Derivation of extended boundary condition method from general definition of -matrix elements and Lippman–Schwinger equation for transition operator

Waterman's surface-integral expressions for the T-matrix elements are derived on the basis of the quantum-mechanical potential scattering approach in electromagnetic scattering problem. We use general definition of the elements of the T-matrix as the matrix elements of the dyadic transition operator and Lippman–Schwinger volume integral equation for the dyadic transition operator. The interrelations of the Q- and Waterman's T-matrix with the transition operator are shown.     

The statistics of derangement—A survey

Given a finite setX of elements, divided into disjoint subsets, we define a derangement ofX as a permutation which leaves none of the elements in their original subsets. The probability of a random permutation being a derangement is discussed, particularly its asymptotic value as the cardinality ofX and the number of subsets tend, under certain conditions, to infinity. Finally, the problem is extended to studying the number of elements which are transferred by a general permutation to a subset other than their initial one.This paper is dedicated to Cyril Domb, in friendship.     

Parton distributions for LO generators

We present a study of the results obtained by combining LO partonic matrix elements with either LO or NLO parton distributions. These are compared to the best prediction using NLO for both matrix elements and parton distributions. The aim is to determine which parton distributions are most appropriate to use in those cases where only LO matrix elements are available, e.g. as in many Monte Carlo generators. Both LO and NLO parton distributions have flaws, sometimes serious, for some processes, so a modified optimal LO set is suggested. We investigate a wide variety of processes, and the new modified LO* PDF works at least as well as, and often better than, both LO and NLO PDFs in nearly all cases.     

Matrix elements for the representations of SO(n) and SO0(n, 1)

Matrix elements of the unitary irreducible representations of the group SO(n) of class higher then 1 (with respect to SO(n−1)) in Gel'fand-Zetlin basis are obtained in explicit form. They are represented as polynomials in cosθ and sinθ of the order equal to the first coordinate of the highest weight. Making use of them the representation matrix elements for the group SO₀(n, 1) in SO(n) basis are calculated.     

Elimination of Rotational Degrees of Freedom in Expansion Methods for Three Nucleons

 Euler angles determining rotations of a system as a whole are conveniently separated in three-particle basis functions. Analytic integration of matrix elements over Euler angles is done in a general form. Results for the Euler angle integrated matrix elements of a realistic NN interaction are listed. The partial wave decomposition of correlated three-body states is considered. E-mail address: efros@mbslab.kiae.ru Received May 4, 2002; accepted July 26, 2002     

Sum rule estimate of the subleading non-perturbative contributions to Bs–$\bar{ B}_{s}$ mixing

We use QCD sum rules to compute the matrix elements of the ΔB=2 operators appearing in the heavy-quark expansion of the width difference of the B _s mass eigenstates. The main focus of our analysis is on the subleading operators R ₂ and R ₃, which appear at next-to-leading order in the 1/m _b expansion. The matrix elements of these operators are already essential for precise phenomenology, but their calculation in lattice QCD is lacking and the values given here provide a first estimate of their values. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1–2%.     

Calculation of Oscillator Strength in the Sc I-Spectrum

The oscillator strengths of the main transition from the 3d 4s 4p-states to the groundstate 3d 4s² of Sc I are calculated on using wave functions derived by diagnolization of the interaction matrix elements of the 3d 4s 4p-, 3d² 4p- and 4s² 4p-configurations. The relevant dipole matrix elements are reduced by application of tensor algebra to the unknown one-electron matrix elements 〈4s‖r‖4p> and <3d‖r‖4p〉. These radial integrals are calculated from experimental lifetimes and oscillator strengths as well as from theoretical models. The resulting absolute oscillator strengths show a fairly good agreement with the experimental data, the uncertainties being smaller than 10 percent for the strongest transitions.     

Sharply Dominating MV-Effect Algebras

Some open questions on Archimedean atomic MV-effect algebras are answered. Namely we prove that there are Archimedean atomic MV-effect algebras which are not sharply dominating. Equivalently, they don’t have a basic decomposition of elements. Moreover, if their set of sharp elements (their center) is a complete lattice then they need not be complete lattices. The existence of infinite orthogonal sums of their elements is discussed.     

The influence of polarization and filtration of beams on the ED spectrometers sensitivity

The topic under discussion is the influence of X‐ray polarization and filtration, as well as the influence of detectors count rate on sensitivity and detection limits (DLs) in spectrometers with energy dispersion (EDS). Parameters calculation technique for searching optimal analysis conditions has been developed. Typical DLs of elements with medium and high atomic numbers on various spectrometers are given (on wave dispersive spectrometers (WDS), energy dispersive spectrometers (EDS) without polarization and energy‐dispersive polarized‐beam X‐ray spectrometers (EDPXRS). Apparently, EDS variants are preferred for determining elements with Z > 62–65, and EDPXRS spectrometers with concave targets and increased aperture are preferred for determining elements with medium atomic numbers.     

Effect of vertical large eddy breakup devices on the drag of a flat plate

Experiments are performed to study the possibility of decreasing the net drag of a flat plate with the use of streamwise-oriented vertical elements mounted normal to the surface in an incompressible equilibrium turbulent boundary layer. The Reynolds number based on the boundary-layer momentum thickness in the section where the vertical elements are placed is 820. It is demonstrated that vertical large eddy breakup elements with the geometry used do not reduce the drag of a flat plate in the major part of the range of Reynolds numbers Re _x examined. It is only at extremely low values of Re _x that a certain gain in the net drag is reached, as compared with the value for a non-modified flow.     

Update of photoelectric absorption coefficients in the tables of McMaster

As a result of a systematic analysis of the compilation of McMaster's x‐ray cross‐sections, the polynomial coefficients of the N range (from edges N₇ to M₅) of elements Z = 61–69 have to be corrected. Furthermore, no detailed information on position and jumps of M edges of elements Z > 53 and N edges of elements Z > 85 are given. Elements Z = 84, 85, 87, 88, 89, 91 and 93 are missing. We have corrected the wrong values of polynomial coefficients and added missing M‐ and N‐edge data and missing elements. Copyright © 2005 John Wiley & Sons, Ltd.     

On the Spatial Density Matrix for the Centre of Mass of a One-Dimensional Perfect Gas

We examine the reduced density matrix of the centre of mass on position basis considering a one-dimensional system of Nnoninteracting distinguishable particles in a infinitely deep square potential well. We find a class of pure states of the system for which the off-diagonal elements of the matrix above go to zero as Nincreases. This property holds also for the state vectors which are factorized in the single particle wave functions. In this last case, if the average energy of each particle is less than a common bound, the diagonal elements are distributed according to the normal law with a mean square deviation which becomes smaller and smaller as Nincreases towards infinity. Therefore when the state vectors are of the type considered we cannot experience spatial superpositions of the centre of mass and we may conclude that position is a preferred basis for the collective variable.     

Relativistic many-body calculations of E1, E2, M1, and M2 transitions rates for the 1 s 2 l′ 2 l′ ′ – 1 s 2 2 l lines in Li-like ions

Reduced matrix elements, oscillator strengths, and transition rates are calculated for all allowed and forbidden 1s2l′ 2l′ ′ – 1s ²2l electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions in lithiumlike ions with nuclear charges ranging from Z?=?6 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1, M1, E2, and M2 matrix elements. The calculations start with a Dirac potential and include all possible 1s2l′ 2l′ ′ configurations, leading to seven odd-parity and nine even-parity states. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order RMBPT is used to determine the matrix elements, which are evaluated for the 22, 20, 16, and 18 possible E1, M1, E2, and M2 transitions, respectively. A detailed discussion of the various contributions to the energy levels and E1, M1, E2, and M2 matrix elements is given for lithiumlike iron, Z?=?26. The transition energies used in the calculation of oscillator strengths and transition rates are evaluated using second-order RMBPT. Trends of E1, M1, E2, and M2 transition rates as functions of nuclear charge Z are shown graphically for 1s2l′ 2l′ ′ – 1s ²2l transitions.     

Allowing for Coulomb effects in the effective range expansion for two coupled channels

A Coulomb-modified matrix of scattering amplitudes (an [(F)\tilde]\tilde F matrix) is considered for the case of two coupled channels of elastic scattering of charged particles with different orbital angular momenta (l ₁ and l ₂ = l ₁ + 2). Matrix elements of the [(F)\tilde]\tilde F matrix are expressed in terms of the matrix elements of a [(K)\tilde] ^{- 1}\tilde K^{ - 1} matrix inverse to a modified reaction K matrix. The elements of the [(K)\tilde] ^{- 1}\tilde K^{ - 1} matrix are written as expansions that are generalizations of single-channel effective range expansion with allowance for the Coulomb interaction. If a system of colliding particles involves a bound state, the analytic continuation of these expansions into the region of negative energies makes it possible to obtain both the position of the pole corresponding to the bound state and the scattering amplitude residues in this pole, in terms of which the corresponding vertex constants and asymptotic normalization coefficients are expressed.     

Quantitative energy-dispersive electron probe X-ray microanalysis for single-particle analysis and its application for characterizing atmospheric aerosol particles

An energy-dispersive electron probe X-ray microanalysis (ED-EPMA) technique using an energy-dispersive X-ray detector with an ultra-thin window, designated as low-Z particle EPMA, has been developed. The low-Z particle EPMA allows the quantitative determination of concentrations of low-Z elements such as C, N and O, as well as higher-Z elements that can be analysed by conventional ED-EPMA. The quantitative determination of low-Z elements (using full Monte Carlo simulations, from the electron impact to the X-ray detection) in individual particles has improved the applicability of single-particle analysis, especially in atmospheric environmental aerosol research; many environmentally important atmospheric particles, e.g. sulphates, nitrates, ammonium and carbonaceous particles, contain low-Z elements. To demonstrate its practical applicability, the application of the low-Z particle EPMA for the characterization of Asian Dust, urban and subway aerosol particles is shown herein. In addition, it is demonstrated that the Monte Carlo calculation can also be applied in a quantitative single-particle analysis using transmission electron microscopy (TEM) coupled with energy-dispersive X-ray spectrometry (EDX), showing that the technique is useful and reliable for the characterization of submicron aerosol particles.     

Multielement Analytical Spectroscopy in Plant Ionomics Research

Abstract: The study of the ionome (ionomics) is defined as quantitative and simultaneous measurement of the element composition of living organisms and changes in this composition in response to physiological stimuli, development stage, and genetic modifications (Salt et al., Ann. Rev. Plant Biol., Vol. 59, 2008). The necessity of understanding the regulation processes of elements in the organisms demands determination of many elements in the organism, tissue, and cell (Baxter, Plant Biol., Vol. 12, 2009). A prospect for ionomics is environmental pollution where great variety of conditions and pollutants exist resulting in concentration and interelemental changes in the plant ionome. The capabilities of and problems with several multielement analytical techniques, including instrumental neutron activation analysis (INAA), X-ray fluorescence, inductively coupled plasma–atomic emission spectrometry (ICP-AES), inductively coupled plasma–mass spectrometry (ICP-MS), and atomic absorption spectrometry (AAS), which are adequate and most promising in ionomic and environmental studies of plants, are reviewed. References are confined mainly to the last 10–15 years. Information about concentrations, roles, binding forms, and pollution sources of the elements and comparison between methods with respect to limits of detection, determined elements, interferences, and economic considerations are tabulated. Some combinations of instrumental techniques supplementing each other are highly valued, namely, ICP-MS and ICP-AES and INAA and AAS or ICP-AES.     

Development of an experimental database of EUV spectra from highly charged ions of medium to high Z elements in the Large Helical Device plasmas

We are developing an experimental database of extreme ultraviolet spectra from highly charged ions using optically thin high-temperature plasmas produced in the Large Helical Device. Spectra from a variety of elements with atomic numbers ranging from 36 to 83 have been systematically recorded in the range of 1–20 nm by a grazing incidence spectrometer. For higher Z elements from tin onward, discrete or quasicontinuum spectral features from n=4 (N-shell) ions are mainly observed depending upon the plasma temperature, which leads to some new experimental identifications of spectral lines. On the other hand, major emitters are n=3 (M-shell) ions for medium Z elements from krypton to ruthenium. The calculated wavelengths for Δn≠0 transitions agree well with the measurements and the calculated wavelengths are systematically shifted to shorter wavelengths for Δn=0 transitions associated with inner-subshell excited configurations.     

硼玻璃中Dy3+及Sm3+的辐射跃迁几率和无辐射跃迁几率

硼玻璃中掺杂Nd3+,Er3+,Tm3+等小能隙的稀土离子,由于硼玻璃声子能量大,多声子无辐射几率大,影响其发光效率。但由于硼玻璃熔点低,加工容易,对于民用上常用的Sm3+,Dy3+,Eu3+,Tb3+等大能隙物质,多声子无辐射跃迁不是主要因素的情况下,发光效率将如何是本文要研究的问题。另外,辐射跃迁性质的研究对于能量传递机理的研究也是很有意义的。     

Some constraints on the Yukawa parameters in the neutrino modification of the Standard Model (ν<Emphasis Type="Italic">MSM</Emphasis>) and CP-violation

The equations connecting elements of the Yukawa matrix to elements of the active neutrino mass matrix in the νMSM theory (an extension of the Standard Model by a singlet of three right-handed neutrinos) was analyzed, and explicit relations for the ratio of the Yukawa matrix elements and elements of the active neutrino mass matrix were obtained. This relation can be used for getting more accurate constraints on the model parameters. Particularly, with the help of the obtained results we investigated CP-violating phase in the νMSM theory. We demonstrate that even in the case when elements of the active neutrino mass matrix are real the baryon asymmetry can be generated also.     

Transfer-matrix for the two-channel scattering problem

The transfer-matrix for the two-channel scattering problem is obtained. The elements of this matrix are expressed in terms of transmission T ₁, T ₂ and reflection R ₁, R ₂ amplitudes. The transfer-matrix for N localized and nonoverlapping scattering centers is presented. Recurrent equations for matrix elements are derived and initial conditions for them are defined.