Four-Nucleon States in the Continuum: A Means to Probe the Nucleon-Nucleon Interaction

 Four-nucleon states in the continuum are studied through exact microscopic calculations based on the solution of the AGS equations for four nonrelativistic quantum particles. Our studies include calculations of cross sections and analyzing powers for all two-body reactions of interest, but here we only show results for n ³He → n ³He. The NN interactions we use are Bonn-CD, Nijmegen II, and Bonn-B. Compared to existing quality data, one finds large discrepancies and some sensitivity to the choice of NN force model. The calculated n + ³He elastic phase shifts show a very strong inelastic resonance at about 0.3 MeV which is not supported by the total cross-section data. This result is due to the existence of a ³ P ₀ (0⁻) resonance in isospin I = 0 at this energy and the undesirable coincidence of n + ³He and p + ³H thresholds in our calculation due to lack of Coulomb repulsion between protons. This interpretation is supported by R-matrix analyses of the data on the basis of coincident thresholds. Calculated 0⁺ and 0⁻ states are compared with modified R-matrix analyses. Received October 30, 2001; accepted for publication November 7, 2001     

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.     

Zero and finite temperature phase diagram of the spinless fermion model in infinite dimensions

The phase diagram of the model of spinless fermions with repulsive nearest neighbour interaction is calculated analytically on a hypercubic lattice in infinite dimensions (d → ∞). In spite of its simplicity the model displays a rich phase diagram depending on the doping δ, the interaction U and the temperature T. The system can be in the homogeneous phase (HOM), the nonsegregated AB charge density wave (AB-CDW), the AB phase separation region (PS-AB/HOM; coexistence of AB-CDW and HOM), the incommensurate phase (IP) or the IP phase separation region (PS-AB/IP; coexistence of AB-CDW and IP). We identify three important values of the interaction U_IPL = 0.572 < U_IPH = 1.914 < U_IP/PS = 4.212 which distinguish four intervals of U. These imply four different types of phase diagrams. In all the three phase diagrams with U below U_IP/PS the IP appears. We propose a new general ansatz for the order parameter of this phase. A competition between the IP, the PS-AB/IP and the PS-AB/HOM is found. The relevance of our findings for the phase scenario of the Hubbard model is shown.     

Five-Body Calculation of Resonance and Scattering States of the uudd\bar{s} System

The scattering problem of the system, in the standard non-relativistic quark model of Isgur-Karl, is solved for the first time, by treating the large five-body model space, including the NK scattering channel, accurately with the Gaussian expansion method and the Kohn-type coupled-channel variational method. The calculated NK scattering phase shift shows no resonance in the energy region of the reported pentaquark Θ⁺(1540) that is, at 0–500 MeV above the NK threshold (1.4–1.9 GeV in mass). The phase shift does show two resonances just above 500 MeV: a broad ⁺ resonance with a width of Γ ∼ 110 MeV located at ∼ 520 MeV (∼ 2.0 GeV in mass) and a sharp ⁻ resonance with Γ = 0.12 MeV at 540 MeV.     

Interaction of ethidium bromide and caffeine with DNA in aqueous solution

Two component (ethidium bromide–caffeine, ethidium bromide–DNA) and three component (ethidium bromide–caffeine–DNA) systems in aqueous saline (0.01 M NaCl) phosphate buffer solutions (pH 6.86, T = 298 K) are studied spectrophotometrically. The equilibrium constants for dimerization of caffeine, K _D  = 1.22 ± 2 M⁻¹, and for heteroassociation of ethidium bromide with caffeine, K = 71 ± 8 M⁻¹, in ethidium bromide–caffeine systems are determined. When the concentration of caffeine is increased, the dynamic equilibrium of the solution shifts toward formation of heterocomplexes which are, presumably, stabilized by dispersive and hydrophobic interactions of chromophores. The equilibrium parameters for ethidium bromide complex formation with DNA are calculated: the coupling constant for the dye with the biopolymer, K ₁ = (232 ± 16)⋅103 M⁻¹, and the number of base pairs of the biopolymer participating in bonding with the ligand, n ₁ = 3.6 ± 0.2, are calculated. Given these values, it is suggested that under these experimental conditions there are two types of bonding between ethidium bromide and the nucleic acid — intercalation and “external” bonds. A McGhee–von Hippel model for a three component system and the numerical values of the parameters for molecular complex formation in two component systems are used to calculate the bonding constant for caffeine with DNA, K ₂ = 127 ± 30 M⁻¹, and the number of base pairs of DNA which bond with caffeine, n ₂ = 1.7 ± 0.2. The concentrations of ethidium bromide and caffeine in the composition of two and three component complexes are calculated as functions of the nucleic acid content in the solution. An analysis of the concentration dependences shows that heteroassociation of ligands has a significant effect on the reduction in the concentration of ethidium bromide–DNA complexes in a three component system for low DNA concentrations, while at high DNA concentrations the bonding of caffeine with the biopolymer has this effect. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 143–151, January–February 2009.     

Optical spectra and spin-Hamiltonian parameters of trivalent ytterbium in lead tungstate

By using crystal-field theory, the optical spectra and spin-Hamiltonian parameters (abbr. SH parameters, i.e. the anisotropic g factors g _∥, g _⊥, and hyperfine structure constants A _∥, A _⊥) of ¹⁷¹Yb^3 + and ¹⁷³Yb^3 + isotopes in the tetragonal PbWO₄ are calculated. The theoretical results agree well with the experimental values. The crystal-field parameters and the signs of the hyperfine structure constants for both ¹⁷¹Yb^3 + and ¹⁷³Yb^3 + isotopes are determined. The validities of the theoretical results are discussed.     

Griffith–Kelly–Sherman Correlation Inequalities for Generalized Potts Model

Inspired by the work of D.G.Kelly and S.Sherman on general Griffiths inequalities on correlations in Ising ferromagnets, we formulate and prove Griffith–Kelly–Sherman-type inequalities for the ferromagnetic Potts model with a general number q of local states. We take as local state space for the q-state Potts model the set F ^c  = { − l, − l + 1, ⋯ ,l − 1,l},where l=\fracq-12l=\frac{q-1}{2}. The important properties of F ^c for what follows are that |F ^c | = q and F ^c  = − F ^c .     

Study of 3He + Nucleus Scattering with a Simplified Resonating-Group Method

 A simplified resonating-group method, called model K, is used to analyze ³He + nucleus scattering data for target nuclei with nucleon number ranging from 40 to 208 and for ³He energies ranging from 70 to 130 MeV. The results show that a rather satisfactory agreement between calculated and experimental differential-scattering cross sections can be obtained if one allows the value of the exchange-mixture parameter in the nucleon-nucleon potential to deviate somewhat from that in the corresponding N + nucleus case. With the model-K nonlocal interaction, an equivalent local internuclear potential is also constructed with a WKB procedure. Here it is found that, with a proper consideration of nucleon-exchange effects, one can explain nearly all of the energy dependence of the real part of the phenomenologically determined optical potential in ³He + nucleus scattering. Received May 31, 1999; revised November 9, 1999; accepted for publication December 20, 1999     

Estimation of applicability of perturbation theory to solution of the kinetic Boltzmann equation in calculations of charge-carrier relaxation time in isotropic polycrystalline <Emphasis Type="Italic">p-</Emphasis>silicon

A condition is formulated for application of perturbation theory to solution of the kinetic Boltzmann equation in calculations of charge-carrier relaxation time in an isotropic silicon polycrystal, where holes are scattered both by a disordered system of potential barriers formed on crystallite surfaces and by a disordered lattice of silicon atoms characterized by local ordering. The total specific resistance of p-type isotropic polycrystalline silicon is estimated for the grain size d = 230 ?, temperature T = 300 K, and hole concentration p = (5.0 – 10.0) ⋅ 10¹⁹ cm⁻³. The calculated specific resistances of p-type polycrystalline silicon are compared with the experimental data.     

On the Uniqueness of Gravitational Centre

The dual volume of order α of a convex body A in R ⁿ is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R³ coincides with the maximizer of dual volume of order 2, thus it is unique.      

Dilute limit of a strongly-interacting model of spinless fermions and hardcore bosons on the square lattice

In our model, spinless fermions (or hardcore bosons) on a square lattice hop to nearest neighbor sites, and also experience a hard-core repulsion at the nearest neighbor separation. This is the simplest model of correlated electrons and is more tractable for exact diagonalization than the Hubbard model. We study systematically the dilute limit of this model by a combination of analytical and several numerical approaches: the two-particle problem using lattice Green functions and the t-matrix, the few-fermion problem using a modified t-matrix (demonstrating that the interaction energy is well captured by pairwise terms), and for bosons the fitting of the energy as a function of density to Schicks analytical result for dilute hard disks. We present the first systematic study for a strongly-interacting lattice model of the t-matrix, which appears as the central object in older theories of the existence of a two-dimensional Fermi liquid for dilute fermions with strong interactions. For our model, we can (Lanczos) diagonalize the 7 x 7 system at all fillings and the 20 x 20 system with four particles, thus going far beyond previous diagonalization works on the Hubbard model.Received: 8 May 2003, Published online: 28 May 2004PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) - 05.30.Jp Boson systems - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.)N.G. Zhang: Present address: Dept. of Physics, George Washington University, Washington, DC 20052     

Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

Pairs of n×n matrices whose commutator differ from the identity by a matrix of rank r are used to construct bispectral differential operators with r×r matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case r = 1, this reproduces well-known results of Wilson and others from the 1990’s relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators.      

Coupled Fermion and Boson Production in a Strong Background Mean Field

 We derive quantum kinetic equations for fermion and boson production starting from a φ⁴ Lagrangean with minimal coupling to fermions. Decomposing the scalar field into a mean-field part and fluctuations we obtain spontaneous pair creation driven by a self-interacting strong background field. The produced fermion and boson pairs are self-consistently coupled. Consequently back reactions arise from fermion and boson currents determining the time-dependent self-interacting background mean field. We explore the numerical solution with cylindric boundary conditions for the time evolution of the mean field as well as for the number- and energy densities for fermions and bosons. We find that after a characteristic time all energy is converted from the background mean field to particle creation. Applying this general approach to the production of “quarks” and “gluons” a typical time scale for the collapse of the flux tube is 1.5 fm/c. Received February 14, 2002; accepted March 29, 2002 Published online June 24, 2002     

Nonphonon mechanism of superconductivity in compounds with quasi-two-dimensional complexes RuO2

The characteristics of nonphonon pairing of hybridized p and d electrons in planar complexes RuO₂ are studied in the presence of a strong short-range Hubbard repulsion. The phase diagram of superconductivity as a function of the degree of underfilling of the 2p ⁶ and 4d ⁶ shells in the RuO₂ complexes is calculated in a generalized Hubbard model. Fiz. Tverd. Tela (St. Petersburg) 40, 980–983 (June 1998)     

Study of the interaction between two electrons in the single band Hubbard model

A single-band Hubbard model has been investigated for two case (1) the 1-D Hubbard ring, (2) the 2-D Hubbard square lattice on a torus. In both cases it is found that the interaction between two electrons is always repulsive in the limit of infiniteU. In 1-D, the pair correlation function is naturally similar to that of spin-less fermions, whilst in 2-D it is quite different.     

Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models. Received 8 February 2000 and Received in final form 25 April 2000     

Neutron skin effect of some Mo isotopes in pre-equilibrium reactions

The neutron skin effect has been investigated for even isotopes of molybdenum at 25.6 MeV ^{94 − 100}Mo(p, xn) reaction using the geometry-dependent hybrid model of pre-equilibrium nuclear reactions. Here the initial neutron/proton exciton numbers were calculated from the neutron/ proton densities obtained from an effective nucleon–nucleon interaction of the Skyrme type. Initial exciton numbers from different radii of even Mo isotopes were used to obtain the corresponding neutron emission spectra. In this investigation the calculated results are compared with the experimental data as also with each other. The results using central densities in the geometry-dependent hybrid model are in better agreement with the experimental data.     

α + 8He Elastic Scattering with the Generator-Coordinate Method

 The elastic α + ⁸He phase shifts are calculated with a two-centre generator-coordinate method. The microscopic α and ⁸He internal wave functions are defined in the harmonic-oscillator model. Bound states and resonances of ¹²Be are obtained. Among them, a 4⁺ resonance with a molecular structure should be observable in elastic scattering. The parity dependence of the microscopic phase shifts is analyzed by fitting them with simple potentials. The odd-even effect is similar in the α + ⁸He and α + ⁶He phase shifts for low partial waves but decreases more rapidly with increasing orbital momentum for α + ⁸He. Received May 14, 1999; accepted for publication July 29, 1999