A model Hamiltonian for MgB $\mathsf{_{2}}$ which takes into account its unusual phononic features

Taking as a starting point the results of LDA calculations, which show that in the phonons have a strong quartic anharmonicity and that the bond-stretching electron-phonon interaction (EPI) has both a linear and a large quadratic component, we propose a model Hamiltonian which successfully matches a number of experimental evidences. We relate the single critical temperature for both superconducting gaps to a phonon-induced inter-band coupling whose amplitude increases with temperature. We also obtain phonon frequencies and linewidths depending on the band filling, as well as band energies and hybridization amplitudes depending on the phonon number.Received: 12 May 2003, Published online: 22 September 2003PACS: 74.20.-z Theories and models of superconducting state - 74.70.-b Superconducting materials     

Electromagnetic form factors of the $\Delta(1232)$ excitation

In the resonance region we have precisely determined the electromagnetic properties of the -resonance, in particular the E2/M1 ratio . For pion electroproduction recent experimental data from Mainz, Bates, Bonn and JLab for Q² up to 4.0 (GeV/c)² have been analyzed with the isobar model MAID. The extracted E2/M1 ratio shows, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and becomes positive with increasing Q². This is a possible indication of a very slow approach toward the pQCD region. The C2/M1 ratio near the photon point is found as . At high Q², the absolute value of the ratio is strongly increasing, a further indication that pQCD is not yet reached. The electromagnetic-transition form factors of the excitation are parameterized and fitted to the electroproduction data. This also shows a zero-crossing of the electric form factor G_E^* at (GeV/c)².Received: 1 November 2002, Published online: 15 July 2003PACS:   13.40.Gp Electromagnetic form factors - 13.60.Le Meson production - 14.20.Gk Baryon resonances with S=0 - 25.20.Lj Photoproduction reactions     

Fluctuation conductivity in layered d-wave superconductors near critical disorder

We consider the fluctuation conductivity in the critical region of a disorder induced quantum phase transition in layered d-wave superconductors. We specifically address the fluctuation contribution to the systems conductivity in the limit of large (quasi-two-dimensional system) and small (quasi-three-dimensional system) separation between adjacent layers of the system. Both in-plane and c-axis conductivities were discussed near the point of insulator-superconductor phase transition. The value of the dynamical critical exponent, z = 2, permits a perturbative treatment of this quantum phase transition under the renormalization group approach. We discuss our results for the system conductivities in the critical region as function of temperature and disorder.Received: 10 October 2003, Published online: 23 December 2003PACS: 74.40. + k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.) - 73.43.Nq Quantum phase transitions     

Stiffness exponents for lattice spin glasses in dimensions $\mathsf{d = 3,\ldots,6}$

The stiffness exponents in the glass phase for lattice spin glasses in dimensions are determined. To this end, we consider bond-diluted lattices near the T = 0 glass transition point p^*. This transition for discrete bond distributions occurs just above the bond percolation point p_c in each dimension. Numerics suggests that both points, p_c and p^*, seem to share the same 1/d-expansion, at least for several leading orders, each starting with 1/(2d). Hence, these lattice graphs have average connectivities of near p^* and exact graph-reduction methods become very effective in eliminating recursively all spins of connectivity , allowing the treatment of lattices of lengths up to L = 30 and with up to 10⁵-10⁶ spins. Using finite-size scaling, data for the defect energy width over a range of p > p^* in each dimension can be combined to reach scaling regimes of about one decade in the scaling variable . Accordingly, unprecedented accuracy is obtained for the stiffness exponents compared to undiluted lattices (p = 1), where scaling is far more limited. Surprisingly, scaling corrections typically are more benign for diluted lattices. We find in for the stiffness exponents y₃ = 0.24(1), y₄ = 0.61(2), y₅ = 0.88(5), and y₆ = 1.1(1).Received: 29 October 2003, Published online: 20 April 2004PACS: 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Nr Spin-glass and other random models - 02.60.Pn Numerical optimization     

Ion trap nuclear resonance on $\mathsf{^{151}Eu^ + }$

Laser-microwave double resonance techniques applied to a cloud of a natural mixture of Eu ⁺ isotopes confined in a Penning trap has been used to induce and detect nuclear Zeeman transitions. In spite of the complex level structure of Eu ⁺ and overlapping spectra from the two isotopes five different transitions could be observed from which the nuclear magnetic moment can be derived. We obtain for ¹⁵¹ Eu ⁺ g _I = 1.377 34(6) demonstrating the potential for high accuracy of the technique. The experiment can be considered as a feasibility test that precise spectroscopy data using the ion storage technique can be obtained of very complex ions and under unfavourable conditions.Received: 13 June 2003, Published online: 12 August 2003PACS: 32.60. + i Zeeman and Stark effects - 32.10.Dk Electric and magnetic moments, polarizability     

Shell model calculations with modified empirical Hamiltonian in the <Superscript>132</Superscript>Sn region

Using recent experimental information for the ¹³²Sn region, an empirical Hamiltonian is obtained by some modifications of a Hamiltonian (CW5082) originally derived from the ²⁰⁸Pb region. Shell model calculations with the new Hamiltonian show a remarkable improvement in the predictive power when compared with the available experimental results. It overcomes many limitations of the CW5082 Hamiltonian in this region, specially for isotones. The calculated level spectra and B(E2) values with the new Hamiltonian, also compare well with the available results calculated with the CD-Bonn and SKX Hamiltonians, reflecting consistency in the wave function structure at least in the low-lying regions. An interesting behaviour of effective charges is revealed in this region. It is shown that a drastic reduction of proton effective charge is necessary for obtaining B(E2) values for the N = 84 isotones. Neutron effective charge is found to be in the range (0.62-0.72)e. We predict the spectroscopic properties of ^135,136Sn not yet known experimentally. Further improvement of the modified Hamiltonian is also initiated.Received: 25 September 2003, Revised: 20 January 2004, Published online: 13 July 2004PACS: 21.60.Cs Shell model - 21.10.-k Properties of nuclei, nuclear energy levels - 23.20.-g Electromagnetic transitions - 27.60. + j      

$\mbox{Log}(1/x)$ gluon distribution and structure functionsin the loop-loop correlation model

We consider the interaction of the partonic fluctuation of a scalar photon with an external color field to calculate the leading and next-to-leading order gluon distribution of the proton following the work done by Dosch-Hebecker-Metz-Pirner. We relate these gluon distributions to the short and long distance behavior of the cross section of an adjoint dipole scattering off a proton. The leading order result is a constant, while the next-to-leading order result shows a enhancement at small x. To get numerical results for the gluon distributions at the initial scale Q²₀ = 1.8 GeV², we compute the adjoint dipole-proton cross section in the loop-loop correlation model. Quark distributions at the same initial scale are parameterized according to Regge theory. We evolve quark and gluon distributions to higher Q² values using the DGLAP equation and compute charm and proton structure functions in the small-x region for different Q² values.Received: 13 September 2003, Revised: 22 November 2003, Published online: 15 January 2003     

$\delta$-pairing forces and collective pairing vibrations

The collective pairing Hamiltonian is obtained in the framework of the generator coordinate method in the Gaussian overlap approximation with a slightly modified BCS function used as a generator function. The collective variable , measuring the monopole moment of the pairing field, and the gauge transformation angle are chosen as generator coordinates. The vibrational ground states are calculated by diagonalisation of the collective pairing Hamiltonian in the harmonic-oscillator basis.Received: 28 April 2003, Revised: 1 October 2003, Published online: 18 June 2004PACS: 21.30.-x Nuclear forces - 21.60.Ev Collective models     

Exact effective force between star-polymers in a $\Theta$-solvent

We re-examine here the computation of the effective force between two star-polymers of respective numbers of branches f₁ and f₂, immersed in a common -solvent. Such a force originates essentially from the repulsive three-body interactions. To achieve this, we take advantage of some established results using renormalization theory for three-dimensional star-polymers, or conformal invariance for two-dimensional ones. We first show that, in dimension d = 3, the force, , decreases with the center-to-center distance r as , with the exact universal amplitude . Second, in dimension d = 2, we find that the force decays more slowly as , with the exact universal amplitude . For high distances compared to the gyration radius, , of a single polymer chain at the -point, an exponential decay of the force is expected.Received: 3 February 2004, Published online: 24 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.20.-y Classical statistical mechanics     

Type IIB 2-form fields and gauge coupling constant of 4D ${\cal N}=2$ super QCD

We study the relation between the Type IIB (NSNS and RR) 2-form fields and the (complex) gauge coupling constant of the 4D SU(N _c ) super Yang-Mills theory with N _f fundamental matter particles. We start from the analysis of the D2-brane world-volume theory with heavy N _c quarks on the N _f D6 supergravity background. After a sequence of T- and S-dualities, we obtain the (generalized) 2-forms in the configuration with N _c D5-branes wrapping on a vanishing two-cycle under the influence of the background. These 2-forms show the same behavior as the gauge coupling constant of the 4D super QCD. The background reduces to the orbifold in the twelve-dimensional space-time formally realized by introducing the two parameters as additional space coordinates. The 10D gravity dual is suggested as the 2D flip in this twelve-dimensional space-time. In the case of N _f = 2N _c , this gravity dual becomes AdS₅ x S⁵/Z₂ with a D3-charge which depends on the constant generalized NSNS 2-form. This is the result expected from the M-theory QCD configuration. Based on the known exact result, we also discuss this configuration after including non-perturbative effects.Received: 2 May 2003, Revised: 21 July 2003, Published online: 19 September 2003     

Break of universality for an Ising model with aperiodic Rudin-Shapiro interactions

We analyze the ferromagnetic Ising model on non-Euclidean scale invariant lattices with aperiodic interactions (J_A,J_B,J_C,J_D) defined by Rudin-Shapiro substitution rules with Migdal-Kadanoff renormalization (MKR) and transfer matrix (TM) techniques. The analysis of the invariant sets of the zero-field MKR transformation indicates that the critical behavior, completely distinct from the one of the uniform model, is described by a new off-diagonal fixed point. This contrasts with other aperiodic models where the new critical behavior is described by a period-two cycle. With the new fixed point, values for the thermal critical exponents, and , as well as the period of log-periodic oscillations, are obtained. Exact recursive maps for all thermodynamical functions are derived within the TM approach. The explicit dependence of the thermodynamical functions with respect to temperature is evaluated by the numerical iteration of the set of maps until a previously chosen convergence is achieved. They also indicate that, depending on the actual choice for the aperiodic coupling constants, the magnetic exponents ( and ) assume different values. However the Rushbrook relation is always satisfied.Received: 27 February 2003, Published online: 11 August 2003PACS: 05.50.+q Lattice theory and statistics - 05.10.Cc Renormalization group methods - 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 61.44.Br Quasicrystals     

Study of a monomer-monomer reaction system with short-range repulsive interactions

The critical behavior of an interacting two species catalytic surface reaction model is studied by means of Monte Carlo simulations and a mean-field approach. The model has two parameters, namely the relative adsorption rate of species p _A and a short-range repulsive interaction r between the same type of adsorbed species. The system exhibits an stationary reactive phase and two symmetrically equivalent absorbing phases. These latter phases are unique and correspond to surfaces saturated by a single type of reacting species. For , the system exhibits a second-order phase transition that belongs to the directed percolation (DP) universality class. However, in the absence of repulsive interaction (r = 0), a bicritical point is found at p _A = 1/2 whose critical behavior is compatible with dynamical mean-field exponents. Our findings indicate that the bicritical point belongs to the Voter Model universality class, whose upper critical dimension is d _c = 2. In addition, we propose a method to study the crossover from MF to DP behavior based on the estimation of the crossover time T _c . We find that T _c diverges according to a power-law as where is the crossover exponent. For strong repulsion, a new transient effect appears associated with the onset of almost inactive chessboad patterns.Received: 8 July 2004, Published online: 31 August 2004PACS: 02.50.-r Probability theory, stochastic processes, and statistics - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 82.45.Jn Surface structure, reactivity and catalysisR.A. Monetti: Permanent address: Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, (INIFTA), CONICET, UNLP. Suc. 4, C. C. 16, (1900) La Plata, Argentina     

Phase diagram of the three-dimensional NJL model

With the exception of confinement the three-dimensional Nambu-Jona-Lasinio (NJL₃) model incorporates many of the essential properties of QCD. We discuss the critical properties of the model at non-zero temperature T and/or non-zero chemical potential . We show that the universality class of the thermal transition is that of the d = 2 classical spin model with the same symmetry. We provide evidence for the existence of a tricritical point in the -plane. We also discuss numerical results by Handset al. which showed that the system is critical for and the diquark condensate is zero.Received: 30 September 2002, Published online: 22 October 2003PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 05.70.Fh Phase transitions: general studies     

Carrier relaxation time divergence in single and double layer cuprates

We report the transient optical pump-probe reflectivity measurements on single and double layer cuprate single crystals and thin films of ten different stoichiometries. We find that with sufficiently low fluence the relaxation time ( of all samples exhibits a power law divergence with temperature . Further, the divergence has an onset temperature above the superconducting transition temperature for all superconducting samples. Possible causes of this divergence are discussed.Received: 30 June 2003, Published online: 23 December 2003PACS: 74.78.Bz High-T _c films - 74.72.-h Cuprate superconductors (high-T _c and insulating parent compounds) - 74.25.Gz Optical propertiesM.L. Schneider: Present address: NIST, mc 816.01, 325 Broadway, Boulder, CO 80305-3328, USA     

Prospects for production of ultracold $\mathsf{X^{1}\Sigma^{ + }}$ RbCs molecules

Recently, we have reported photoassociation of laser-cooled Rb and Cs atoms, decay of the RbCs photoassociation resonances to high levels of the state, and reexcitation to vibronic levels of the state [Kerman et al. , Phys. Rev. Lett. 92, 033004; 153001 (2004)]. Considering the reexcitation spectrum, we report here a preliminary analysis of perturbations in the c state by high levels of the and low levels of the state. Mixing with the B state provides the singlet character needed to stimulate decay to v = 0 of the ground state. We conclude that an experimental procedure that involves photoassociation of laser-cooled atoms, radiative decay, and stimulated Raman transfer to the ground electronic state is a feasible method for producing translationally, rotationally, vibrationally and electronically cold RbCs molecules. Electronic supplementary material to this article is available at and is accessible for authorized users. Received: 1 September 2004, Published online: 23 November 2004 PACS: 33.80.Ps Optical cooling of molecules; trapping - 34.50.Gb Electronic excitation and ionization of molecules; intermediate molecular states (including lifetimes, state mixing, etc.) - 33.20.Kf Visible spectra - 34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions - 33.15.Pw Fine and hyperfine structure A supplementary table (Tab. I) is only available in electronic form at http: //www.eurphysj.org     

Isospin breaking in $K \rightarrow \pi\pi$ decays

We perform a complete analysis of isospin breaking in amplitudes in chiral perturbation theory, including both strong isospin violation ( ) and electromagnetic corrections to next-to-leading order in the low-energy expansion. The unknown chiral couplings are estimated at leading order in the 1/N_c expansion. We study the impact of isospin breaking on CP conserving amplitudes and rescattering phases. In particular, we extract the effective couplings g₈ and g₂₇ from a fit to branching ratios, finding small deviations from the isospin-limit case. The ratio measuring the enhancement is found to decrease from in the isospin limit to in the presence of isospin breaking. We also analyze the effect of isospin violation on the CP violation parameter , finding a destructive interference between three different sources of isospin violation. Within the uncertainties of large-N_c estimates for the low-energy constants, the isospin violating correction for is below 15%.Received: 21 November 2003, Published online: 4 February 2004Work supported in part by IHP-RTN, Contract No. HPRN-CT2002-00311 (EURIDICE) and by Acciones Integradas, Project No. 19/2003 (Austria), HU2002-0044 (MCYT, Spain)     

Diffusion of gelation clusters in the Zimm model

Starting from a Zimm model, we study self-diffusion in a solution of crosslinked monomers. We focus on the effects of the hydrodynamic interaction on the dynamics and the critical behaviour at the sol-gel point. Hydrodynamic interactions cause the clusters diffusion constant to depend not only on the clusters size but also on the clusters shape --in contrast to the Rouse model. This gives rise to a non-trivial scaling of the Kirkwood diffusion constant averaged over all clusters of fixed size n, with given in terms of the spectral dimension of critical percolation clusters. The long-time decay of the incoherent scattering function is determined by the diffusive motion of the largest clusters. This implies the critical vanishing of the cluster-averaged effective diffusion constant at the gel point with exponent .Received: 24 July 2003, Published online: 21 November 2003PACS: 64.60.Ht Dynamic critical phenomena - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling