Elastic scattering of 81 keVγ rays by aluminium,nickel, tantalum,gold and lead

A recently reported study [Phys. Rev. A49, 3664 (1994)] of elastic scattering of 81 keVγ rays in the angular range from 60° to 133° has been extended to smaller and larger angles. Previously reportedS matrix calculations of atomic Rayleigh scattering have been shown to require a subtraction of contributions from spurious resonances. Most of the experimental data are in agreement with the calculations. Calculations (MF + ASF) based on a combination of relativistic modified form factors (MF’s) and angle independent anomalous scattering factors (ASF’s) are found to be inadequate for an explanation of experimental cross-sections in the case of highZ elements at angles larger than about 120°.     

Statistics of S-matrix poles in few-channel chaotic scattering: Crossover from isolated to overlapping resonances

We derive an explicit expression for the distribution of resonance widths in a chaotic quantum system coupled to continua via M equivalent open channels. It describes a crossover from the χ ² distribution (regime of isolated resonances) to a broad, power-law-like distribution typical for the regime of overlapping resonances. The first moment is found to reproduce exactly the Moldauer-Simonius relation between the mean resonance width and the transmission coefficient. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 970–973 (25 June 1996) Petersburg Nuclear Physics Institute, 188350, Gatchina, St. Petersburg District, Russia Published in English in the original Russian journal. Edited by Steve Torstveit.     

Kinematic mechanism of the modulation of the spectral intensity in the spatially uniform system of Hubbard fermions

Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions leads to significant variations in the spectral intensity A(k, ω) in the Brillouin zone. As a result, the modulation of A(k, ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by the contour section, where A(k, ω) decreases according to the angle-resolved photoemission spectroscopy data.     

Vibrational transitions in experiments with a scanning tunneling microscope

A method of in-cavity scanning tunneling spectroscopy is proposed by which one can observe distinct spectra of electronic-vibrational field-emission resonances. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 4, 306–310 (25 February 1997)     

Competition between single-and multiparticle resonances in tunneling

A new mechanism is proposed for the anomalous tunneling transmittance of a double-barrier quantum-well structure doped with a transition-metal impurity and possessing an intrinsic two-dimensional continuum. The new tunneling channels are due to exponentially-narrow single-particle resonances arising near the edge of a 2D band during tunneling. They are temperature-independent and their contribution to the transmittance can exceed the contribution of the Kondo resonance even at temperatures T<T _K . Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 459–464 (25 March 1997)     

A Characteristic Decay Semigroup for the Resonances of Trace Class Perturbations with Analyticity Conditions of Semibounded Hamiltonians

To asymptotic complete scattering systems {M ₊+V,M ₊} on H₊:=L²(R₊,K{\mathcal{H}}_{+}:=L^{2}(\mathbf{R}_{+},{\mathcal{K}}, d λ), where M ₊ is the multiplication operator on H₊{\mathcal{H}}_{+} and V is a trace class operator with analyticity conditions, a decay semigroup is associated such that the spectrum of the generator of this semigroup coincides with the set of all resonances (poles of the analytic continuation of the scattering matrix into the lower half plane across the positive half line), i.e. the decay semigroup yields a “time-dependent” characterization of the resonances. As a counterpart a “spectral characterization” is mentioned which is due to the “eigenvalue-like” properties of resonances.     

Properties of activated states of oxygen and carbon atoms during diffusion in α-Ti

Activated energy states of interstitial atoms in α-Ti crystals are investigated. Previous precision experiments on the anisotropy of the diffusion coefficients D _zz /D _xx in this system revealed that d(D _zz /D _xx )/dT has different signs for oxygen and carbon. It is shown that the anomalous positive sign of the effect for carbon atoms is due to the presence of a double-well potential for a diffusing atom at the saddle points. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 502–506 (25 September 1998)     

Overlapping identical resonances and double radiative interference effects in recombination of heavy multicharged ions

The purely QED effect of double radiative interference in the recombination of electrons with heavy multicharged ions is discussed. Numerical calculations of the corresponding cross sections in the vicinities of the KL ₁₂ M ₁₂ and KM ₁₂ M ₁₂ dielectronic recombination resonances of heliumlike uranium are reported. The possibility of near-future experimental observation of the effect with the Super-EBIT facility is suggested. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 552–556 (10 October 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Finitary-Algebraic ‘Resolution’ of the Inner Schwarzschild Singularity

A ‘resolution’ of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Differential Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machinery of Abstract Differential Geometry (ADG) is employed. As in previous works [Mallios, A. and Raptis, I. (2001). Finitary spacetime sheaves of quantum causal sets: Curving quantum causality. International Journal of Theoretical Physics, 40, 1885 [gr-qc/0102097]; Mallios, A. and Raptis, I. (2002). Finitary Čech-de Rham cohomology. International Journal of Theoretical Physics, 41, 1857 [gr-qc/0110033]; Mallios, A. and Raptis, I. (2003). Finitary, causal and quantal vacuum Einstein gravity. International Journal of Theoretical Physics 42, 1479 [gr-qc/0209048]], which this paper continues, the starting point for the present application of ADG is Sorkin's finitary (:locally finite) poset (:partially ordered set) substitutes of continuous manifolds in their Gel'fand-dual picture in terms of discrete differential incidence algebras and the finitary spacetime sheaves thereof. It is shown that the Einstein equations hold not only at the finitary poset level of ‘discrete events,’ but also at a suitable ‘classical spacetime continuum limit’ of the said finitary sheaves and the associated differential triads that they define ADG-theoretically. The upshot of this is two-fold: On the one hand, the field equations are seen to hold when only finitely many events or ‘degrees of freedom’ of the gravitational field are involved, so that no infinity or uncontrollable divergence of the latter arises at all in our inherently finitistic-algebraic scenario. On the other hand, the law of gravity—still modelled in ADG by a differential equation proper—does not break down in any (differential geometric) sense in the vicinity of the locus of the point-mass as it is traditionally maintained in the usual manifold-based analysis of spacetime singularities in General Relativity (GR). At the end, some brief remarks are made on the potential import of ADG-theoretic ideas in developing a genuinely background-independent Quantum Gravity (QG). A brief comparison between the ‘resolution’ proposed here and a recent resolution of the inner Schwarzschild singularity by Loop QG means concludes the paper. PACS numbers: 04.60.−m, 04.20.Gz, 04.20.−q     

Polymorphism of biperiodic stripe domain structures

Magnetic-field-induced polymorphism of biperiodic stripe domain structures of films with a positive anisotropy constant and easy axis parallel to the normal to the surface is studied. A symmetry classification of the observed types of domain structures is performed, and the phase diagram of the films in the (H _⊥, H _∥) plane, where H _⊥ and H _∥ are, respectively, the components of the magnetic field vector perpendicular and parallel to the normal to the surface, is determined. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 701–706 (10 May 1998)     

Mechanism of stratification of turbulent heat transfer in a sound field in the presence of rotational anisotropy of the flow

It is established that the stratification of the heat transfer intensity coefficients into n discrete levels, as discovered previously in the turbulent flow accompanying rotation of a supersonic flow, is described by the formula α _n ² /α ₁ ² =2 ⁿ⁻¹, n=1,2,3,.... It is found that the ratio of the measured amplitudes of the discrete components of the pressure-pulsation spectrum is of a similar form and corresponds to the pressure field from multipole sources. As expected, similarly to the case of acoustic paramagnetic resonance, the selection of discrete frequencies of intense acoustic radiation from the external flow occurs under the influence of resonances with the radiation of multipoles of turbulent vortices oriented in the rotational anisotropy field. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 145–149 (25 January 1997)     

Meson-baryon s-wave resonances with strangeness -3

Starting from a consistent SU(6) extension of the Weinberg-Tomozawa (WT) meson-baryon chiral Lagrangian ( Phys. Rev. D 74, 034025 (2006)), we study the s-wave meson-baryon resonances in the strangeness S = - 3 and negative-parity sectors. Those resonances are generated by solving the Bethe-Salpeter equation with the WT interaction used as kernel. The considered mesons are those of the 35-SU(6)-plet, which includes the pseudoscalar (PS) octet of pions and the vector (V) nonet of the rho-meson. For baryons we consider the 56-SU(6)-plet, made of the 1/2⁺ octet of the nucleon and the 3/2⁺ decuplet of the Delta. Quantum numbers I(J ^P) = 0(3/2^-) are suggested for the experimental resonances Ω ^*(2250)^- and Ω ^*(2380)^-. Among other, resonances with I = 1 are found, which minimal quark content is sssˉl', being s the strange quark and l, l' any of the the light up or down quarks. A clear signal for such a pentaquark would be a baryonic resonance with strangeness -3 and electric charge -2 or 0, in proton charge units. We suggest looking for K ^- Ξ ^- resonances with masses around 2100 and 2240MeV in the sector 1(1/2^-), and for π ^± Ω ^- and K ^- Ξ ^*- resonances with masses around 2260MeV in the sector 1(3/2^-).     

Hamiltonian dynamics of vortex lines in hydrodynamic-type systems

It is shown that the degeneracy of the noncanonical Poisson bracket operating on the space of solenoidal vector fields that arises due to the freezing-in of the curl of the velocity [E. A. Kuznetsov and A. V. Mikhailov, Phys. Lett. A 77, 37 (1980)] is lifted when the vorticity Ω is represented in terms of vortex lines. This representation makes it possible to integrate the equation of motion of the vorticity for a system with the Hamiltonian H=∫∣Ω∣d r. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 1015–1020 (25 June 1998)     

Anomalous Hall effect in granular alloys

A theoretical study is performed of the anomalous Hall effect in granular alloys with giant magnetoresistance. The calculation is carried out within the Kubo formalism and the Green’s function method. The mechanism of asymmetric scattering of the spin-polarized current carriers is considered with allowance for a size effect associated with scattering not only by one grain, but also with more complicated processes of transport among two and three grains. It is shown that scattering of conduction electrons by the interfaces of the grains and the matrix has a substantial effect on the magnitude of the anomalous Hall effect and determines its sign. In general, correlation between the quantities ρ _H and ρ ² is absent, where ρ _H is the Hall resistivity and ρ is the total resistivity of the granular alloy. However, numerical calculation shows that for certain values of the model parameters ρ _H∼ρ ^3.8 and for these same parameter values the amplitude of the giant magnetoresistance reaches 40%, which is found to be in quantitative agreement with the experimental data for Co₂₀Ag₈₀ alloys [P. Xiong, G. Xiao, J. Q. Wang et al., Phys. Rev. Lett. 69, 3220 (1992)]. It is also shown that increasing the resistivity of the matrix leads to a significant growth in the anomalous Hall effect, and more substantial growth for alloys with small grain size, which is in good agreement with experiment [A. B. Pakhomov, X. Yan, and Y. Xu, J. Appl. Phys. 79, 6140 (1996); [X. N. Jing, N. Wang, and A. B. Pakhomov, Phys. Rev. B 53, 14032 (1996)]. Zh. éksp. Teor. Fiz. 112, 2198–2209 (December 1997)     

High orders of perturbation theory. Are renormalons significant?

According to Lipatov [Sov. Phys. JETP 45, 216 (1977)], the high orders of perturbation theory are determined by saddle-point configurations, i.e., instantons, which correspond to functional integrals. According to another opinion, the contributions of individual large diagrams, i.e., renormalons, which, according to t’Hooft [The Whys of Subnuclear Physics: Proceedings of the 1977 International School of Subnuclear Physics (Erice, Trapani, Sicily, 1977), A. Zichichi (Ed.), Plenum Press, New York (1979)], are not contained in the Lipatov contribution, are also significant. The history of the conception of renormalons is presented, and the arguments in favor of and against their existence are discussed. The analytic properties of the Borel transforms of functional integrals, Green’s functions, vertex parts, and scaling functions are investigated in the case of ϕ ⁴ theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou-Zinn-Justin hypothesis [Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B 21, 3976 (1980)] is proved. It rules out the existence of the renormalon singularities pointed out by t’Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of ϕ ⁴ theory. Zh. éksp. Teor. Fiz. 116, 369–389 (August 1999)     

On the experimental verification of the Landau-Pomeranchuk-Migdal effect

A theoretical explanation is given for the “unexpected” behavior recently observed in the radiation spectrum of ultrarelativistic electrons in a thin layer of matter in an experimental investigation of the Landau-Pomeranchuk-Migdal effect at SLAC [S. R. Klein et al., Preprint SLAC-6378, Stanford (1993); P. L. Anthony et al., Phys. Rev. Lett. 75, 1949 (1995)]. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 837–840 (10 June 1996)     

"Positronic" effective charges of anions in polar substances

The "positronic" effective charges of anions in polar substances are investigated further on the basis of the optical — positron model proposed in 1966 by Gol’danskii and Prokop’ev [Fiz. Tverd. Tela,8, No. 2, 515 (1966)] and developed in 1990 by Aref’ev and Prokof’ev [Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, 52 (1990)] (modified optical model). High productivity of this model in determining anion effective charges in various polar substances (ionic crystals, semiconductors with ionic chemical bonds, etc.) is demonstrated. A. Yu. Malinin Scientific Research Institute for Materials Science. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 23–29, February, 1997.     

Sign phase transition and directed paths in random media

We consider a lattice model which corresponds to the high temperature expansions of disordered Ising and Heisenberg models and to the deeply localized regime of the disordered Anderson model. The spin correlation functions for the Ising and Heisenberg model and the amplitude of electron tunneling for the Anderson model exhibit a “sign phase transition.” At small concentration x of scatterers with a negative scattering amplitude these quantities have predictable signs while at large x their signs are unpredictable. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 283–288 (25 August 1996) Published in English in the original Russian Journal. Edited by J. R. Anderson.     

Photocurrent resonances in short-period AlAs/GaAs superlattices in an electric field

The photocurrent was measured as a function of the external electric field in short-period AlAs/GaAs superlattices for various photon energies. Transport resonances, whose positions do not depend on the photon energy, were observed in these dependences together with optical resonances due to interband transitions in Wannier-Stark levels. It is shown that the transport resonances are due to tunneling of photoelectrons from the p-GaAs contact region into the first level in GaAs wells located 2–5 lattice periods from the contact layer. Fiz. Tverd. Tela (St. Petersburg) 41, 159–164 (January 1999)