Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.     

Amplitude-distortion factors for the inelastic scattering of an electron at a neon atom in an electric field

Inelastic electron scattering at a neon atom in the presence of an external electric field is considered. The distortion factors of the cross section _M (F) are calculated for a series of 4d and 5d levels. It is shown that the distortion factor in strong fields is a nonlinear and nonmonotonic function of the field. The distortion factors and transition probabilitiesA , are compared. The correlation between the behavior ofA , and _M (F) is explained by the dependence of the mean dipole moment of the Stark state on the field strength.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–110, January, 1996.     

String structures and the index of the Dirac-Ramond operator on orbifolds

We discuss the relationship between string structures and the topological class H ⁴(M,Z) on non-simply connected manifolds. We also investigate to what extent the index formula for the Dirac-Ramond operator detects the class, .Supported by the NSF Grant #84-07109 and by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069On leave from the University of Wroclaw, Wroclaw, Poland     

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.     

Laser nitriding of iron: Influence of the laser parameters on the nitriding efficiency

Laser nitriding of Armco iron in nitrogen was studied for KrF-excimer-laser irradiation. The influence of the energy density and number of pulses on the nitrogen take-up and the nitride phases formed was investigated using Resonant Nuclear Reaction Analysis (RNRA) and Mössbauer spectroscopy. Besides the original a-iron, austenite-Fe(N), martensite-Fe(N),-Fe₂₊N, and-Fe₁₆N₂ were identified. The fraction of the e-phase was found to increase with the number of pulses and the energy density. A threshold energy density of 1.8(2) J/cm² for the laser nitriding process was found.     

Precision PAC measurements in Er2O3 and Ho2O3 single crystals and structure refinement

The structure of C-form Ho₂O₃ and Er₂O₃ single crystals and powder samples was investigated by the electric quadrupole hyperfine interaction of¹¹¹In(EC)¹¹¹Cd probe ions using the perturbed - angular correlation method (PAC). The resulting set of refined atomic coordinates is compared to X-ray data and used to calculate the orientations of the electric field gradients (EFG) which are reproduced by the PAC measurements in single crystals. The temperature dependence of the coordinates was measured for both substances.     

Behavior at small distances and low temperatures of the ion-ion distribution function of the two-dimensional Coulomb gas

We compute upper and lower bounds for the canonical ion-ion distribution functiong ₁₁ ^(N) (r) of the two-dimensional Coulomb gas for smallr and 1<<2, where is the plasma parameter. Both bounds are proportional tor ^2-/(-1), which proves thatg ₁₁ ^(N) (r) behaves asr ^2-, as conjectured by Hansen and Viot. We conjecture that, in the thermodynamic limit,g ₁₁(r) ~ 2(-1)^-1(r/a)^2-, wherea=(n)^–1/2 is the mean interionic distance. We also compute the canonical one-body distribution function with one pair (+,–) in a disk, for anyr and any.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Levels in <Superscript>127</Superscript>La fed by the <Superscript>127</Superscript>Ce beta-decay

The low-lying levels in ¹²⁷La have been studied through the -decay of ¹²⁷Ce ( T_1/2 = 29s) produced by bombarding a ^natMo target with a 185-MeV ³⁵Cl beam. Reaction products were on-line mass-separated, and -ray singles and - coincidence measurements were performed. Conversion electrons were also measured and multipolarities of transitions have been derived. The half-life of the 210.9-keV level was determined to be (1.9±0.3)ns by the - delayed coincidence technique. The level scheme obtained has been compared with calculations based on the Nilsson model.     

Electrical properties of p-type ZnGeP2 irradiated by H+ ions

The properties of p-type ZnGeP₂ [p₀=(5–10)·10¹⁰ cm^–3, ₀=(2–5)·10^–7 (·cm)^–1], irradiated with H⁺ ions [E=5 MeV, T_irr=300 K, D=(1·10¹²–1.7·10¹⁶) cm^–2] are studied. An increase in the resistivity (to gr_max - 5·10¹¹ ·cm) and subsequent reduction in for large currents of H⁺ ions ( - 9·10⁸ ·cm for D - 1.7·10¹⁶ cm^–2), is observed in irradiated crystals. The resistivity of irradiated p-type ZnGeP₂ is found to be very sensitive to hydrostatic pressure [(4–5)·10^–5 bar^–1]. The annealing of radiation defects in the temperature interval (20–600) °C is examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 91–93, October, 1991.     

Direct calculation of centrifugal-distortion constants and inertial defects of XY3-type plane molecules from experimental data

A simple direct method is proposed for the calculation of the centrifugal-distortion constants and inertial defects of plane symmetric molecules of type XY₃ from the experimental frequencies, Coriolis constant ₃₃, and geometric parameters. The calculation formulas are given, together with the results obtained for the BF₃, BCl₃, BI₃, BBr₃, and SO₃ molecules.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 110–112, August, 1978.     

Mechanism transition of self-pumped phase conjugation in KTa1 −xNbxO3:Fe crystals

Mechanism transitions of Self-Pumped Phase Conjugation (SPPC) with wavelength and doping concentration are observed in KTN:Fe (KTa_{1 –x} Nb _x O₃:Fe with _x = 0.48) crystals. The SPPC mechanism in KTN: Fe (0.4 wt. %) crystal transforms from Stimulated Photorefractive Backscattering and Four-Wave Mixing (SPB-FWM) to cat (or total internal reflection) as the wavelength increases from 514.5 nm to 620 nm. SPPC at 514.5 nm is formed with the cat mechanism in a 0.2 wt. % doped KTN:Fe crystal, while with the SPB-FWM mechanism in a 0.4 wt. % doped one. These mechanism transitions are discussed with respect to the dependence of the backscattering gain coefficient of the crystals on wavelength and doping concentration.     

Field-theoretical approach to static critical phenomena in semi-infinite systems

The critical behaviour of a semi-infinite system withO(n) spin symmetry is studied in 4- dimensions near the ordinary transition using renormalization-group methods of field theory and -expansion techniques. It is found that, to all orders in , all surface exponents can be expressed in terms of two bulk exponents and a single surface exponent which follows from the anomalous dimension of the derivative (x ,0) of The order parameter (x,x ) at the surface (x =0). As a byproduct, Barber's scaling law 2₁ – ₁₁ = + is obtained. The surface exponents are calculated to second order in . Our results show that the scaling relation = ^–1 proposed by Bray and Moore is incorrect. The behaviour of various scaling functions close to the surface (i.e. forx correlation length) is determined with the help of short-distance expansions. We also treat corrections to scaling and logarithmic corrections in four dimensions. Our results for the logarithmic corrections of the layer and local susceptibilities disagree with those obtained by Guttmann and Reeve.A brief account of some of the results presented here was given in [1]. The surface exponents were independently calculated to order ² by Reeve and Guttmann [2] using an alternative method     

A repetitively pulsed sealed-TE CO2 laser using an oxygen tolerant discharge scheme

A repetitively pulsed (40 Hz) TE CO₂ laser using an oxygen tolerant discharge scheme is described. Long lived (>10⁵ shots) stable discharges at high pump energy density (200 J.l^–1 atm^–1) have been achieved both with and without the use of additive gases.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

Interaction of ultrasonic phonons with defects in hydrogenated amorphous germanium

The attenuation of acoustic surface waves of 300 MHz has been measured in sputtered films of amorphous Ge and a-GeH_x (0x0.25) at temperatures between 0.5 K and 475 K. A strong absorption maximum due to structural relaxation is found at 135 K in pure a-Ge. This absorption maximum is shifted by annealing and is suppressed by hydrogen incorporation. Below 20 K the attentuation varies linearly with temperatures in all films investigated so far.On leave from: Department of Physics, Maharshi Dayanand University, Rohtak, 124001, India     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

Role of Activator and Vacancy Centers in the Decay of the Gamma Scintillators of CsI–Na Crystals

The influence of the concentration of an activator (C _NaI) and of plastic deformation on a change in the contribution of a slow component to the decay of the -scintillations of CsI–Na crystals was investigated, as well as the influence of C _NaI on a change in the shape of the luminescence excitation spectrum in the region of absorption of activator centers (AC) and of vacancy-related centers (VRC) and also on a change in the intercenter time of deexcitation of the centers indicated. It is shown that AC and VRC participate in the photoluminescence and -scintillations of CsI–Na crystals. In the -scintillations, AC are responsible for the component ₁ = 370 nsec, whereas the components ₁ = 460 nsec and ₂ 2 sec are associated with VRC. The reduction of ₁ from 770 to 560 nsec with an increase in C _NaI from 2·10^–3 to 3·10^–2 mole% and from 570 to 470 nsec after plastic deformation of the crystals ( = 5%) along the 111 axis is caused by a decrease in the number of VRC. The mechanisms underlying the -scintillations of the CaI–Na crystals containing AC and VRC and also the decrease in the number of VRC are discussed.     

Correlation between the “fishtail” effect in the magnetization and the Schottky contribution in the specific heat of high purity YBA2Cu3O7−δ crystals

The irreversibility of the magnetization and the low temperature specific heat of high purity YBa₂Cu₃O_7– crystals are investigated. We find that the heat treatment that suppresses the magnetic fishtail effect also suppresses the Schottky component of the heat capacity. Both effects originate from the distribution of oxygen states.     

Free carrier scattering mechanism in Bi2Se3 crystals

The single valley model proposed byKöhler andLandwehr is used for the calculation of transport parameters corresponding to pure Bi₂Se₃ crystals. From the measurements of transmission, reflectivity and the Hall constant the effective masses are determined,m _c =0·13m ₀ andm _c=0·56m ₀; using a simplification described in the paper the Fermi level is calculated to lie 0·14 eV above the bottom of the conduction band. This result allows us to conclude that a mixed mechanism of free carrier scattering exists inn-Bi₂Se₃ crystals, viz., the scattering by acoustic phonons prevails contributing about 75% and the scattering on ionized impurities contributes the remaining 25%. This result applies to pure Bi₂Se₃ crystals with free electron concentration 2×10¹⁹cm^–3.