Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

Interpolation and extrapolation of gamma detection efficiency curve as a function of distance

Summary The paper deals with the common mistake of interpolating calculation of the efficiency of gamma-detectors by the inverse square law of the distance of the source from the detector cap and suggests the use of the distance from the virtual point detector instead.     

A two-fraction model for the calculation of the resonance spectra of the complex permittivity of ice in the far infrared

A two-fraction model that makes it possible to calculate analytically the complex dielectric permittivity of ice in the far infrared and submillimeter wavelength ranges is proposed. The librational and vibrational fractions are considered. The first fraction, consisting of rigid dipoles executing anharmonic reorientations in defects of the structure, gives rise to the librational band of ice at 800 cm^?1. The second fraction consists of elastically vibrating oppositely charged H-bonded molecules. This fraction describes two bands of ice in the range 100–300 cm^?1, and the nonresonant background of dielectric losses in the submillimeter wavelength range. The dielectric permittivity spectra of ice calculated for the temperature of ?7°C are consistent with the experimental spectra. The spectra of ice at the temperature ?30°C are predicted.     

On the model of divacancies in germanium

A model of a divacancy which explains a number of experimental facts for Ge exposed to a flow of accelerated electrons at temperature T=77 K is proposed. The model explains the absence of photoconduction associated with photoexcitation of infrared absorption bands at 0.44 and 0.52 eV corresponding to divacancies; the difference in the values of activation energy for divacancy energy levels determined by optical and electrical methods; and the existence of the limiting position of the Fermi level in the forbidden gap in the case of irradiation with large radiation fluxes.     

On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ⁻¹. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx). Received: 30 June 2000 / Accepted: 25 June 2001     

An improved injector bunching geometry for ATLAS

The bunching system of the ATLAS positive ion injector (PII) has been improved by relocating the harmonic buncher to a point significantly closer to the second stage sine-wave buncher and the injector LINAC. The longitudinal optics design has also been modified and now employs a virtual waist from the harmonic buncher feeding the second stage sine-wave buncher. This geometry improves the handling of space charge for high-current beams, significantly increases the capture fraction into the primary rf bucket and reduces the capture fraction of the unwanted parasitic rf bucket. Total capture and transport through the PII has been demonstrated as high as 80% of the injected dc beam while the population of the parasitic, unwanted rf bucket is typically less than 3% of the total transported beam. To remove this small residual parasitic component a new traveling-wave transmission-line chopper has been developed reducing both transverse and longitudinal emittance growth from the chopping process. This work was supported by the U.S. Department of Energy under contract W-31-109-ENG-38.     

Polarization experiments with the SPIN setup at the ITEP synchrotron

New experimental data on the spin-rotation parameters A and R measured for elastic π ^± p scattering in the resonance region and on the asymmetry in pC scattering at primary momenta in the range 1.35–2.02 GeV/c, as well as in quasielastic proton scattering on nuclei in the same momentum range, are summarized. All these data were recently obtained by using the proton synchrotron installed at the Institute of Theoretical and Experimental Physics (ITEP, Moscow). The spectrum and features of seven isospin-3/2 baryon resonances that form a peak in the total cross section at a c.m. energy of 1.9 GeV are analyzed on the basis of new data on the parameters A and R, and the results of this analysis are presented. The experiments surveyed in this article were performed by a collaboration of researchers from ITEP and the Petersburg Nuclear Physics Institute (PNPI, Gatchina), the ITEP-PNPI collaboration.     

Spectra of second-order Raman scattering in porous silicon

Spectra of second-order Raman scattering in porous silicon are investigated. A band shift towards lower energies in second-order spectra is observed, as well as the correlation between the values of band shift in first-and second-order spectra. It is demonstrated that the observed effect cannot be interpreted using the conventional concepts of the mechanisms of scattering in microcrystalline samples. An interpretation of the revealed effect is suggested.