A note on grating based soft X-ray monochromators

A few facts related to the aberrations for toroidal and plane gratings are presented. Some design aspects of the plane grating-based monochromator devised by Petersen (1982) are discussed. We also point out that for a cylindrical grating astigmatic correction can be reduced and suggest that following Petersen’s scheme some improvements in the monochromator performance could be achieved with such a grating.     

A contribution to the theory of some photographic effects

The increase in sensitivity of a photographic layer by pre-illumination, the Clayden effect and the Villard effect are explained as special cases of the influence of multiple exposure on a sensitive layer. It is shown that the known fact can be explained by the theory of the intermittent effect which is based on the assumption of the inertia of electron processes in AgBr crystals.     

A contribution to the Rainich theory of the neutrino field

The neutrino-gravitational field is divided into fourteen distinct classes. This classification is shown also to determine the class of the space-time. Then for four particular classes of space-time, necessary and sufficient conditions on the concomitants of the Ricci tensor are given for it to admit a neutrino field. It is further shown that for three of these classes the neutrino field is determined uniquely by the metric of space-time.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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A contribution to the rainich theory of the neutrino field II

Conditions are given on the metric of a space-time for it to admit a neutrino-gravitational field. The method described involves comparing the spin coefficients of a suitably defined tetrad of null vectors. It is used to obtain the class of space-times which admits a neutrino field or a non-null electromagnetic field. The classes of space-time which admit two different neutrino fields are also described.     

A contribution to the theory of the exchange narrowing of spectral lines

The intensity distribution of a composite spectral line with exchange narrowing is calculated by integrating a matrix expression derived by Anderson     

A non-perturbative contribution to the vacuum energy in supersymmetric Yang-Mills theory

It is shown that the quantum fluctuations around an interacting instanton-anti-instanton field configuration induce negative vacuum energy in supersymmetric Yang-Mills theory.     

A contribution to the theory of ferromagnetic resonance at high power levels

The instability of spin waves at ferromagnetic resonance is discussed. An equation of the stationary state of spin wavesk0 is derived by means of the quantum theory of spin waves. It is shown when discussing this equation that the concept of the critical uniform precession angle may be obtained when using an approximation which neglects the action of spin wavesk0 backward on their own excitation. We believe we are justified in supposing that, due to this effect, a stable stationary state can exist even above the critical amplitude of uniform precession, given by theories up to now.

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In conclusion the author thanks G. A. Smolenskij for enabling him to carry out this work in his laboratory. Thanks also go to the theoretical staff of the Institute of Semi-conductors of Acad. Sci. USSR in Leningrad for valuable discussions, especially to A. I. Anselm, V. L. Gurevic and J. A. Firsov.     

Small d-spacing WSi2/Si multilayers for X-ray monochromators

A WSi2 /Si multilayer, with 300 bi-layers and a 2.18-nm d-spacing, is designed for X-ray monochroma-tor application. The multilayer is deposited using direct current magnetron sputtering technology. The reflectivity of the 1st-order Bragg peak measured at E = 8.05 keV is 38%, and the angular resolution (Δθ/θ) is less than 1.0%. Fitting results of the reflectivity curve indicate a layer thickness drift of 1.6%, mainly accounting for the broadening of the Bragg peaks. The layer morphology is further characterized by transmission electron microscopy, and a well-ordered multilayer structure with sharp interfaces is observed from the substrate to the surface. The material combination of WSi2 /Si is a promising candidate for the fabrication of a high-resolution multilayer monochromator in the hard X-ray region.     

A contribution to the theory of ferromagnetism in the Hubbard model with degeneracy

The possibility of ferromagnetic ordering in a generalized Hubbard model taking account of degeneracy is studied for an infinite Hubbard energy. The existence region of ferromagnetism for electron density greater than 1 is determined. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 12, 881–886 (25 June 1997)     

Geometrical aberrations and physical characteristics of approximately focusing X-ray monochromators of Johann's type

A model is described for the computation of the diffracted intensity distribution on monochromating crystals in approximatively focusing monochromators of Johann's type. Numerical examples and graphs illustrate the influence of geometrical aberrations in some practical cases. Results of computations allow rules to be drawn up for the choice of parameters of these monochromators according to the requirements of the diffraction problem which is being solved.     

A contribution to the theory of the Faraday effect of excitons in rare-gas crystals

An expression for the Faraday rotation of excitons in rare-gas crystals was found for the case of a weak magnetic field. The wave functions of an exciton in a magnetic field were found in first order of perturbation theory in an approximation including spin-orbit interaction and overlapping of atomic wave functions. The general theory was used for the estimation of Faraday rotation in crystalline argon.It is a pleasure for the author to acknowledge her debt to Dr. M. Trlifaj for suggesting the problem and for helpful discussions.     

A contribution to the theory of the space-charge region in thin semiconductor monocrystalline films

The potential distribution in films the thickness of which is equal to or smaller than the Debye length is derived from Poisson's equation under general boundary conditions. It is shown that there exist three basic forms of this distribution depending on the densities and character of charges on both surfaces, on the geometrical thickness of the thin film and on the Debye length of the semiconductor.Notation E _S 1,E _S 2 dimensionless surface field intensities - F ₁ F ₂ space-charge functions - L _D Debye length - k Boltzmann's constant - n _b bulk electron density - N _S 1,N _S 2 concentration of surface charges - p _b bulk hole density - q electron charge - T absolute temperature - thickness of thin film measured in Debye lengths - coordinate perpendicular to the surface measured in Debye lengths - ₀ permittivity of free space - _s relative permittivity of semiconductor - dimensionless potential (multiples of kT/q) - E _cb energy of bulk conduction-band edge - E _c energy of conduction-band edge - E _i energy line that runs parallel to band edges and coincides in the bulk (assumed homogeneous) withE _ib , the intrinsic Fermi level - E _v energy of valence-band edge - E _vd energy of bulk valence-band edge - V potential     

A further contribution to the theory of the transient hot-wire technique for thermal conductivity measurements

We study the density of states of a one-dimensional tightbinding electron model with random hopping elements. The Hamiltonian is $\text{H = -∑}{}_{\mathrm{i}}\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i+1}}\text{+a}{}^{\mathrm{+}}{}_{\mathrm{i+1}}\text{a}{}_{\mathrm{i}}\text{)}$, where the $\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}$'s are independent identically distributed random variables. It is proved that the single particle density of states D(E) diverges near E = 0 as $\text{1}\text{|(E}\text{log}{}^3\text{|E|)|}$.