Comparative yields of alkali elements and thallium from uranium irradiated with GeV protons,3He and12C

Mass-separated ion beams of the alkali elements Na, K, and Fr, and of the element Tl, were produced by bombarding a uranium target with 600 MeV protons, 890 MeV³He^{2 +}, and 936 MeV¹²C^{4 +}. Isotopic production yields are reported. In the case of the¹²C beam, these are thick target yields. Absolute cross-sections for the proton beam data were deduced by normalizing the delay-time corrected yield curves to measured cross-sections. For products farthest away from stability, the³He^{2 +} beam generally gives the highest yields.     

A constructive method for uniform approximation by means of integrated Lagrange interpolation polynomials in the spaceC 1[a,b]

Пусть интерполяционные уз лыa <x ₁ <x ₂ < ... <х _n <b являются корнямиn-го полинома системы полиномов {w _n(x)} _n ^∞ =1, ортогонально й с весомρ(х), 0 < ρ(х) ∈L[a, b], причем 1/ρ(x) ∈L[a, b]. Доказано, что еслиf(х) ∈С ¹ [a, b], то проинтегрированн ые полиномы $$Q_n (x) = \smallint _a^x L_{n - 1} (f',t)dt + f(a)$$ интерполяционных по линомов Лагранжа $$L_{n - 1} (f,x) = \sum\limits_{k = 1}^n {f'(x_k )\frac{{\omega _n (x)}}{{\omega '_n (x_k )(x - x_k )}}}$$ порядкаn?1 функцииf′(x) сходятся равномерно к функцииf(х) в замкнуто м интервале [а,b]. Во второй части стать и, где вместо условия 1/ρ(х) ∈L[a, b] предполагается, чтоρ(х) ∈С ²[а, b],ρ(х) > 0,ρ′ (х) > 0, доказываются подобные утверждени я для проинтегрированных интерполяционных по линомов Лагранжа и для прибли жений рациональными дробя ми. В работе даются неулу чшаемые порядковые о ценки и описываются примене ния полученных результа тов в теории дифферен циальных уравнений.     

Diffusion approximations for the scattering of resonance-line photons: Interior and boundary layer solutions

Resonance-line scattering in static low density media with large optical thickness has a diffusive behavior in both space and frequency because photons belonging to the Lorentzian wings of the line may be scattered almost monochromatically a very large number of times. This diffusive behavior holds on frequency scales and spatial scales, χ_c and τ_c, much larger than the scales associated with one elementary scattering of a wing-photon.A method developed for diffusion approximations in neutron transport theory, suitably generalized to handle diffusion in frequency space, is applied to the case of conservative scattering in a bounded medium with interior sources and zero incoming radiation. The method is to separate the line radiation field into an interior part and a boundary layer part which goes to zero in the interior. Each part is expanded in terms of a small parameter ?, which is the ratio of the mean free-path at frequency χ_c to the characteristic spatial scale τ_c.It is shown that the leading term in the interior asymptotic expansion is isotropic, zero on the boundary, and obeys a space and frequency diffusion equation. In the boundary-layer expansion, the leading term is of order ? and is a solution to a monochromatic transfer equation in a semi-infinite, plane-parallel medium. The emergent radiation field is shown to be of order ? and proportional to the gradient of the interior solution at the boundary. Its angular dependence, in the case of isotropic scattering in the atom frame, is given by the Ambartsoumian H-function. A comparison is presented between numerical solutions of the full transfer equation and asymptotic solutions. Non-conservative scattering and time-dependent problems are briefly discussed.     

Elementary operators with H∞-symbols

Let T be a c.n.u. contraction on a Hilbert spaceH and let u-(u₁,...,u_n) be an n-tuple of H(T). We calculate various joint spectra of u(T) and apply the results to study the spectral and index theories of elementary operators associated with n-tuples of the above type.Both authors have been partially supported by NSF grants.     

An optimal semiclassical bound on commutators of spectral projections with position and momentum operators

Letters in Mathematical Physics - We prove an optimal semiclassical bound on the trace norm of the following commutators $$[{varvec{1}}_{(-infty ,0]}(H_hbar ),x]$$ , $$[{varvec{1}}_{(-infty...     

Casimir friction force between polarizable media

This work is a continuation of our recent series of papers on Casimir friction, for a pair of particles of low relative particle velocity. Each particle is modeled as a simple harmonic oscillator. Our basic method, as before, is the use of quantum mechanical statistical mechanics, involving the Kubo formula, at finite temperature. In this work we begin by analyzing the Casimir friction between two particles polarizable in all spatial directions, this being a generalization of our study in [J.S. Høye, I. Brevik, Europhys. Lett. 91, 60003 (2010)], which was restricted to a pair of particles with longitudinal polarization only. For simplicity the particles are taken to interact via the electrostatic dipole-dipole interaction. Thereafter, we consider the Casimir friction between one particle and a dielectric half-space, and also the friction between two dielectric half-spaces. Finally, we consider general polarizabilities (beyond the simple one-oscillator form), and show how friction occurs at finite temperature when finite frequency regions of the imaginary parts of polarizabilities overlap.     

Delayed fracture in porous media

The fracture of porous media subjected to a constant load is studied. Contrary to homogeneous solids in which fracture usually happens instantaneously at a well-defined breaking strength, the fracture of a porous medium can occur with a delay, allowing us to quantify the average lifetime of the unbroken material. We show that the average fracture probability, a key property for risk analysis in civil engineering, is given by the probability of crack nucleation. The nucleation process can be understood qualitatively by calculating the activation energy for crack nucleation, taking into account the porosity of the medium.     

New source of dense, cryogenic positron plasmas

We have developed a new method, based on the ballistic transfer of preaccumulated plasmas, to obtain large and dense positron plasmas in a cryogenic environment. The method involves transferring plasmas emanating from a region with a low magnetic field (0.14 T) and relatively high pressure (10(-9) mbar) into a 15 K Penning-Malmberg trap immersed in a 3 T magnetic field with a base pressure better than 10(-13) mbar. The achieved positron accumulation rate in the high field cryogenic trap is more than one and a half orders of magnitude higher than the previous most efficient UHV compatible scheme. Subsequent stacking resulted in a plasma containing more than 1.2 x 10(9) positrons, which is a factor 4 higher than previously reported. Using a rotating wall electric field, plasmas containing about 20 x 10(6) positrons were compressed to a density of 2.6 x 10(10) cm(-3). This is a factor of 6 improvement over earlier measurements.     

Electro-optic fiber sensor for amplitude and phase detection of radio frequency electromagnetic fields

We present a miniature fiber-optic electromagnetic field (EMF) sensor that is capable of simultaneously detecting the amplitude and phase of an EMF in the range of 0.1-6 GHz. We focus on magnetic field measurements, since the H-field is more significant in our target applications due its direct relation to the current. The sensor is based on an open optical platform to which various antennas can be attached and contains a radio-frequency amplifier for signal conditioning and a vertical-cavity surface-emitting laser as an electro-optic converter. The millimeter size and the full electrical isolation of the sensor allow EMF detection with minimal disturbance. We have characterized the sensor in the near field of a lambda/2 dipole, a rectangular waveguide, and a microstrip line, and we explain the experimental results with a simple theoretical model confirming the mapped near-field distribution of the investigated field source.