The electronic structure of Rhodium: Angle-resolved studies of photoelectron and secondary electron emission

We report electron spectroscopic studies of the Rh(111) surface, with the aim to obtain bulk band-structure information. We have measured normal photoemision using tunable synchrotron radiation in the range of photon energies between 11 eV and 55 eV, and angle-dependent photoemission along the LUX and LKL azimuths using the He resonance lines (=21.2 eV, 40.8 eV). To complement these data, we studied angleresolved secondary electron emission after excitation with electrons and photons. We derive parts of the one-electron energy dispersionE(k) along L, and determine the energies of several bulk critical points (in eV):E(> ₇₊/₈₊)=–2.75±0.10,E(> ₈₊=–0.85±0.10,E(> _7–=16.1±0.5,E(> _6–/> _8–)=20.5±0.5,E(X ₇₊)=–5.0±0.1,E(L ₆₊)=–5.6±0.5,E(L ₆₊/L ₄₊₊₅₊)=–2.65±0.10,E(L ₆₊)=9.0±0.5 eV. Our results are compared to several available band structure calculations.     

The effect of the crystal-field ground-state splitting on the electrical resistivity of dilute (La,Pr)B6

We have measured the resistivity and the magnetoresistivity of some dilute (La, Pr)B₆ single crystals. At temperatures below 1 K a pronounced step in the resistivity occurs which shifts to higher temperatures with increasing Pr concentration as well as with increasing external magnetic fields. The observed resistance anomaly is caused by Pr–Pr interactions which remove the degeneracy of the ₅ crystal field ground state of Pr³⁺ in LaB₆. The resistance step reflects the temperature-dependent probability that conduction electrons are scattered from the ₅ crystal field sublevels of the Pr³⁺ ions. The shift of the resistance step in a magnetic field can be simply explained as Zeeman effect of the ₅ triplet.     

ГЕОМАГНИТНЫЙ ЭФФЕКТ ШИРОКИХ ЛИВНЕЙ КОСМИ ЧЕСКИХ ЛУЧЕЙ

( - .). , - , - , - . , D=30 40% , ; D=50 60%. .     

On interesting walks in a graph

Notions of interesting walks and of their equivalence are introduced. A general formula for the number _l, of equivalence classes of interesting walks of lengthl in a given graphG is derived and applied forl 5 so as to express _l in terms of the adjacency matrix ofG.     

Pseudo-Jahn-Teller effect in tetragonal local centers

The shape of the light absorption band by a local tetragonal center at the transition _{1 5}(x, y) is investigated in a semiclassical approximation. In addition to interaction with fully-symmetric (₁), Jahn-Teller (₃, ₄) vibrations, inter-action is also taken into account with vibrations ₅, which admix an electron level ₄(z) to the electronic state ₅, which is separated from ₅ by the energetic gap . An analytic computation of the band shape is performed in the first order of the expansion of the form function in ^–1. An asymmetric two-hump band is obtained, where the long-wave maximum always has higher intensity than the shortwave maximum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 62–67, December, 1987.     

Estimating the strength of chaos from the power spectrum

It is rigorously proved that for nonlinear dynamical systems whose time dependence is described by one dimensional, everywhere expanding maps, the width of broadband noise in the power spectrum is bounded by the generalized entropiesK ₂ andK ₃, which measure the strength of chaos in this system asK ₂2K ₃.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

From monotonic to oscillatory decay of correlations: Analytical approximation for the two-dimensional,one-component plasma

An approximate evaluation of the pair distribution and the structure factor is performed analytically for the two-dimensional, one-component plasma at any value of the coupling constant. The approximate distribution remains positive and satisfies three sum rules, including the compressibility one. When 0 or 2, exact results are found. At=2 the transition from monotonie (<2) to oscillatory (>2) decay of correlations takes place. Comparison with the Monte Carlo simulations shows good agreement for 0<<4.     

Long range atomic potentials in Thomas-Fermi theory

We prove that the interaction among neutral atoms in Thomas-Fermi theory behaves, for large separationl, likel ^–7. The constant is independent of the atomic nuclear charges, but does depend on the relative positions of the nuclei. We also show that is not a simple sum of pair terms, i.e. in TF theory three and higher body terms persist into the asymptotic (inl) region.Work partially supported by U.S. National Science Foundation grant MCS 75 21684 A02     

Some properties of an “aesthetic” field theory

We continue our study of the Lorentz-invariant field theory based on the equations _jk;l ⁱ =0 and g_ij;k=0. To first order in a perturbation expansion, we find _jk;l ⁱ =0 reduces to the wave equation. In orders higher than the first, we find that _jk;l ⁱ =0 cannot be linearized. We also find that the simple wave-type equation g^ij2g/xⁱx^j=0 is contained in the theory when an appropriate choice is made for the parameters at the origin point.     

Resonant tunnelling in asymmetrical double barrier structures – complex coordinate approach

The complex coordinate approach of theoretical atomic spectroscopy is applied to the study of resonant tunnelling in (Ga,In)As/(Al,In)As-based asymmetrical double-barrier heterostructures within applied electric field. The method yields complex eigenvalues E = E _r – i/2 of the Hamiltonian matrix evaluated in a normalizable basis, where E _r is the resonant energy and = / is the tunnelling lifetime. The dependence of E _res on the field and barrier asymmetry is discussed.     

jj-Type of coupling in the scheme to construct the energy levels of a shallow acceptor in semiconductors

There is examined the classification of shallow acceptor energy levels by jj-type coupling, whose wave functions are converted by sets of irreducible representations by one of the subgroupsD _4h ^/ ,D _3d ^/ ,D _2h ^/ of the group o _h ^/ . The representations ₅ ⁺ of the groupD _4h ^/ are obtained in the one-function approximation by using a variational method, and systems of eight radical second-order differential equations are solved for two functions ₅ ⁺ in the case of a shallow acceptor in germanium by the method of orthogonal differential factorization. A comparison is made of the two low levels found and their radial functions for each of the functions ₅ ⁺ with the computed levels and the functions of LS-type coupling.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 103–107, September, 1981.The authors are grateful to N. P. Konyukhova for great assistance in the numerical solution of the system of radial equations.     

Estimates of general Mayer graphs. II. Long-range behavior of graphs with two root points occurring in the theory of ionized systems

We find the asymptotic behavior of general Mayer 2-graphs (Mayer graphs with two root points), which occur in the theory of ionized systems. This problem arises when one wants to compute corrections to the Debye length for large values of the plasma parameter. For a given 2-graph (r) with Debye-Hückel linese ^– /r, we prove the inequalitiesC _m r ^– e ^– (r) (r ₀)C_Mr^3k–l e ^– , for anyrr ₀, and whereC _m andC _M are positive and finite constants which depend only on . These bounds are finite whenever (r) is not infinite everywhere. The integersl, k, and denote, respectively, the number of lines of the graph , its number of field points, and its local line connectivity (the maximum number of chains linking the root points, which have no line in common). From this result, we deduce that the simple irreducible 2-graphs dominant at large distances decay exponentially likee ^– and have an isthmus between the root points (an isthmus is a line whose deletion separates the graph into two disjoint components, each one containing a root point). We prove also that 2-graphs that have a number of linesl > 3k+ are infinite. We exhibit simple, irreducible prototypes satisfying this condition, for anyk 6. This implies that the Abe-Meeron theory of ionized gases as applied to a classical plasma is not free from divergences. Finally, we extend the preceding results to 2-graphs with lines F_L=(e ^– /r)^k L, withk _L real positive. We prove that they still decay exponentially likee ^– , where is now the maximal flow in a network associated to by assigning the capacityk _L to each lineL.     

Monte Carlo Simulations of the Yukawa One-Component Plasma

The excess free energy f of the Yukawa one-component plasma is investigated by means of Monte Carlo simulations. These simulations are performed in the canonical ensemble within hyperspherical boundary conditions and f is computed for various values of the coupling parameter in the range 0.1100 and of the screening parameter * in the range 0.1*6.     

The magnetic behavior of CeB6: Comparison between elastic and inelastic neutron scattering,initial susceptibility and high-field magnetization

We report measurements of the elastic and inelastic neutron scattering, initial susceptibility and high-field magnetization on thoroughly prepared poly- and single crystalline samples of CeB₆. Part of these experiments have been performed at temperatures down to 60 mK and magnetic fields up to 70 kØe. Our neutron-diffraction data provide the first proof that CeB₆ is an antiferromagnet belowT _N2K as has been suggested by previous bulk experiments. The reduced value of the low-temperature magnetic moment both below and aboveT _N points to the existence of a Kondo effect of the ₇ crystal-field (CF) ground state of Ce³⁺. From the low-temperature width of the quasielastic neutron line, the Kondo temperature is inferred to beT _K3 K. The thermal variation of the initial susceptibility (forT>20K) is semiquantitatively explained invoking, besides the Kondo effect, a ₇- ₈ CF splitting of 70 K and magnetic interactions, which are about 10 times stronger between ₈ states than those between ₇ states. This large ₈- ₈ exchange interaction is also assumed to account for the most striking result of this work, i.e. the lack of any CF-transition peak up to 44 meV in our inelastic neutron-scattering spectra.     

SPA-LEED studies of growth of Ag on Ag(111) at low temperatures

The surface morphology after deposition of Ag on Ag(111) at low temperatures (130–200 K) has been studied in detail with SPA-LEED (Spot-Profile Analysis of Low-Energy Electron Diffraction). The surface roughness and the mean terrace size have been quantitatively determined under various conditions. At 130 K the surface roughness increases with coverage exactly according to the relation = ^1/2, which indicates that the inter-layer diffusion can be neglected at 130 K. Although the mean terrace length decreases with increasing coverage (following an approximate power law of ^–2/3) for all studied coverages, it is much larger than expected for a pure random or Poisson-growth mode without any diffusion of the adatoms. Therefore, Ag grows on Ag(111) at this temperature without interlayer diffusion but with intra-layer diffusion. The intralayer diffusion barrierE _d has been determined by measuring the temperature dependence of the two-dimensional island density according to the nucleation theory (supposing a critical nucleus size of one). The obtained valueE _c=0.18 eV agrees with the theoretical calculations and previous measurements. Furthermore, from comparing measured and Monte-Carlo-simulated (MC) surface roughness at different deposition temperatures we obtain E=0.05 eV as a lower limit for the additional barrier at steps.     

Charge Fluctuations in the Two-Dimensional One-Component Plasma

We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density –e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N , the number of mobile particles of charge e. As expected, the distribution of N has, for large , a Gaussian form with a variance which grows only as ^||, where || is the length of the perimeter of . The properties of this system depend only on the coupling parameter =kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^() decreases to an asymptotic value ^()^(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length _L=2^/ associated with charge fluctuations behaves very differently from that of the Debye length, _D1/ , which it approaches as 0. The pair correlation function of the OCP is also studied.     

Differential algebras for quantum groups of type B, C, and D

We study higher order bicovariant differential calculi on the quantum groups O_q(N) and Sp _q (N). We show that the second antisymmetrizer exterior algebra _u is the quotient of the universal exterior algebra _u by the principal ideal generated by . Here denotes the unique up to scalars biinvariant 1-form. Moreover is central in _u and _u is an inner differential calculus. We show that the quadratic dual to the left-invariant algebra _{s L} is isomorphic to the reflection equation algebra. Let be an arbitrary left-covariant first order differential calculus. We show that the dimension of the space of left-invariant 2-forms in the universal exterior algebra equals the number of linearly independent quadratic-linear relations in the quantum tangent space.     

Elastic constants and quadrupolar interactions in the (LaCe)B6 series

Elastic constants of (La_1–xCe_x)B₆(x=0.01, 0.03, 0.1) dilute alloys have been determined by ultrasonic measurements at temperatures between 0.5 K and 4.2 K. The temperature dependence ofc ₄₄ and (c ₁₁–c ₁₂)/2 is in excellent agreement with calculations including magnetoelastic and interionic quadrupolar interactions. The single ion coupling constantsg (=₃, ₃) are independent of concentration. The systematic concentration dependence of quadrupolar coupling constants g'g(x) from the dilute (x=0.01) alloy to the compound CeB₆ (x=1) has been studied. Evidence of Grüneisenparameter coupling in the bulk modulus but no indication for a ₈ ground state splitting or a quadrupolar Kondo effect has been found. In addition the magnetic field dependence of elastic constants up to 6.5 Tesla was investigated.     

Higher order differential calculus on SL q(N)

Let be a bicovariant first order differential calculus on a Hopf algebra . There are three possibilities to construct a differential N ₀-graded Hopf algebra which contains as its first order part. In all cases is a quotient = /J of the tensor algebra by some suitable ideal. We distinguish three possible choices _u J, _s J, and _W J, where the first one generates the universal differential calculus (over ) and the last one is Woronowicz' external algebra. Let q be a transcendental complex number and let be one of the N ²-dimensional bicovariant first order differential calculi on the quantum group SL _q(N). Then for N 3 the three ideals coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant k-forms. In this case each bi-invariant form is closed. In case of 4D _± calculi on SL _q(2) the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed.     

Monte Carlo simulation of phase separation and clustering in the ABV model

As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump rates _A and _B, respectively. For a small concentration of vacancies (c _v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk ₁(t),k ₂ ² (t) is studied during the early stages of phase separation, for several choices of concentrationc _B of B atoms. Forc _B=0.18 also the time evolution of the cluster size distribution is studied. Apart from very early times, the mean cluster sizel(t) as well as the moments of the structure function depend on timet and the ratio of the jump rates (= _B/ _A) only via a scaled timet/(). Qualitatively, the behavior is very similar to the direct exchange model containing no vacancies. Consequences for phase separation of real alloys are briefly discussed.