Basic features of coherent nuclear resonant scattering of synchrotron radiation

The time dependences of spatially coherent nuclear resonant scattering of synchrotron radiation show a wealth of characteristic features which originate from the interference of several radiation components and from dynamical nuclear scattering. These effects will be of importance for the future fields of time domain Mössbauer spectroscopy and of nuclear resonant -ray optics. The basic features are discussed and experimental evidence is reviewed.     

Techniques for inelastic X‐ray scattering with μeV‐resolution

A new spectroscopic technique is introduced that allows tuning of a eVwide beam of synchrotron radiation over a range of a few meV. It relies on nuclear resonant scattering that is subject to the Doppler effect in high speed rotary motion. Two mechanisms are discussed how to extract the resonantly scattered radiation out of the broad band of synchrotron radiation: (a) grazing incidence reflection from a rotating disk in combination with a polarization filtering technique and (b) deflection of resonantly scattered radition via the recently discovered Nuclear Lighthouse Effect. Implications for inelastic Xray scattering and elastic nuclear resonant scattering are discussed.     

Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

A dynamical phase transition in a caricature of a spin glass

This paper studies the rate of convergence to equilibrium of Glauber dynamics (Gibbs Sampler) for a system ofN Ising spins with random energy (at inverse temperature >0). For each of the 2 ^N spin configurations the energy is drawn independently from the values 0 and-logN with probabilities 1-N ^–7, resp.N ^– (>0), and is kept fixed during the evolution. The main result is an estimate of the coupling time of two Glauber dynamics starting from different configurations and coupled via the same updating noise. AsN the system exhibits two dynamical phase transitions: (1) at =1 the coupling time changes from polynomial (>1) to stretched exponential (<1) inN; (2) if <1, then at = the almost coupling time [i.e., the first time that the two dynamics are within distanceo(N)] changes from polynomial (<) to stretched exponential (>) inN. The techniques used to control the randomness in the coupling are static and dynamic large-deviation estimates and stochastic domination arguments.     

Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids

We construct a family of probability spaces,P ), <0 associated with the Euler equation for a two dimensional inviscid incompressible fluid which carries a pointwise flow _t (time evolution) leavingP globally invariant. _t is obtained as the limit of Galerkin approximations associated with Euler equations.P is also in invariant measure for a stochastic process associated with a Navier-Stokes equation with viscosity, , stochastically perturbed by a white noise force. Dedication. After completion of this work the terrible news of the sudden death of Raphael Høgh-Krohn reached us. In deep sorrow we mourn his departure. The present work has its roots in previous inspiring work by him and we dedicate it to him as a small sign of our gratitude.     

Structural state of Cu-Be-Ag alloys in the process of decomposition of solid solution

Investigation of aging Cu-1.5% Be-2% Ag and Cu-1% Be-4% Ag alloys was carried out in this study by the methods of x-ray analysis of monocrystals, and electron microscopy. In the aging process at 218, 300, and 450C, laminar zones of Guinier-Preston, enriched with beryllium and silver atoms were formed. Entry of silver into the zones widens the upper temperature interval of the zone stage to 450C. With the increase of annealing time the metastable-phase was precipitated. The crystals of -phase are precipitated with orientation in the direction (100) in consequence of interactions of the fields of elastic stresses occurring around -precipitations, and periodic structure is formed in the alloy. The stable phase-CuBe and Ag was precipitated in the Cu-1% Be-4% Ag-alloy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 21–25, August, 1972.     

Monochromatization of synchrotron radiation for nuclear resonant scattering experiments

An introduction to monochromatization of synchrotron radiation in the energy range of 5–30 keV is presented for applications involving nuclear resonant scattering. The relevant relationships of the dynamical theory of Xray diffraction are used to explain basic concepts of monochromatization. These relations are combined with raytracing techniques to design highenergyresolution monochromators. Transmissionoptimized and energyresolutionoptimized designs that achieve high energy resolutions (10⁶)< E/E < 10⁸) are discussed separately. Practical silicon monochromators of both types are presented for a variety of nuclear resonances in this energy range.     

On the Long Time Behavior of Infinitely Extended Systems of Particles Interacting via Kac Potentials

We analyze the long time behavior of an infinitely extended system of particles in one dimension, evolving according to the Newton laws and interacting via a non-negative superstable Kac potential (x)=(x), (0, 1]. We first prove that the velocity of a particle grows at most linearly in time, with rate of order . We next study the motion of a fast particle interacting with a background of slow particles, and we prove that its velocity remains almost unchanged for a very long time (at least proportional to ^–1 times the velocity itself). Finally we shortly discuss the so called Vlasov limit, when time and space are scaled by a factor .     

SYNFOS

An expression for the amplitude of a pulse of synchrotron radiation coherently scattered in the forward direction by a Mössbauer absorber consisting of randomly oriented paramagnetic ironcontaining molecules (for example, a frozen solution of a ⁵⁷Fe protein) in an applied magnetic field is derived from the theory of optics. It is assumed that the hyperfine splittings present in the Mössbauer nuclei can be described in the framework of the spinHamiltonian formalism. In the general case of a thick Mössbauer sample of this kind the response on an incident monochromatic and fully polarized beam cannot be given analytically because of the integrations involved. How nuclear forwardscattering for this general case is evaluated in the program package called SYNFOS is outlined.     

Generalized Stefan-Boltzmann law

Thermodynamics arguments have been employed to derive how the energy density depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = ( –1), where is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expression = T/( –1), where is a constant. This result also appears naturally in the framework of general relativity for spacetimes with constant spatial curvature. Some particular cases are vacuum (p = –), cosmic strings (p= –1/3), radiation (p = 1/3), and stiff matter (p = ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions.     

Tree graph inequalities and critical behavior in percolation models

Various inequalities are derived and used for the study of the critical behavior in independent percolation models. In particular, we consider the critical exponent associated with the expected cluster sizex and the structure of then-site connection probabilities =_n(x₁,..., x_n). It is shown that quite generally 1. The upper critical dimension, above which attains the Bethe lattice value 1, is characterized both in terms of the geometry of incipient clusters and a diagramatic convergence condition. For homogeneousd-dimensional lattices with (x, y)=O(¦x -y¦^–(d–2+), atp=p _c, our criterion shows that =1 if > (6-d)/3. The connectivity functions _n are generally bounded by tree diagrams which involve the two-point function. We conjecture that above the critical dimension the asymptotic behavior of _n, in the critical regime, is actually given by such tree diagrams modified by a nonsingular vertex factor. Other results deal with the exponential decay of the cluster-size distribution and the function ₂ (x, y). A. P. Sloan Foundation Research Fellow. Research supported in part by the National Science Foundation Grant No. PHY-8301493.Research supported in part by the National Science Foundation Grant No. MCS80-19384.     

Structure of the145Sm states from the145Eu Decay

The -radiation from¹⁴⁵Eu has been studied by means of an anti-Compton spectrometer, the construction and operation of which are described. Altogether 91 -transitions have been observed, 20 of them for the first time. A decay scheme of¹⁴⁵Eu has been constructed incorporating 85 -transitions. Low-lying excited states in¹⁴⁵Sm have been analysed within the quasiparticle-phonon nuclear model as well as within the interacting boson-fermion model. Some systematic features in the positions of low-lying positive parity levels inN=83 nuclei have been revealed.     

Microscopic selection principle for a diffusion-reaction equation

We consider a model of stochastically interacting particles on , where each site is assumed to be empty or occupied by at most one particle. Particles jump to each empty neighboring site with rate/2 and also create new particles with rate 1/2 at these sites. We show that as seen from the rightmost particle, this process has precisely one invariant distribution. The average velocity of this particle V() then satisfies ^–1/2V() as. This limit corresponds to that of the macroscopic density obtained by rescaling lengths by a factor ^1/2 and letting. This density solves the reaction-diffusion equation , and under Heaviside initial data converges to a traveling wave moving at the same rate .     

A model for peak-gain coefficient in InGaAsP/InP semiconductor laser diodes

A parabolic model of the formg =n ² +n + has been suggested for long-wavelength InGaAsP laser diode peak-grain coefficient variations with the carrier density. The parameters, and, which are dependent on doping, bandgap-wavelength and temperature, have been calculated by applying the least-mean-square method to fit the results of the Lasher and Stern theory of the recombination in semiconductors. p ]This model is superior to the commonly used linear model in accuracy and range of applicability.     

Intensity of γ radiation back-scattered as a result of the Mössbauer effect

In the geometry of total backscattering, the intensity of scattered Mössbauer radiation is calculated. The contribution of various scattering channels to the spectrum is discussed: resonant and nonresonant, elastic and inelastic. Scattering at samples of different thickness is considered. Only one-time scattering of quanta in the material is taken into account.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii. Fizika, No. 8, pp. 23–29, August, 1989.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

The positron beam at the stuttgart pelletron accelerator and its applications toβ +γ positron lifetime measurements

A slow-positron source has been installed in the therminal of an electrostatic 6.5 MeV accelerator and provides a monoenergetic positron beam in the few-MeV range. It will be used to operate a fast positron lifetime spectrometer based on ⁺ coincidences. The properties of the beam, the expected performance of the spectrometer, its advantages over conventional lifetime measurements, a number of intended applications, as well as recent positron-electron scattering experiments and plans for positron channelling and channelling-radiation studies are outlined.This paper is based on a talk given by W.B. at the Int. Symp. Production of Low-Energy Positrons with Accelerators and Applications, held at Justus-Liebig-Universität Giessen, FRG, September 25–27, 1986     

Baryon decays and gamma-spectroscopy of hypernuclei

The applicability of (K ^–,^–) - and (K ^–,^– N)-reactions on^13,14C and^14,15N nuclei to the study of -transitions in primary and daughter -hypernuclei is discussed. The intensity of -deexcitation of ¹³C state |S ¹²C(15·11 MeV; 1⁺1): 1/2⁺ has been shown to be comparable with the intensity of baryon decay. Isospin selection rules are used to distinguish excitation energy ranges of primary hypernuclei, where the identification of the secondary -lines is probable.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.