Electron paramagnetic resonance of scandium in silicon carbide

The EPR spectra of scandium acceptors and Sc²⁺(3d) ions are observed in 6H-SiC crystals containing a scandium impurity. The EPR spectra of scandium acceptors are characterized by comparatively small hyperfine interaction constants, whose values are consistent with the constants for other group III elements in SiC: boron, aluminum, and gallium acceptors. The EPR spectra of scandium acceptors undergo major changes in the temperature interval 20–30 K. In the low-temperature phase the EPR spectra are characterized by orthorhombic symmetry, whereas the high-temperature phase has higher axial symmetry. The EPR spectra observed at temperatures above 35 K and ascribed by the authors to Sc²⁺(3d) ions, or to the A ²⁻ state of scandium, have significantly larger hyperfine structure constants and narrower lines in comparison with the EPR spectra of scandium acceptors. The parameters of these EPR spectra are close to those of Sc²⁺(3d) in ionic crystals and ZnS, whereas the parameters of the EPR spectra of scandium acceptors correspond more closely to the parameters of holes localized at group III atoms, in particular, at scandium atoms in GeO₂. It is concluded that in all centers the scandium atoms occupy silicon sites. Fiz. Tverd. Tela (St. Petersburg) 39, 52–57 (January 1997)     

Bases for qudits from a nonstandard approach to <Emphasis Type="Italic">SU</Emphasis>(2)

Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for quantum information and quantum computation are constructed from angular momentum theory and su(2) Lie algebraic methods. We report on a formula for deriving in one step the (1 + p)p qupits (i.e., qudits with d = p a prime integer) of a complete set of 1 + p mutually unbiased bases in C ^p . Repeated application of the formula can be used for generating mutually unbiased bases in C ^d with d = p ^e (e ≥ 2) a power of a prime integer. A connection between mutually unbiased bases and the unitary group SU(d) is briefly discussed in the case d = p ^e .     

Coordinate space form of interacting reference response function ofd-dimensional jellium

Summary The interacting reference response functionX _I ^[3](k) of three-dimensional jellium ink space was defined by Niklasson in terms of the momentum distribution of the interacting electron assembly. Here the Fourier transformF _I ^[d](r) ofX _I ^[d] (k) is studied for the jellium model withe ²/r interactions in dimensionalityd=1,2 and 3, in an extension of recent work by Holas, March and Tosi for the cased=3. The small-r and large-r forms ofF _I ^[d] (r) are explicitly evaluated from the analytic behaviour of the momentum distributionn _d(p). In the appendix, a model ofn _d (p) is constructed which interpolates between these limits.     

Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

Independent electron theory of multiple ionization of xenon by intense laser pulses

The intensity dependence of the multiphoton ionization spectra of Xe atoms has been investigated with an improved accuracy and well-controlled laser parameters. In particular, we have examined the ionization rates for X³⁺, X²⁻, X⁺ as functions of the laser intensity and the pressure in the target chamber. The apparatus used for these measurements is characterized by a high-energy resolution (better than 200 meV) and a completely digital acquisition system. The time-of-flight spectra clearly show the contributions of the different isotopes present in Xe gas. The laser pulses have been characterized with great accuracy by monitoring the energy, pulse width and divergence shot by shot. The ionization rates of the different ions have been used for testing the basic assumption of the Geltman theory of multiple ionization based on the single electron ionization model. We have found that for the small intensity range investigated the quantity (dXe ⁺/dI)·(dXe ³⁺/dI)/(dXe ²⁺/dI)² appears to be quite close to the value 0.5 predicted by this model.     

The group-theoretical structure of the atomic d shell and the energies of the corresponding terms

The icosahedral symmetry I?≈?A ₅ of the atomic d shell can arise from the symmetries of the five-dimensional d orbital space through the subgroup chain SO(5)???SO(3)???I or O(5)???S ₆???S ₅???I. In the latter case the symmetric group S ₅ can be generated from I?≈?A ₅ by addition of the period 4 kaleidoscope operator K, which mixes the d orbitals with m?=?±1 and those with m?=?±2. Furthermore, separation of the d ⁿ configurations into two sets according to the parity of n (even or odd) and the irreps of SO(5) is found to lead to new relationships between the multiplicities and seniorities of the corresponding terms. Thus the sums of the seniorities and multiplicities for even and odd n for a given irrep of SO(5) lead to a constant, namely 12. Furthermore, new pseudodegeneracies are found to arise when the energy expressions of pairs of otherwise equivalent terms with different seniorities for a given d ⁿ are adjusted to remove the radicals arising from solution of the quadratic secular equation. In addition to the well-known ²H/²P degeneracy for d³, ³F/³P degeneracies are found for d⁴ and a ²D/²S pseudodegeneracy is found for d⁵.     

Search for d' in pion inclusive spectra from pp-interactions

We report on our measurement of the inclusive spectrum of positive pions from the reaction pp→π⁺+X on a CH ₂ internal target of the ITEP proton synchrotron at 1.5 GeV/c with a missing mass resolution of about 1 MeV/c². The goal of our experiment was the search for the hypothetical narrow πNN resonance (0.5\ MeV/c² width and a mass of 2.06\ GeV/c²) with I(J ^P P)=even(0⁻), called d′. We do not see any statistically significant d′-signal. The upper limit for d′ production cross-section in pp-interactions is near 2μb at 84%C.L. Received: 5 November 1997     

The influence of cone-covered surface structures on sputtering and secondary electron emission: Model

Abstract

The yield and the polar angular distributions of secondary particles emitted from cone-covered surfaces were studied. A model taking into account both the influence of the local incidence angle I and the blocking of the emitted particles by the surface relief was elaborated. For an emission angle a, the transport effect of the particles generated inside the solid was simulated by the standard relation F(a) = (cos a) ⁿ and the emission dependence on the local incidence angle was assumed to behave as E(I) = (cos I) ^-m . Calculations showed that for m= 1 the surface topography only slightly alters the polar angular distribution shape but the yield of the collected particles is always higher than that from a flat surface when m is more than unity. For n= 2, the shape of the distribution curve is significantly different from that of the corresponding flat surface whatever the m values. For n=0, when E(I) very rapidly increases with the incidence angle both the angular distributions shape and the yield are strongly modified by the surface topography.     

A Derivative Formula for the Free Energy Function

We consider bond percolation on the Z ^d lattice. Let M _n be the number of open clusters in B(n)=[−n,n] ^d . It is well known that E _p M _n /(2n+1) ^d converges to the free energy function κ(p) at the zero field. In this paper, we show that s²_p(M_n)/(2n+1)^d\sigma^{2}_{p}(M_{n})/(2n+1)^{d} converges to −p(1−p)κ′(p).     

Precision measurement of vector and tensor analyzing powers in elastic deuteron-proton scattering

High-precision vector and tensor analyzing powers of elastic deuteron-proton ( d + p) scattering have been measured at intermediate energies to investigate effects of three-nucleon forces. Angular distributions in the range of 70^°-120^° in the center-of mass frame for incident-deuteron energies E _d ^lab = 130 and 180 MeV were obtained using the RIKEN facility. The beam polarization was unambiguously determined by measuring the ^12C (d, α)^10B(2⁺) reaction at 0^°. Results of the measurements are compared with state-of-the-art three-nucleon calculations. The present modeling of nucleon-nucleon forces and its extension to the three-nucleon system is not sufficient to describe the high-precision data consistently and requires, therefore, further investigation.     

Stretched Exponential Fixation in Stochastic Ising Models at Zero Temperature

We study a class of continuous time Markov processes, which describes ± 1 spin flip dynamics on the hypercubic latticeℤ ^d , d≥ 2, with initial spin configurations chosen according to the Bernoulli product measure with density p of spins + 1. During the evolution the spin at each site flips at rate c= 0, or 0 < α≤ 1, or 1, depending on whether, respectively, a majority of spins of nearest neighbors to this site exists and agrees with the value of the spin at the given site, or does not exist (there is a tie), or exists and disagrees with the value of the spin at the given site. These dynamics correspond to various stochastic Ising models at 0 temperature, for the Hamiltonian with uniform ferromagnetic interaction between nearest neighbors. In case α= 1, the dynamics is also a threshold voter model. We show that if p is sufficiently close to 1, then the system fixates in the sense that for almost every realization of the initial configuration and dynamical evolution, each site flips only finitely many times, reaching eventually the state + 1. Moreover, we show that in this case the probability q(t) that a given spin is in state − 1 at time t satisfies the bound: for arbitrary ɛ > 0, q(t) ≤ exp(−t ^{(1/ d ) −ɛ}), for large t. In d= 2 we obtain the complementary bound: for arbitrary ɛ > 0, q(t) ≥ exp(−t ^{(1/2) +ɛ}), for large t. Received: 12 July 2001 / Accepted: 1 February 2002     

Singlet—triplet oscillations of spin-correlated radical pairs due to the Larmor precession in low magnetic fields

Singlet—triplet oscillations in spin-correlated radical pairs have been studied at magnetic field strengths low for one radical and high for the other. Oscillations with frequencies close to the Larmor frequency ω₀ of electron spin precession have been predicted under these conditions. Both numerical and exact analytical solutions in arbitrary magnetic fields are presented for three cases of hyperfine couplings in wide-spectrum radical. For the case of unresolved spectrum, singlet—triplet evolution was found to contain a single oscillating term with frequency ω₀. In the case of one spin-I magnetic nucleus, there are two low frequency oscillating terms with frequencies ω_? = ω₀ ? ω₀/(2I + 1) and ω₊ = ω₀ + ω₀/(2I + 1), the amplitude of the first term being larger than that of the second. The case of a number of equivalent protons also has been analysed as a superposition of one-nucleus oscillations. The predicted oscillations were observed in a time resolved magnetic field effect for several radical ion pairs produced by X-ray irradiation of alkane solutions with charge acceptors. For pairs (p-terphenyl-d ₁₄)^?./(isooctane)^+. and (p-terphenyl-d ₁₄)^?./(2,4-dimethylpentane)^+. the oscillation frequency in a field B ₀ of 0.5–4mT is about 20% lower than ω₀. Oscillations were observed also in pairs with equivalent nuclei: (p-terphenyl-d ₁₄)^+./(C₆F₆)^?. and (p-terphenyl-d ₁₄)^?./(hexamethylethane)^+.     

Fine structure and isotope shift of the 3s4d 3 D-3s3p 3 P, 3s5d 3 D-3s3p 3 P and 3p 2 3 P-3s3p 3 P Transitions of MgI

Summary We report the measurements of the³ D(3s4d)-³ P(3s3p)³ D(3s5d)-³ P(3s3p), and³ P(3p ²)-³ P(3s3p) transition frequency of MgI, the fine-structure separation and isotope shift between²⁴Mg and²⁶Mg. The measurements have been performed in a metastable atomic beam; a good agreement is found for data already existing in the literature. The accuracy of the measurements reported in this paper is mainly limited by the Doppler broadening of theI ₂ transitions used as a reference and by the precision in the knowledge of the related wavelengths.     

Reacting polymers with highly correlated initial conditions

We propose and theoretically study an experiment designed to measure short-time polymer reaction kinetics in melts or dilute solutions. The photolysis of groups centrally located along chain backbones, one group per chain, creates pairs of spatially highly correlated macroradicals. We calculate time-dependent rate coefficients κ(t) governing their first-order recombination kinetics, which are novel on account of the far-from-equilibrium initial conditions. In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved. This leads to a generalised mean-field kinetics in which the rate of radical density decay - ∼S(t), where S(t) ∼t ^{- (1 + g/3)} is the equilibrium return probability for 2 reactive groups, given initial contact. Here g≈ 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time τ, - ∼S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) ∼t ^1/2 and S(t) ∼ 1/x ³(t). At the shortest times ( t 10^-6s), recombination is inhibited due to spin selection rules and we find ∼tS(t). In melts, kinetics are intrinsically diffusion-controlled, leading to entirely different rate laws. During the regime limited by spin selection rules, the density of radicals decays linearly, n(0) - n(t) ∼t. At longer times the standard result - ∼d ³(t)/d (for randomly distributed ends) is replaced by ∼d2x ³(t)/d ² for these correlated initial conditions. The long-time behavior, t > τ, has the same scaling form in time as for dilute solutions. Received 18 May 2000     

The effect of ligands on the first hyperpolarizabilities of rich d electron molecular system: iridium clusters,a TDDFT study

A systematically varied series of tetrahedral iridium clusters have been studied using a TDDFT method focusing on their electronic and nonlinear optical properties. The clusters W₂Ir₂(CO)₁₀(η⁵-C₅H₄Me)₂ (1), WIr₃(μ-dppe)(CO)₉(η⁵-C₅H₄Me (2), W₂Ir₂(μ-L)(CO)₈(η⁵-C₅H₄Me)₂(L = dppe 3, dppf 4), Ir₄(μ-L)(CO)₁₀(L = dppm 5, dppe 6, Ph₂P(CH₂)₃PPh₂ 7, Ph₂P(CH₂)₄PPh₂ 8, (Ph₂P)₂CHMe 9), Ir₄(CO)₁₀(phen)(phen = 1,10-phenanthroline) (10) exhibit the first static hyperpolarizabilities of medium magnitude (β _tot ～ 10 × 10^?30esu). The origination of β is discussed in terms of the electronic structure calculation and the expanded orbital decomposition scheme. The result suggests the origination of β for all the clusters are mainly d–d electron transitions intra metal skeleton, and d–π* electron transitions from metals to carbonyls. For cluster 5, which contains the ferrocenyl group, the main origination of β involves charge transfer from d orbitals of ferrocene to d orbirals of Ir and W.     

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

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^-).     

Speckle correlations in the light scattered from weakly rough random metal surfaces

Abstract

Diagrammatic perturbation theory and computer simulation methods are used to compute the angular intensity correlation function C(q, k|q′,k′)=([I(q|k) - (I(q|k))] × [I(q′|k′) - (I(q′|k′))]) for p-polarized light scattered from a weakly rough, one-dimensional random metal surface. I(q|k) is the squared modulus of the scattering matrix for the system, and q, q′ and k, k′ are the projections on the mean scattering surface of the wavevectors of the scattered and incident light, respectively. Contributions to C include: (a) short-range memory effect and time-reversed memory effect terms, C ⁽¹⁾; (b) an additional short-range term of comparable magnitude C ⁽¹⁰⁾; (c) a long-range term C ⁽²⁾; (d) an infinite-range term C ⁽³⁾; and (e) a term C ^(1.5) that along with C ⁽²⁾ displays peaks associated with the excitation of surface plasmon polaritons. The diagrammatic methods are also extended to treat the angular intensity correlation function for the scattering of p to p, p to s, s to p, and s to s polarizations of light from a two-dimensional randomly rough surface. These correlations are again described in terms of C ⁽¹⁾, C ⁽¹⁰⁾, C ^(1.5), C ⁽²⁾, and C ⁽³⁾ contributions to C for the two-dimensional surfaces. Short-range memory and time-reversed memory effects are observed in the two-dimensional C ⁽¹⁾ correlations, and peaks associated with the excitation of surface polaritons are observed in the two-dimensional C ^(1.5) and C ⁽²⁾ correlations. Most of the results for the one- and two-dimensional systems are presented for incident electromagnetic plane waves. In addition, results for one-dimensional systems are presented for incident electromagnetic beams of finite width. Some of the results for one-dimensional surfaces are corroborated by means of computer simulation techniques.     

Zero-Temperature Dynamics of ±J Spin Glasses¶and Related Models

We study zero-temperature, stochastic Ising models σ ^t on Z ^d with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type ℐ (resp., type ℱ) if, for every x in Z ^d , σ _x ^t flips infinitely (resp., only finitely) many times as t→∞ (with probability one) – or else mixed type ℳ. Models of type ℒ and ℳ exhibit a zero-temperature version of “local non-equilibration”. For d=1, all types occur and the type of any μ is easy to determine. The main result of this paper is a proof that for d=2, ±J models (where μ=αδ _J +(1-α)δ_{- J} ) are type ℳ, unlike homogeneous models (type ℐ) or continuous (finite mean) μ's (type ℳ). We also prove that all other noncontinuous disordered systems are type ℳ for any d≥ 2. The ±J proof is noteworthy in that it is much less “local” than the other (simpler) proof. Homogeneous and ±J models for d≥ 3 remain an open problem. Received: 3 November 1999 / Accepted: 10 April 2000     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002