Multiparticle perturbation theory and an accurate calculation of parity nonconservation in cesium

A method of calculating higher-order correlation corrections, using Green's functions and the Feynman diagrammatic technique, is developed. A basis of the single-electron orbitals is computed using the relativistic Hartree-Fock method. The interaction of an atom with an external field is computed by solving the time-dependent Hartree-Fock equations. In the methodology presented, we consider all the second-order correlation corrections and the dominating classes of higher order diagrams: the screening of the Coulomb interaction of electrons, particle-hole interaction and mass operator iterations. The calculation of the energy levels, the intervals of hyperfine structure and the amplitudes of the allowed EI-transitions in C_s shows that the method developed ensures precision at the 0.1–1% level. A calculation of the parity nonconservation of the El-amplitude of the transition 6s–7s in Cs is produced. The result <6s¦D_z¦7s> = –(0.91 ± 0.01)·10^–11 i¦e¦a^B (–Q_W/N) is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 108–119, August, 1990.     

Kinetic theory of nonlinear viscous flow in two and three dimensions

On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦^3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is proportional to the velocity gradient in the shear flow. The origin of these terms is closely related to the hydrodynamic tails t^–d/2 in the current-current correlation functions. These results also imply that a nonlinear shear viscosity exists in two-dimensional systems. An extensive discussion is given on the range ofX values where the present theory can be applied, and numerical estimates of the effects are given for typical circumstances in laboratory and computer experiments.Supported by National Science Foundation grant No. CHE-73-08856 (to HvB, JRD, and JS) and the Center for Theoretical Physics of the Univ. of Md. (to HvB).On leave from Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.     

The sub-micrometer thickness n-InSb/i-GaAs epilayers for magnetoresistor applications at room temperatures of operation

Magnetotransport at fields up to 500 mT and LF-noise characteristics are reported for miniature magnetoresistors with ferrite concentrators based on Sn-doped n-InSb/i-GaAs heterostructures grown by MBE. The thickness of the InSb epilayers lie in the range 0.55–1.5 μm giving room temperature mobilities of 2.5–5.5 m² V⁻¹ s⁻¹ with carrier densities of (0.5–1.5)×10¹⁷ cm⁻³. The room temperature magnetoresistance (MR) for our two terminal devices could be as high as 115% at 50 mT which is comparable to the extraordinary MR (ExMR) recently reported in microscopic composite van der Pauw disks four terminal devices [Science 289 (2000) 1530]. In addition, a high signal-to-noise ratio and a good temperature stability of R(B)/R₀=0.5–0.83% K⁻¹ was observed for B<60 mT (below the saturation field B_sat for ferrite). Device resistance stability R₀(T) was equal to 0.27–0.66% K⁻¹ in zero field with a nominal device resistance R₀=197–224 Ω for DC currents in the range I=0.01–1.0 mA. The minimum detectable magnetic field is estimated from the reduced differential MR (∂R/∂B)/R=2000% T⁻¹ at B=31 mT and normalised 1/f current noise power spectral density measured at the same field. The resolution limit B_min=2.6 nT at 10² Hz and B_min=0.82 nT at 10³ Hz. These resolution limits are seven times better than those recently reported for the same material n-InSb/i-GaAs and ferrite fabricated Hall sensors [Magnetotransport and Raman characterization of n-InSb/i-GaAs epilayers, for Hall sensors applications over extremely wide ranges of temperature and magnetic field, Proceedings NGS 10, IPAP Conference Series 2, IPAP, Tokyo, 2001, pp. 151–154].     

Spin coupling in distorted high-valent Fe(IV)-porphyrin radical complexes

In order to study structural influences on the interaction of Fe(IV) (S=1) and porphyrin cation radical (S=1/2) in high-valent iron porphyrin complexes of the type ¦X-(TMP)Fe=O¦⁺(Cl^–), X=I, Br₂, Br₄ were generated by mCPBA oxidation of corresponding Fe(III) porphyrins. The halogen substitution at the peripheral positions of the porphyrin leads to distortion of the planar porphyrin ring of ¦(TMP)Fe=O¦⁺. The new species have beeen investigated by temperature-dependent EPR and field-dependent Mössbauer spectroscopy; for the evaluation of spectra, we adopted the spin-Hamiltonian formalism including exchange interaction explicitly. As in ¦(TMP)Fe=O¦⁺, strong ferromagnetic spin coupling was observed with|J₀|D=0.9–1 and a zero-field spltting ofD32 cm^–1. For consistent parametrization of EPR and Mössbauer results, anisotropic coupling had to be introduced. Compared to ¦(TMP)Fe=O¦⁺ [1], analysis of the spectroscopic data shows that zero-field splitting and spin coupling is only slightly affected by the halogen distortion of the porphyrin structure.     

G v,CKM unitarity,neutron decay; WR?

Superallowed Fermi beta-decay is analyzed in the light of new experimental data, new methodology and new treatment of the radiative and charge-dependent corrections. The following values are recommended:G _v /(c) ³=(1.13769±0.00091)×10^–5 GeV^–2;G _v ^* /(c) ³ =(1.15128±0.00084) × 10^–5GeV^–2 whereG _v is purged of radiative corrections suitably for combining withG to gain: ¦V _ud ¦=0.97539±0.00080 which leads to:¦V _ud ¦ ² +¦V _us ¦ ² +¦V _ub ¦²=1.0000+0.0017 and whereG _V ^* is the operational constant, incorporating the inner radiative correction, suitable for use in ordinary nuclear physics. It is noted that present results on the beta-decay of the neutron, when confronted by the above values, are inconclusive as to possible conflict with the minimal standard model and that judgement as to, for example, the intervention of a right-handed sector, should be suspended. The valueG _A ^* =1.2657±0.0030 is also recommended.     

Critical behavior of the two-dimensional first passage time

We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1–p, respectively. We prove that as the zero-time bonds approach the percolation thresholdp _c, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys(p) ¦p–p _c¦^–v, then the first passage time constant satisfies(p)¦p–p _c¦^v. At p_c, where it has been asserted that the first passage time from 0 tox scales as ¦x¦ to a power with 0<<1, we show that the passage times grow like log ¦x¦, i.e., the fluid spreads exponentially rapidly.     

Detection on NMR via the anisotropy of X-rays (X-NMR-ON)

Nuclear magnetic resonance on oriented nuclei has been detected for the first time via the destruction of the anisotropy of characteristic L_x-rays. The new method can be applied to isomeric states which decay only via highly converted transitions, for which the standard NMR-ON technique — detection of NMR via the anisotropy of -rays — is not applicable. The X-NMR-ON technique has been used to measure the magnetic hyperfine splitting of^193mpt (I=1322⁺; E=149.8 keV; T_1/2= 4.3 d) to be ¦ g _NB_HF/h¦=111.3 (3) MHz. with the known hyperfine field of –1280(27) kG the magnetic moment of^193mpt is deduced to be ¦¦=0.7417(14) _N. This magnetic moment differs strongly from the known magnetic moments of the 13/2⁺ isomeric states in Hg and Pb and^195mPt.     

Thermal property of binary tetrahedral semiconductors

In this paper we present an expression relating the lattice thermal expansion coefficient α_L (10⁻⁶ K⁻¹) for the A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z₁Z₂), melting temperature (T_m) and nearest neighbor distance d (Å). The lattice thermal expansion coefficient of these compounds exhibit a linear relationship when plotted on a log–log scale against the melting temperature (T_m), but fall on different straight lines according to the ionic charge product of the compounds. A good agreement has been found between the experimental and calculated values of the lattice thermal expansion coefficient for A^IIIB^V and A^IIB^VI semiconductors.     

Dipolar magnetic field and fermi contact field at the μ+ site in α-Fe at very low temperatures

In a longitudinal ⁺SR experiment on a high-purity-Fe single crystal sphere magnetically saturated in a 111 direction damped oscillations (wiggles) were observed in a temperature range 30 mK to 600 mK and in a certain regime of applied magnetic fieldsB _appl. Meassurements of the wiggle frequency as a function ofB _appl give us directly the Fermi fieldB _Fermi=(–1.13±0.02)T and the dipolar magnetic field ¦B _dip ¦=(0.66±0.03)T.B _dip was used to determine the prefactor in the Arrhenius law obeyed by the ⁺ hopping rate between 100 K and 1000 K. A comparision with the corresponding values for protons and deuterons suggests diffusion via the adiabatic mechanism.     

Electric field gradient in Mg and Zn detected by β-emitters,8Li and12x0392;x0392;x0392;

The quadrupole coupling constants of⁸Li and¹²B in hcp Mg and Zn are determined by use of a newly developed nuclear quadrupole resonance technique (NNQR) as ¦eqQ(⁸Li in Mg)/h¦=3.0±0.3 kHz, ¦eqQ(⁸Li in Zn)/h¦=33.5±2 kHz, and ¦eqQ(¹²B in Mg)/h¦=47.0±0.1 kHz. Correspondingly, the electric field gradients at room temperature are deduced: ¦q(⁸Li in Mg)¦=(3.81±0.39)×10¹⁸, ¦q(⁸Li in Zn)¦=(4.25±0.27)×10¹⁹, and ¦q(¹²B in Mg)¦=(1.47±0.03)×10²⁰, all in V/m². The experiments are compared with the results of first-principles super-cell band structure calculations which can treat local lattice relaxations around the impurity nuclei. The calculations show that the most favorable location of these light interstitials in hcp Mg is not the octahedral-like sites which have the biggest interstitial volume, but the basal trigonal sites with a local lattice expansion of as big as 30%. Calculated electric field gradients at the impurity nuclei reproduce the experimental values fairly well.     

The runaway effect in a Lorentz gas

The Lorentz gas of charged particles in a constant and uniform electric field is studied. The gas flows through the medium of immobile, randomly distributed scatterers. Particles with velocity v suffer collisions with frequency proportional to ¦v¦ ⁿ . Forn < 0 runaway of the gas is forced by the field: the mean velocity of the flow increases without bounds. By a simple physical argument an integral relation is established between the probability of collisionless motion and the velocity distribution. It is then shown that whenn < –1 a fraction of particles moves as if the scattering centers were absent. The detailed discussion of this uncollided runaway is presented. Some qualitative features of the velocity distribution are illustrated on rigorous solutions in one dimension.     

Excited Even-Symmetry States of Metallocomplexes of Porphin and Its Derivatives

Based on calculations by the CNDO/S method, data on the excited molecular states of even parity of the magnesium complexes of porphin (P), tetraazaporphin (TAP), tetrabenzoporphin (TBP), and phthalocyanine (Phc) are obtained. It is only in MgP that the first excited g-state 1¹ B _2g (29,000 cm^–1) is located 300 cm^–1 higher than the B level (28,700 cm^–1). In MgTBP, the two states 1¹ B _1g (24,700 cm^–1) and 1¹ B _2g (25,500 cm^–1) are found to be near the B level (27,500 cm^–1), while the states 1¹ B _2g (25,500 cm^–1) in MgTAP and 1¹ B _2g (21,000 cm^–1) and 1¹ B _1g (23,100 cm^–1) in MgPhc are located much lower than the B level; the energy of the latter is 31,900 and 32,400 cm^–1 in MgTAP and MgPhc respectively. The results obtained are in good agreement with experimental data on two-photon absorption: in the zinc complex of tetraphenylporphin (TPhP), the g-state is detected in the region of the B level, while in ZnPhc, two bands at 20,400 and 21,700 cm^–1 show up.     

Appearance of a purely singular continuous spectrum in a class of random schrödinger operators

We consider a discrete Schrödinger operator on l²() with a random potential decaying at infinity as ¦n¦^–1/2. We prove that its spectrum is purely singular. Together with previous results, this provides simple examples of random Schrödinger operators having a singular continuous component in its spectrum.     

Diffusion in layered random flows,polymers, electrons in random potentials,and spin depolarization in random fields

Several related models are studied in a common framework. We first reconsider the model of Matheron and de Marsilly for (anomalous) tracer dispersion in a stratified porous medium. In each horizontal layer the flow velocity is constant, parallel to the layer, and depends randomly on the vertical coordinate z. This model is mapped onto ad=1 localization problem in a random potential and, equivalently, onto ad=1 polymer. At larget theaveraged distribution of horizontal displacementsx takes the scaling form [P(x, t, z=0)]=at ^–5/4 Q(bxt ^–3/4), whereQ(y) is independent of the details of the model.Q(y),a, andb are obtained exactly for a large class of models. From the Lifschitz tails of the localization problem we find in the regionxt ^3/4, i.e.,y, thatQ(y)¦y¦ exp(–C¦y¦^4/3). We also obtain exactly ind=1 the scaling functions for the local and total average magnetization of spins diffusing in a random magnetic field, by mapping onto a polymer problem, as well as the average local concentration for diffusion in the presence of random sources and sinks. These mappings are then used to study higher-dimensional extensions of these models.     

Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by _t =2 fort=2, 3,. Scaling theory predicts thatP _p (¦C ₀¦S(p))–(p _c –p) andE _p (1/¦C ₀¦; ¦C ₀¦S(p))–(p _c –p)³, whereS(p) is the typical cluster size. It is found that (p _c –p)P _p (|C ₀S(p) ^1–)(p _c –p)^1–2 and (p _c –p)³E _p (1/|C ₀|;|C ₀|S(p) ^1–))(p _c –p)^3–4.     

Diffusion of silicon in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained film structure (B ₊ films) have been examined as diffusion barriers, preventing the silicon diffusion in silicon devices. The silicon diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) after annealing at temperatures up to 900° C, in view of application of high-temperature processes. The diffusivity from 400 to 900° C: D (m² s^–1)=2.5×10^–18 exp[–31 kJ/mol/(RT)] in B ₀ layers and D (m² s^–1)=3×10^–19 exp[–26 kJ/mol/(RT) in B ₊ TiN layers. The diffusivities determined correspond to grain boundary diffusion, the difference being due to the different microstructure. The very low diffusivity of silicon in B ₊ TiN layer makes it an excellent high-temperature barrier preventing silicon diffusion.     

Some more universal scaling laws for critical mappings

We study such nonlinear mappingsx _n +1=F(x _n ;b _cr) of an intervalI into itself for which the Feigenbaum scaling laws hold (i.e., for which b_cr is an accumulation point of bifurcation points). Letx ₀ be a random variable with some absolutely continuous distribution inI. We show in particular that (i) the geometric average distance ofx _n from the nearest point of the attractor decreases liken ^–1.93387; (ii) the geometric average of ¦x _n /x ₀¦ increases liken ^0.60; (iii) the geometric mean distance ¦x _n –y _n ¦ between the iterates of two close-by pointsx ₀,y ₀ asymptotically tends towards a value ¦x ₀–y ₀¦^0.77. These-and other-properties are also borne out from a simple probabilistic model which depicts the evolution as a random walklike process.     

Parity violation in the 17/2−–17/2+ doublet in93Tc

The parity-violating mixing of the 17/2^– and 17/2⁺ levels in⁹³Tc nuclei, polarized by the tilted multifoil interaction, was measured by the observation of the forward-backward-ray asymmetry. The nuclear polarization, induced by the tilted multifoils, was measured directly for the neighboring^88,90Zr isomers. The forward to backward asymmetry was determined to be A=(2.5±2.1) 10^–3 which implies a parity violating matrix element ¦H _PV )¦=(4.0±3.7)meV.     

The tortuosity of occupied crossings of a box in critical percolation

We consider the length of an occupied crossing of a box of size [0,n]×[0, 3n] ^D–1 (in the short direction) in standard (Bernoulli) bond percolation on ^D at criticality. Let ¦s _n¦ be the length of the shortest such crossing. It is believed that ¦s _n¦ ^1+c in some sense for somec>0. Here we show that if the correlation length(p) satisfies (p)p _c}–p) ^– for some <1, then with a probability tending to 1, ¦s _n¦>/C ₁ n ^1/(logn)^–(1–)/. The assumption (p)C ₃(p _c–p)^– with <1 has been rigorously established^(1,2) for largeD, but cannot hold⁽³⁾ forD=2. In the latter case, let ¦l _n¦ be the length of the lowest occupied crossing of the square [0,n]². We outline a proof ofP _pc(¦l_n¦ n ^1+c)n ^– for somec, >0. We also obtain a result about the length of optimal paths in first-passage percolation.     

Electric field effect on the density of localized electron states

The effect of a weak external homogeneous electric field on the density of localized electron states has been investigated. While the density of strongly localized states increases exponentially with the electric field, the relative decrease in the density of weakly localized states is found to decrease asn(E)/n(E) –f ²¦E¦ into the gap.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.Editorial notice: We regret to record the death of Professor Trlifaj on 10. 2. 1982.