Study of the 3He(4He,γ)7Be and 3H(4He,γ)7Li Reactions in an Extended Two-Cluster Model

 The ³He(⁴He, γ)⁷Be and ³H(⁴He, γ)⁷Li reactions are studied in an extended two-cluster model which contains α + h/t and ⁶Li + p/n clusterizations. We show that the inclusion of the ⁶Li + p/n channels can significantly change the zero-energy reaction cross sections, S(0), and other properties of the ⁷Be and ⁷Li nuclei, like the quadrupole moments Q. However, the results agree with the known correlation trend between S(0) and Q. Moreover, we demonstrate that the value of the zero-energy derivatives of the astrophysical S-factors are more uncertain than currently believed. Received June 17, 1999; revised February 22, 2000; accepted for publication April 17, 2000     

Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition

This paper is contributed to explore all possible single peakon solutions for the Degasperis–Procesi (DP) equation m _t  + m _x u + 3mu _x  = 0, m = u − u _xx . Our procedure shows that the DP equation either has cusp soliton and smooth soliton solutions only under the inhomogeneous boundary condition lim_|x|→ ∞ u =A ≠0, or possesses the regular peakon solutions ce ^{− |x − ct|} ∈ H ¹ (c is the wave speed) only when lim_|x|→ ∞ u = 0 (see Theorem 4.1). In particular, we first time obtain the stationary cuspon solution of the DP equation. Moreover we present new cusp solitons (in the space of ) and smooth soliton solutions in an explicit form. Asymptotic analysis and numerical simulations are provided for smooth solitons and cusp solitons of the DP equation.      

Measurement of light mesons at RHIC by the PHENIX experiment

The PHENIX experiment at RHIC has measured a variety of light neutral mesons (π ⁰, K _S ⁰, η, ω, η ^′, φ) via multi-particle decay channels over a wide range of transverse momentum. A review of the recent results on the production rates of light mesons in p + p and their nuclear modification factors in d + Au, Cu + Cu and Au + Au collisions at different energies is presented.     

Strange particle production at RHIC

We report STAR measurements of mid-rapidity yields for the Λ , , K _S ⁰ , Ξ ⁻, , Ω ⁻, particles in Cu + Cu and Au + Au  GeV collisions. We show that at a given number of participating nucleons, bulk strangeness production is higher in Cu + Cu collisions compared to Au + Au collisions at the same center of mass energy, counter to predictions from the Canonical formalism. We compare both the Cu + Cu and Au + Au yields to AMPT and EPOS predictions, and find they reproduce key qualitative aspects of the data. Finally, we investigate other scaling parameters and find bulk strangeness production for both the measured data and theoretical predictions, scales better with the number participants that undergo more than one collision.     

On the Residual Entropy of the Blume-Emery-Griffiths Model

By means of a transfer matrix method, we show that the residual entropy S of the two dimensional square lattice Blume-Emery-Griffiths model on the antiquadrupolar-disordered and ferromagnetic-antiquadrupolar-disordered phase boundaries satisfies the inequalities (ln λ _1,n )/(n+1)≤S≤(ln λ _1,n )/n, where λ _1,n is the largest eigenvalue of a transfer matrix F _n on a strip of width n. These bounds imply the existence of a O(1/n) correction in the approximation of S by (ln λ _1,n )/n. Using these bounds, we calculate numerically the value of S, with precise estimates on the errors.     

Results from PAMELA,ATIC and FERMI: Pulsars or dark matter?

It is well known that dark matter dominates the dynamics of galaxies and clusters of galaxies. Its constituents remain a mystery despite an assiduous search for them over the past three decades. Recent results from the satellite-based PAMELA experiment show an excess in the positron fraction at energies between 10 and 100 GeV in the secondary cosmic ray spectrum. Other experiments, namely ATIC, HESS and FERMI, show an excess in the total electron (e ⁺ + e ⁻) spectrum for energies greater than 100 GeV. These excesses in the positron fraction as well as the electron spectrum can arise in local astrophysical processes like pulsars, or can be attributed to the annihilation of the dark matter particles. The latter possibility gives clues to the possible candidates for the dark matter in galaxies and other astrophysical systems. In this article, we give a report of these exciting developments.     

Bound-state versus collective-coordinate approaches in chiral soliton models and the width of the Θpentaquark

We thoroughly compare the bound-state and rigid-rotator approaches to three-flavored chiral solitons. We establish that these two approaches yield identical results for the baryon spectrum and kaon-nucleon S-matrix in the limit that the number of colors (N_C) tends to infinity. After proper subtraction of the background phase shift the bound-state approach indeed exhibits a clear resonance behavior in the strangeness S = + 1 channel. We present a first dynamical calculation of the widths of the Θ⁺ and Θ^* pentaquarks for finite N_C in a chiral soliton model.     

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     

Separation of different wave components in the Bethe–Salpeter wave function

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by L–S coupling analysis. The cancelation formula is given, by which the terms with pure L = J + 1 wave components in the Salpeter wave function for the bound state with h_P=(-1)^J\eta_{\rm P}=(-1)^J can be obtained by separating the L = J − 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of L = J − 1 and J + 1 wave states, and for solving the Salpeter equation exactly without approximation.     

On Noncommutative Multi-Solitons

 We find the moduli space of multi-solitons in noncommutative scalar field theories at large θ, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/θ is a consequence of a Bogomolnyi bound obeyed by the kinetic energy of the θ=∞ solitons. In two spatial dimensions, the parameter space for k solitons is a K?hler de-singularization of the symmetric product (ℝ²) ^k /S _k . We exploit the existence of this moduli space to construct solitons on quotient spaces of the plane: ℝ²/ℤ _k , cylinder, and T ² . However, we show that tori of area less than or equal to 2πθ do not admit stable solitons. In four dimensions the moduli space provides an explicit K?hler resolution of (ℝ⁴) ^k /S _k . In general spatial dimension 2d, we show it is isomorphic to the Hilbert scheme of k points in ℂ ^d , which for d>2 (and k>3) is not smooth and can have multiple branches. Received: 29 May 2001 / Accepted: 16 August 2002 Published online: 7 November 2002 Communicated by R.H. Dijkgraaf     

A Remark on the Residual Entropy of the Antiferromagnetic Ising Model in the Maximal Critical Field

By means of a transfer matrix method, we show that the residual entropy S of the two-dimensional square lattice antiferromagnetic Ising model in the maximal critical field satisfies (ln λ _n )/(n+1)≤S≤(ln λ _n )/n, where λ _n is the largest eigenvalue of the transfer matrix F _n on a strip of width n. Using these bounds, we numerically calculate the value of S, with precise estimates on the errors, namely, S=0.394198±0.020747.     

Antisymmetry in Strangeness −1 and −2 Three-Baryon Systems

 Using the generalized Pauli principle by adding particle labels to the usual space and spin labels a symmetric Hamiltonian and a corresponding antisymmetric wave function are constructed for systems of three baryons in the strangeness sectors S = −1 and −2. Applications are the ΞNN-ΛΛN and NNΛ-NNΣ systems. Minimal sets of generalized coupled Faddeev equations for breakup and rearrangement operators as well as (possible) bound states are derived that have the ordinary Pauli principle for identical particles built in. The equations found confirm our previous sets of coupled Faddeev equations whose derivation was made for distinguishable particles and not using the generalized Pauli principle. Received August 21, 2000; accepted for publication September 29, 2000     

Inelastic x-ray scattering measurements of dynamical cross-over in liquid As2Se3 at high temperature and high pressure

Liquid As₂Se₃ undergoes the semiconductor-metal transition with increasing temperature when pressure is applied to avoid evaporation of the liquid. To investigate the atomic dynamics of liquid As₂Se₃, we have carried out inelastic x-ray scattering experiments of this system at 1073 K and 6 MPa and obtained the dynamic structure factor S(Q,E), from approximately 1.6 nm⁻¹ to 11 nm⁻¹, where Q and E are momentum and energy transfer, respectively. The excitation energy in the semiconducting state at 1073 K disperses as fast as the ultrasonic sound velocity at Q < 2.5 nm⁻¹ but at Q > 2.9 nm⁻¹ it disperses approximately 1.8 times faster. We analyzed S(Q,E) at 1073 K using a simple viscoelastic model and discussed Q dependence of the propagation of the acoustic mode.     

Femtosecond photodissociation dynamics of HNO3 after exitation of the S3-state at 200 nm

The photodissociation dynamics of HNO₃ in the electronic S₃ (2 ¹ A ^′ ) state leading to the fragments OH and NO₂ was investigated in real time. HNO₃ was prepared either in a fluorescence cell at room temperature (LIF probing of OH) or rotationally cold in a molecular beam (probing of NO₂ by three-photon ionization). A 2 ¹ A ^′ lifetime of 60–80 fs could be obtained from the experimental results, indicating essentially barrierless dissociation. In addition, secondary dissociation of internally excited nascent fragments NO₂ ^* leading to products NO(X ² Π) and O(³ P) with a characteristic dissociation time of 2.3 ps was observed. This time is surprisingly long when compared with dissociation lifetimes of NO₂ from the literature, obtained after direct photoexcitation. The discrepancy is explained by differences in the preparation conditions of the dissociative state of NO₂. Received: 12 November 1999 / Published online: 13 July 2000     

Effect of externally injected radiation on amplified spontaneous emission in CO

The effect of externally injected radiation on the two-photon laser-induced amplified spontaneous emission (TP-LIASE) is reported. The wave generated via the same LIASE process in a seeder cell acts as a seeder field for the inverted medium created in a main cell. A nearly tenfold gain is achieved in the B¹ Σ ⁺ ?A¹ Π (0, 3) transition of the CO molecule. We demonstrate that the single rotational transition in the B¹ Σ ⁺ ?A¹ Π (0, 4) band is selectively amplified by injection of laser radiation. This pump and seed arrangement facilitates detection of molecular spectra by simply tuning the seed-laser frequency. The polarization effect of the input laser radiation is briefly discussed. Received: 9 June 2000 / Revised version: 2 October 2000 / Published online: 21 February 2001     

Magnetic properties of LiNi<Subscript>0.5</Subscript>Mn<Subscript>0.47</Subscript>Al<Subscript>0.03</Subscript>O<Subscript>2</Subscript> as positive electrode for Li-ion batteries

The layered LiNi_0.5Mn_0.47Al_0.03O₂ was synthesized by wet chemical method and characterized by X-ray diffraction and analysis of magnetic measurements. The powders adopted the α-NaFeO₂ structure. This substitution of Al for Mn promotes the formation of Li(Ni_0.47²⁺Ni_0.03³⁺Mn_0.47⁴⁺Al_0.03³⁺)O₂ structures and induces an increase in the average oxidation state of Ni, thereby leading to the shrinkage of the lattice unit cell. The concentration of antisite defects in which Ni²⁺ occupies the (3a) Li lattice sites in the Wyckoff notation has been estimated from the ferromagnetic Ni²⁺(3a)–Mn⁴⁺(3b) pairing observed below 140 K. The substitution of 3% Al for Mn reduces the amount of antisite defects from 7% to 6.4–6.5%. The analysis of the magnetic properties in the paramagnetic phase in the framework of the Curie–Weiss law agrees well with the combination of Ni²⁺ (S = 1), Ni³⁺ (S = 1/2) and Mn⁴⁺ (S = 3/2) spin-only values. Delithiation has been made by the use of K₂S₂O₈. According to this process, known to be softer than the electrochemical one, the nickel ions in the (3b) sites are converted into Ni⁴⁺ in the high spin configuration, while Ni²⁺(3a)–Mn⁴⁺(3b) ferromagnetic pairs remain, as the Li⁺(3b) ions linked to the Ni²⁺(3a) ions in the antisite defects are not removed. The results show that the antisite defect is surrounded by Mn⁴⁺ ions, implying the nonuniform distribution of the cations in agreement with previous NMR and neutron experiments.     

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 .     

Absolute frequency and isotope shift measurements of the cooling transition in singly ionized indium

We report greater than two orders of magnitude improvements in the absolute frequency and isotope shift measurements of the In⁺ 5s^{2 1}S₀ (F = 9/2)–5s5p ³P₁ (F = 11/2) transition near 230.6 nm. The laser-induced fluorescence from a single In⁺ in a radio-frequency trap is detected. The fourth-harmonic of a semiconductor laser is used as the light source. The absolute frequency is measured with the help of a frequency comb referenced to a Cs atomic clock. The resulting transition frequencies for isotopes ¹¹⁵In⁺ and ¹¹³In⁺ are measured to be 1 299 648 954.54(10) MHz and 1 299 649 585.36(16) MHz, respectively. The deduced cooling transition frequency difference is 630.82(19) MHz. By taking into account of the hyperfine interaction, the isotope shift is calculated to be 695.76(1.68) MHz.     

A Novel Fluorescent Cesium Ion-Selective Optode Membrane based on 15-Crown-5-Anthracene

An optode system based on a plasticized polymer membrane containing cesium ion-selective fluoroionophore and lipophilic anions for the determination of cesium ions has been developed. In this work, 15-crown-5 derivative including anthracene was used as a fluoroionophore. Emission intensity of the optode membrane incorporating 15-crown-5-anthracene was measured at 500 nm with excitation at 360 nm in the presence of Tris-HCl buffer solution. Under optimum experimental condition, the relative fluorescence intensity was linear with the concentration of cesium ion in the range of 1.0 × 10^-4 M to 1.0 × 10^-1 M and the detection limit was obtained 4.2 × 10^-5 M, as defined by LOD = 3 × S_b/m (where S_b=standard deviation of blank signal and, m=slope of the calibration curve). The effect of pH of sample solution on the fluorescent response, the selectivity, response time and reproducibility of the optode membrane were also discussed. The fluorescent optode system shows a high selectivity and sensitivity for cesium ion with respect to other cations such as K⁺, Na⁺ and Li⁺.     

Use of combined Hartree–Fock–Roothaan theory in evaluation of lowest states of K[Ar]4s03d1 and Cr?+?[Ar]4s03d5 isoelectronic series over noninteger n-Slater type orbitals

By using noninteger n-Slater type orbitals in combined Hartree–Fock–Roothaan method, self-consistent field calculations of orbital and lowest states energies have been performed for the isoelectronic series of open shell systems K[Ar]4s ⁰3d ¹ (² D) (Z = 19–30) and Cr⁺[Ar]4s ⁰3d ⁵ (⁶ S) (Z = 24–30). The results of the calculations for the orbital and total energies obtained by using minimal basis-sets of noninteger n-Slater type orbitals are given in the tables. The results are compared with the extended-basis Hartree–Fock computations. The orbital and total energies are in good agreement with those presented in the literature. The results can be useful in the study of various properties of heavy atomic systems when the combined Hartree–Fock–Roothaan approach is employed.