Die Anlagerung von radioaktiven Atomen und Ionen an Aerosolteilchen

The attachment of radioactive atoms and ions to spherical aerosol particles has been studied theoretically. For uncharged atoms the deposition is considered to be solely governed by thermal diffusion. With calculations based on the “limiting-sphere”-method ofArendt-Kallman it is found, that the attached activity is proportional toΦ ² for aerosol particle diametersΦ smaller than 0.1 μm, and proportional toΦ forΦ greater than 1 μm. For charged ions the diffusion process is modified by the influence of electrostatic forces between the diffusing ions and the aerosol particles. In the frequently occurring case of a symmetrically bipolar charged aerosol this influence can be expressed by a functionG _p(Φ), which depends on the diameterΦ and the effective numberp of elementary charges on the aerosol particle. For an aerosol particle diameterΦ greater than 0.1 μm the attached activity is proportional toΦ ^1.1, and forΦ smaller than 0.01 μm it is proportional toΦ ^1.55. The effects of neglecting various terms in the calculation are considered. The distribution of natural radioactivity on atmospheric aerosols has been calculated for various particle size distributions according toJunge. The calculation shows that about 90% of the total natural activity should be attached to particles smaller thanΦ=0.5 μm, and about 35% to particles smaller thanΦ=0.1 μm. The time T_1/2, in which the concentration of the radioactive particles decreases to half the initial value, depends on the concentration of the aerosol particles and on their size distribution. For 10⁴ aerosol particles per cm³ and the size distributions mentioned,T _1/2 varies between 15 and 30 seconds for radioactive ions. For radioactive atomsT _1/2 is greater than it is for ions in the range of aerosol particle diameters belowΦ=0.25 μm, and smaller ifΦ greater than 0.25 μm.     

Die Anlagerung radioaktiver Atome an Aerosole (Schwebstoffe)

The attachment of the decay products of thorium emanation to aerosol particles has been studied. The dependence of the attached activity on the particle size was determined for spherical particles with radiiR ranging from 0·04 to 0·6 microns. The particles used were homogeneous dioctylphthalate droplets and polystyrene micro-spheres. It is found that the attached activity is proportional toR ²/(1+hR). This dependence can be derived theoretically by considering the deposition to be solely governed by the diffusion process (not by electrostatic forces) and assuming a quasi-stationary density distribution for the diffusing atoms. The constanth is uniquely determined by the average gaskinetic velocity and the diffusion constant of the diffusing atoms. For the decay products of thorium and radium emanation (atomic weight ≈210)h ≈ 7 · 10⁴ cm^?1. The derived equation holds for a wide range of particle sizes: For the particles with radii larger than about 10^?4 cm this means that the attachment is proportional to the radius; for particle radii below about 10^?6 cm it is proportional to the surface (R²) of the particles. It is also possible to derive an expression for the time-dependence of the attachment process from the theoretical considerations. The rate at which the average concentration of the radioactive atoms decreases is proportional to exp ?t/τ where τ=1+hR/πR² N¯ v (¯ v=average gaskinetic velocity of the diffusing atoms;N=aerosol concentration).     

Dependence of the surface energy on the size and shape of a nanocrystal

An expression is derived for the surface energy σ as a function of the size and shape of a nanocrystal. It is shown that the wider the deviation of the shape parameter f from unity, the more pronounced the decrease in the surface energy σ with a decrease in the number N of atoms in the nanocrystal. The dependences of the average coordination number, the surface energy, and the melting temperature on the number N exhibit an oscillatory behavior with maxima at points corresponding to numbers of atoms forming a defect-free cube. The surface energy decreases with an increase in the temperature T. It is found that the smaller the nanocrystal size or the greater the deviation of the nanocrystal shape from the thermodynamically most stable shape (a cube), the larger the quantity-(dσ/dT). It is established that the nanocrystal undergoes melting when the surface energy decreases to a value at which it becomes independent of the nanocrystal size and shape. The conditions providing fragmentation and dendritization of the crystal are discussed. It is demonstrated that, at N>1000, the dependence σ(N) coincides, to a high accuracy, with the dependence of the surface tension of the nanocrystal on N. The inference is made that bimorphism is characteristic of nanocrystals. This implies that nanocrystals can have platelike and rodlike shapes with equal probability.     

Determination of nuclear excitation energies from the number of evaporated particles

The mean number ?N_b〉 of particles evaporated in the interaction of ²²Ne, ³²S, and ⁵⁶Fe nuclei with photoemulsion nuclei was measured as a function of the number of alpha particles emitted within the fragmentation cone. It is found that ?N_b〉 decreases with increasing number of the alpha particles and increases with increasing number of projectile nucleons involved in the interaction with a target nucleus and that ? N_b〉 is a linear function of the excitation energy E_ex of the target-nucleus residue. The maximum experimental value of the mean number of evaporated particles is ?N_bmax〉 ? 12–13, which corresponds to E_exc ? 540 ± 60 MeV.     

Chiral and deconfinement phase transitions in QED<Subscript>3</Subscript> with finite gauge boson mass

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and d-wave superconducting (dSC) phases, the influences of gauge boson mass m _a on chiral symmetry restoration and deconfinement phase transitions in QED₃ are investigated simultaneously within a unified framework, i.e., Dyson–Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass m _a is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors N ^c _f decreases as the gauge boson mass m _a increases, which implies that there exists a boundary that separates the N ^c _f –m _a plane into chiral symmetry breaking/confinement region for (N ^c _f , m _a ) below the boundary and chiral symmetry restoration/deconfinement region for (N ^c _f , m _a ) above it.     

Untersuchung des „Auroral Afterglow“ und seiner Präparationsstadien

The intensity decay of negative bands of N ₂ ⁺ and of first positive bands of N₂ in the auroral afterglow has been measured. An explanation, seeming possible for the decay curves of the first ones is proposed. By this the intensity decay in the beginning of the afterglow at high ionic densities is determined by the recombination of N ₂ ⁺ with electrons. Later, the ambipolar diffusion of the charge carriers to the wall causes the time dependance. A value of the ambipolar diffusion coefficient in nitrogen, derived from the measurements is given by the relationD _a ·p ≈ 124cm² sec^?1 Torr. The temperature of the charge carriers is estimated to be 313? K. The intensity decay of the pos. group in the afterglow seems mainly to be due to the diffusion of metastable particles to the wall.     

Proximity effect of a superconductor on an antiferromagnetic metal

There should be two contributions to the pair breaking energy in an antiferromagnetic metal. The first, already discussed byde Gennes andSarma, is due to disorder on the magnetic sites. The second is a temperature dependent contribution from electron magnon scattering. This term is calculated for the temperature rangeT _N(J/μ)²?T?T _N and found to be of orderT ²/T _N. (T _N = Néel temperature,μ = Fermi energy,J = exchange coupling between conduction electrons and magnetic ions.)     

Universal Low-energy Behavior in a Quantum Lorentz Gas with Gross-Pitaevskii Potentials

We consider a quantum particle interacting with N obstacles, whose positions are independently chosen according to a given probability density, through a two-body potential of the form N²V (Nx) (Gross-Pitaevskii potential). We show convergence of the N dependent one-particle Hamiltonian to a limiting Hamiltonian where the quantum particle experiences an effective potential depending only on the scattering length of the unscaled potential and the density of the obstacles. In this sense our Lorentz gas model exhibits a universal behavior for N large. Moreover we explicitely characterize the fluctuations around the limit operator. Our model can be considered as a simplified model for scattering of slow neutrons from condensed matter.     

On the superconducting transition temperature for metallic nanocrystals

A new approach is proposed for calculating the Debye temperature of a nanocrystal in the form of an n-dimensional rectangular parallelepiped with an arbitrary microstructure and the number of atoms N ranging from 2ⁿ to infinity. The geometric shape of the system is determined by the lateral-to-basal edge ratio of the parallelepiped. The size dependences of the Debye and melting temperatures for a number of materials are calculated using the derived relationship. The theoretical curves thus obtained agree well with the experimental data. The calculated dependences of the superconducting transition temperature T _c on the size d of aluminum, indium, and lead nanocrystals are also in reasonable agreement with the experimental estimates of T _c (d). It is demonstrated that, as the nanocrystal size d decreases, the greater the deviation of the nanocrystal shape from an equilibrium shape (in our case, a cube), the higher the temperature of the superconducting transition T _c (d). The superconducting transition temperature is calculated as a function of the thickness (diameter) of a plate (rod) with an arbitrary length. It is found that a decrease in the thickness (diameter) of the plate (rod) leads to an increase in the temperature T _c (z): the looser the microstructure of the metallic nanocrystal, the higher the temperature T _c (z).     

Intercluster conduction in lightly doped La<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript> manganites in the paramagnetic temperature range

The magnetotransport and magnetic properties of La _{1 ? x} Ca _x MnO₃ polycrystalline samples (x = 0–0.3) annealed under vacuum and in the oxygen environment are investigated in the temperature range from 77 to 400 K. The magnetic studies of lightly doped manganites reveal persistence of short-range magnetic order up to a temperature T* ≈ 300 K, which is about 2–3 times higher than their Curie temperature T _C. The temperature dependence of the electrical resistivity measured from T* down to nearly T ≈ T _C is fitted by the relation logρ ～ T ^?1/2, which is characteristic of granular metals with electrons tunneling among nanoclusters of magnetic metals embedded in a dielectric host. The magnetoresistance of polycrystalline samples annealed in the oxygen environment has been observed to increase. The electrical, magnetic, and magnetotransport properties of the manganites can be accounted for by the formation of magnetic nanoclusters below T*, tunneling (or hopping) of carriers among the nanoclusters, variation in the magnetic cluster size, and tunneling barrier thickness with variations in temperature and magnetic field strength, as well as by the effect of annealing in different media on the cluster properties.     

Ostwald ripening under conditions of mixed-type diffusion

The Ostwald ripening in metallic alloys and quasi-zero-dimensional semiconductor structures is investigated under conditions of mixed dislocation-matrix diffusion, when none of the terms j _d and j _v in the expression for the total diffusion flux can be ignored. The size distribution functions and time dependences of the maximum size r _g and critical (average) size r _k(〈r〉) of particles for different ratios x between the fluxes are obtained. It is demonstrated that mixed dislocation-matrix diffusion can occur in the course of the formation of CdS quantum dots prepared through chemical deposition.     

On the effect of heating and cooling rates on the melting and crystallization of metal nanoclusters

The effect of heating and cooling rates on melting (T_m) and crystallization (T_c) temperatures of metal nanoclusters is investigated in terms of the isothermal molecular dynamics. We report on the results obtained for nickel nanoclusters, although analogous results were also obtained for gold and aluminum nanoclusters. It is found that T_m increases, while T_c decreases with increasing heating and cooling rates, both T_m and T_c tending to the same value for heating and cooling rates tending to zero. The results indicate that the hysteresis of melting and crystallization of nanoparticles must be completely due to nonequilibrium conditions of heating and cooling. The transition of Ni nanoclusters to the amorphous state begins at very high cooling rates exceeding 10 TK/s.     

Quark microscopic picture for vector and pseudoscalar mesons in the nucleon and their quasielastic knockout by high-energy electrons

A technique for projecting a multiquark wave function in the microscopic model of a ³P⁰ scalar fluctuation onto the virtual-decay channels N → N + ρ and N → N + π is formulated (at a more general level for the latter than previously). The amplitude for the electromagnetic transition ρ + γ _T ^* → π in electron-induced quasielastic rho-meson knockout followed by rho-meson conversion to a pion is considered. Theoretical results obtained in this way are contrasted against available experimental data, and reasonable agreement is found for cross-section values. This confirms a universal character of the ³P₀ model. The precision of relevant experiments is as yet insufficient for comparing the momentum distribution of the rho meson from the channel N → N + ρ with its theoretical counterpart.     

GPU-accelerated simulation of colloidal suspensions with direct hydrodynamic interactions

Solvent-mediated hydrodynamic interactions between colloidal particles can significantly alter their dynamics. We discuss the implementation of Stokesian dynamics in leading approximation for streaming processors as provided by the compute unified device architecture (CUDA) of recent graphics processors (GPUs). Thereby, the simulation of explicit solvent particles is avoided and hydrodynamic interactions can easily be accounted for in already available, highly accelerated molecular dynamics simulations. Special emphasis is put on efficient memory access and numerical stability. The algorithm is applied to the periodic sedimentation of a cluster of four suspended particles. Finally, we investigate the runtime performance of generic memory access patterns of complexity O(N ²) for various GPU algorithms relying on either hardware cache or shared memory.     

Possibility of electrical conduction in filled bands

It is shown that a moving neutral particle interacting with electrons may cause an “electron drag” within a filled band. The calculation uses perturbation theory and periodic boundary conditions and is based on the one-electron model. WithN being the number and ¯v the average velocity of the electrons, one finds that for largeN the electronic velocity sumN¯v induced by the motion of the neutral particle is independent ofN, i.e. of the size of the system. The lowest-order contributions toN¯v that do not necessarily vanish are seen to be those of second order in the interaction potential. These second-order contributions are studied. In a simple one-dimensional model they are found to be, in fact, not necessarily zero and to be proportional to the velocity of the neutral particle. An order-of-magnitude formula forN¯v is derived for this case. The calculation suggests that mobile neutral particles may act as charge carriers, their effective charge possibly being much smaller than the elementary charge. In real systems, neutral particles which interact with electrons might be represented by phonons and excitons.     

Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model

The localization properties of eigenfunctions for two interacting particles in theone-dimensional Anderson model are studied for system sizes up to N = 5000 sitescorresponding to a Hilbert space of dimension ≈10⁷ using the Green function Arnoldi method. Theeigenfunction structure is illustrated in position, momentum and energy representation,the latter corresponding to an expansion in non-interacting product eigenfunctions.Different types of localization lengths are computed for parameter ranges in system size,disorder and interaction strengths inaccessible until now. We confirm that one-parameterscaling theory can be successfully applied provided that the condition of N being significantlylarger than the one-particle localization length L₁ is verified.The enhancement effect of the two-particle localization length L₂ behaving asL₂ ~ L₂¹ is clearly confirmed for a certain quite large intervalof optimal interactions strengths. Further new results for the interaction dependence in avery large interval, an energy value outside the band center, and different interactionranges are obtained.     

Investigation of the electronic properties of Au nanoclusters in SiO<Subscript>2</Subscript> by combined scanning tunneling/atomic force microscopy

The tunneling of electrons through Au nanoc lusters formed by pulsed laser deposition in a SiO₂ thin film on a Si substrate has been investigated by combined scanning/atomic force microscopy (STM/AFM). Conducting Pt-coated Si cantilevers were used. The feedback was maintained via the AFM channel, and the current-voltage (I-V) characteristics of the tunnel contact between the AFM probe and the n ⁺-Si substrate through a =4-nm-thick SiO₂ film with Au nanoclusters =2 nm in diameter were measured simultaneously. The current image of the structure contained areas of increased current (tunnel-current channels) 2–15 nm in size, related to tunneling of electrons through Au nanoclusters in SiO₂. The I-V characteristics recorded in the tunnel-current channels exhibit specific features related to the Coulomb blockade of electron tunneling through Au nanoclusters.     

Dynamical Formation of Correlations in a Bose-Einstein Condensate

We consider the evolution of N bosons interacting with a repulsive short range pair potential in three dimensions. The potential is scaled according to the Gross-Pitaevskii scaling, i.e. it is given by N ² V(N(x _i ? x _j )). We monitor the behaviour of the solution to the N-particle Schrödinger equation in a spatial window where two particles are close to each other. We prove that within this window a short-scale interparticle structure emerges dynamically. The local correlation between the particles is given by the two-body zero energy scattering mode. This is the characteristic structure that was expected to form within a very short initial time layer and to persist for all later times, on the basis of the validity of the Gross-Pitaevskii equation for the evolution of the Bose-Einstein condensate. The zero energy scattering mode emerges after an initial time layer where all higher energy modes disperse out of the spatial window. We can prove the persistence of this structure up to sufficiently small times before three-particle correlations could develop.     

Shape phase transitions in nuclei: Effective order parameters and trajectories

We analyze systematically the effective order parameters in nuclear shape phase transition both in experiments and in the interacting boson model. We find that energy ratios and B(E2) ratios can distinguish the first- from the second-order phase transition in theory above a certain boson number N (about 50), but in experiments, only those quantities, such as E(L ₁ ⁺)/E(0₂ ⁺) and B(E2; (L+2)₁ → L ₁)/B(E2; 2₁ → 0₁), etc., of which the monotonous transitional behavior in the second-order phase transition is broken in the first-order phase transition independent of N, are qualified as the effective order parameters. By implementing the originally proposed effective order parameters and the new ones, we find that the isotones with neutron number N _n = 62 are a trajectory of the secondorder phase transition. In addition, we predict that the transitional behavior of isomer shifts of Xe, Ba isotopes and N _n = 62 isotones is approximately monotonous due to the finiteness of nuclear system.     

Weyl’s Type Estimates on the Eigenvalues of Critical Schrödinger Operators

We consider on a bounded domain \(\Omega \subset {\mathbb{R}}^N\) , the Schrödinger operator ? Δ ? V supplemented with Dirichlet boundary solutions. The potential V is either the critical inverse square potential V(x) = (N ? 2)²/4|x|^?2 or the critical borderline potential V(x) =  (1/4)dist(x, ?Ω)^?2. We present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator in each case, based on recent results on improved Hardy–Sobolev type inequalities.