocity selective optical pumping. The shape of the resulting spectra strongly depended on the buffer gas (He, Ar) pressure due to velocity-changing collisions (VCC): the sign of the effect could be reversed from the dark to the bright resonance. The observed spectra are interpreted within the framework of the hard-sphere collision model. The role of VCC in the formation of the dark state in the -system is discussed.     

Finite-size effects in a field-theoretic model with long-range exchange interaction

We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/r ^d+2–2,0⁺,0⁺. Renormalization group calculations ind=d _u – are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.     

Shearing apparatus for neutron scattering studies on fluids: Preliminary results for colloidal suspensions

In this paper we study the transient diffusion-limited A+B0, A₀ = B₀ annihilation via deterministic reaction-diffusion equations and via simulation of the stochastic many-particle problem. We show that the two approaches are not equivalent and that the deterministic expressions capture only part of the picture. A lower bound is derived for the density decay which indicates that the overall density follows the power law t^–x with = mm(d/4, 1). Hierarchical oscillations superimposed on the power-law decay are observed for reactions on Sierpinski gaskets.This work is dedicated to Prof. George H. Weiss.     

Intrinsical Randomness of Kolmogorov ℤd-Actions on a Lebesgue Space

We introduce a concept of an intrinsically weak and strong randomness of a ^d -action on a Lebesgue space and we show that Kolmogorov ^d -actions are intrinsically weak random, and Bernoulli ^d -actions are intrinsically strong random.     

Collective structures of the <Superscript>131</Superscript>Cs nucleus

The collective structures of ¹³¹Cs have been investigated by in-beam -ray spectroscopic techniques following the ¹²⁴Sn (^11B , 4n) reaction at a beam energy E_lab = 57MeV. The previously established rotational bands, built on g_7/2, d_5/2 and the unique-parity h_11/2 orbitals, have been extended and evolve into new bands involving rotationally aligned (h_11/2)² and (h_11/2)² quasiparticles. In addition, a new multiquasiparticle band based on the g_7/2 g_7/2 h_11/2 configuration has also been observed. Theoretical interpretations for the assigned configurations are discussed in the framework of Total Routhian Surface (TRS) and Tilted Axis Cranking (TAC) model calculations. TAC model calculations predict a decrease in the B(M1) values with increasing rotational frequency for the g_7/2/d_5/2 (h_11/2)² and h_11/2 (h_11/2)² bands, thus indicating a magnetic rotation character for these bands.     

Decay studies of <Superscript>214-216</Superscript>Ac by α- γ- γ-coincidences

The -decay fine structure of ²¹⁴Ac, ²¹⁵Ac and ²¹⁶Ac has been studied using the --coincidence technique. The nuclei were produced by ²⁰⁹Bi( ¹²C, xn)^221-xAc-reactions. Evaporation residues were separated in-flight from the primary beam using the velocity filter SHIP at GSI, Darmstadt. The separated nuclei were implanted into a position-sensitive 16-strip PIPS Si detector and their subsequent decays were measured. In these studies new and improved decay data for ^214-216Ac were obtained.