Corrections to the wave function and the hyperfine structure in exotic atoms

We present an analytical evaluation of radiative corrections in exotic atoms induced by the one-loop electronic vacuum polarization. We evaluate corrections to the energy levels, to the wave function (at the origin) and to the hyperfine structure. We treat all corrections analytically within a non-relativistic approximation. Agreement is found with a few available numerical results. The analytical treatment allows to determine the asymptotic forms of the corrections in the limit of a small atomic radius, which for the atomic systems considered corresponds to a large mass of the constituent particle as compared to the electron mass. The asymptotics can be verified using the effective charge approach. Received: 28 January 1998 / Accepted: 13 March 1998     

Effect of electron correlation on superconducting pairing symmetry

The role of electron correlation on different pairing symmetries are discussed in details where the electron correlation has been treated within the slave boson formalism. It is shown that for a pure s or pure d wave pairing symmetry, the electronic correlation suppresses the s wave gap magnitude (as well as the ) at a faster rate than that for the d wave gap. On the other hand, a complex order parameter of the form () shows anomalous temperature dependence. For example, if the temperature () at which the d wave component of the complex order parameter vanishes happens to be larger than that for the s wave component (), then the growth of the d wave component is arrested with the onset of the s wave component of the order parameter. In this mixed phase however, we find that the suppression in different components of the gap as well as the corresponding due to coulomb correlation are very sensitive to the relative pairing strengths of s and d channels as well as the underlying lattice. Interestingly enough, in such a scenario (for a case of )the gap magnitude of the d wave component increases with electron correlation but not for certain values of electron correlation. However, this never happens in case of the s wave component. We also calculate the temperature dependence of the superconducting gap along both the high symmetry directions ( and ) in a mixed symmetry pairing state and the thermal variation of the gap anisotropy [0pt][0pt] with electron correlation. The results are discussed with reference to experimental observations. Received: 26 August 1997 / Revised: 31 December 1997 / Accepted: 28 January 1998     

Polarisation effect of laser field in inelastic electron - hydrogen collisions

We study the influence of the laser polarization on the electron impact excitation of atomic hydrogen. Our method takes into account the “dressing” of the target states by including the laser-atom interaction to first order time-dependent perturbation theory, while the interaction of the laser field with the incident electron is treated to all orders by using the non relativist Volkov function. The interaction of the fast projectile with the target atom is treated in the first Born approximation. The calculations are performed via two distinct computations. The first one is based on a direct calculation, the second based on a Sturmian approach. Important differences appear between the angular distributions depending on the polarization chosen. Received : 17 february 1998 / Revised : 20 july 1998 / Accepted : 2 september 1998     

Polarizabilities and hyperfine structure constants of the low-lying levels of barium

The results of ab initio calculation of energies, hyperfine structure constants and static polarizabilities for several low-lying levels of barium are reported. The effective Hamiltonian for the valence electrons has been constructed in the frame of CI+MBPT method and solutions of many electron equation were found. Using the wave functions obtained the hyperfine structure constants and static polarizabilities were calculated. Received: 22 June 1998 / Revised: 2 September 1998 / Accepted: 15 September 1998     

Cubic superspace symmetry and inflation rules in metastable MgAl alloy

The diffraction properties of a quenched Al-Mg alloy which has been recently termed as a “cubic quasicrystal” are quantitatively reanalyzed. It is shown that the phase can be interpreted within the superspace formalism as an ordinary incommensurately modulated structure. The cubic six-dimensional superspace group that describes its symmetry properties has been determined. The additional inflation symmetry features exhibited by the diffraction diagram can be summed up by its invariance for the inflation factor , but this property has its origin in the specific value of the modulus of the modulation wave vectors, which is composition dependent. Other particular values of this modulus can give rise to similar scaling properties. Further experiments are required to ellucidate if the mentioned inflation symmetry is a fortuitous situation in a composition dependent wave vector, or has indeed the physical significance which would allow to describe the system as a “cubic quasicrystal”. Received: 25 June 1998 / Received in final form and Accepted: 23 September 1998     

Local environment and electron correlation effects on the magnetic properties of clusters

The electronic and magnetic properties of clusters are investigated in the framework of the Hubbard model by treating electron correlations effects in a saddle-point slave-boson approximation. The size dependent single-particle spectrum is calculated using a third moment real-space expansion of the local density of states. Results for the magnetic moments, magnetic order, average number of double occupations and hopping renormalizations are given as a function of the local coordination number z, for different representative values of the Coulomb interaction strength U/t and band filling n. Several transitions between paramagnetic, ferromagnetic and antiferromagnetic behaviors are obtained as a function of z. The environment dependence of the magnetic behavior and of the degree of electron delocalization is analyzed. Advantages and limitations of the present approach are discussed. Received: 8 January 1998 / Revised: 22 June 1998 / Accepted: 6 August 1998     

Electron detachment and fragmentation in collisions between 1.25 keV/carbon and clusters and

The destruction cross-section for 22.5 and 50 keV C^1- , for 10 and 50 keV C₈ ^1- and for 50 and 75 keV C₆₀ ^1- clusters in collisions with H₂ has been measured by an attenuation method. The destruction of the cluster anions is dominated by electron detachment rather than fragmentation and is of the order of the geometric cross-section. The cross-sections vary little with bombarding energy. Received: 16 September 1998 / Received in final form: 23 February 1999     

Collision of a 1-D column of beads with a wall

An experimental study of the collision of a column of N beads () with a fixed wall is presented. For a fixed height of fall and a rigid wall, we show that the maximum force felt by the wall is independent of the number of beads N. The duration of impact, the velocity of the deformation wave in the column and an effective restitution coefficient of the column are also measured as a function of N. For a soft wall, we show that the maximum force depends on N. A non-dissipative numerical model, based on a nonlinear interaction law between nearest neighbours, gives results in agreement with the experimental data. Moreover, we show that, after the compression phase, the beads of the top of the column separate one after the other from the column with a velocity greater than the initial one. The beads at the bottom then bounce upwards in block, with a velocity smaller than the initial one. We emphasize that this detachment effect results from the energy redistribution within the whole system during the collision and not from any dissipative effect. Received: 6 February 1998 / Revised and accepted: 26 May 1998     

The smooth structural change in mesoscopic Peierls chains

We investigate the Peierls transition in finite chains by exact (Lanczos) diagonalization and within a seminumerical method based on the factorization of the electron-phonon wave function (Adiabatic Ansatz, AA). AA can be applied for mesoscopic chains up to micrometer sizes and its reliability can be checked self-consistently. Our study demonstrates the important role played for finite systems by the tunneling in the double well potential. The chains are dimerized only if their size N exceeds a critical value N_c which increases with increasing phonon frequency. Quantum phonon fluctuations yield a broad transition region. This smooth Peierls transition contrasts not only to the sharp mean field transition, but also with the sharp RPA soft mode instability, although RPA partially accounts for quantum phonon fluctuations. For weak coupling the dimerization disappears below micrometer sizes; therefore, this effect could be detected experimentally in mesoscopic systems. Received: 3 January 1998 / Revised: 13 March 1998 / Accepted: 3 April 1998     

A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in [#!bcre!#] to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We relate the critical wave vector to the mean hopping length and to the ratio of the flight time to the `stick' time. We provide an intuitive interpretation of the instability. Received: 30 January 1998 / Revised: 12 May 1998 / Accepted: 8 June 1998     

Effect of electron correlation on positronium formation in positron-helium scattering

A three-parameter correlated wave function for the helium ground state is used to study the scattering reaction , where Ps stands for positronium atom. An exact analytical expression is constructed for the first Born scattering amplitude for Ps formation from helium. Based on this numerical results are presented for both differential and total cross-sections. It is demonstrated that the inner electronic correlation of the target atom plays a crucial role in explaining the discrepency between theory and experiment. Received: 9 April 1998 / Revised: 29 September 1998 / Accepted: 19 October 1998     

One-dimensional moving polarons with extended coherent states

The general properties of one-dimensional large Fr?hlich polarons in motion are investigated with the previous extended coherent states where two-phonon correlations are considered. As a result, the polaron energy, velocity, effective mass, and average number of virtual phonons as a function the polaron total momentum are evaluated in a wide range of the coupling constant. In addition, rich information about virtual phonons emitted by the electron in motion is obtained. More importantly, some intrinsic features of 1D moving polarons are presented for the first time, which may also be suited to moving polarons in more than one dimensions. Received: 23 October 1997 / Revised and Accepted: 27 January 1998     

The topological structure of vortex in BEC

We find that there exists an elementary topological current in Bose-Einstein condensation. Based on the -mapping topological current theory, the implicit function theorem and the Taylor expansion, the topological structure of vortex lines is detailed in the neighborhoods of the bifurcation points of the condensate wave function. Received: 9 April 1998 / Revised: 28 August 1998 / Accepted: 31 August 1998     

Scattering from solutions of star polymers

We study the scattering intensity of dilute and semi-dilute solutions of star polymers. The star conformation is described by a model introduced by Daoud and Cotton. In this model, a single star is regarded as a spherical region of a semi-dilute polymer solution with a local, position dependent screening length. For high enough concentrations, the outer sections of the arms overlap and build a semi-dilute solution (a sea of blobs) where the inner parts of the actual stars are embedded. The scattering function is evaluated following a method introduced by Auvray and de Gennes. In the dilute regime there are three regions in the scattering function: the Guinier region (low wave vectors, ) from where the radius of the star can be extracted; the intermediate region () that carries the signature of the form factor of a star with f arms: ; and a high wavevector zone () where the local swollen structure of the polymers gives rise to the usual q ^-5/3 decay. In the semi-dilute regime the different stars interact strongly, and the scattered intensity acquires two new features: a liquid peak that develops at a reciprocal position corresponding to the star-star distances; and a new large wavevector contribution of the form q ^-5/3 originating from the sea of blobs. Received: 3 September 1997 / Revised: 13 January 1988 / Accepted: 31 March 1998     

Controlling nonspreading wavepackets

We show how a static electric field can be used to control the localization of nonspreading wavepackets of a hydrogen atom driven by a linearly polarized microwave field. This allows for creation of wavepackets localized on fully stable resonance islands which, at the same time, can easily be excited by a direct optical transition from a low lying state. A semiclassical analysis is used to predict the energies and properties of such states. Received: 27 November 1997 / Accepted: 27 January 1998     

An experimental test of the critical behaviour of fracture precursors

The statistical properties and the localization of fracture precursors on heteregeneous materials is studied by recording their acoustic emission as a function of the applied load. It's found that the microcrack cluster together as the load increases and the instantaneous acoustic energy has an invariant power law distribution. The integrated acoustic energy presents a critical divergency close to the failure load for the sample. These result support the idea that fracture can be viewed as a critical phenomenon. Finally a measure of the concentration of microcraks, which allows us to predict the failure load, is introduced. These properties are studied also when a periodic load is applied to the sample. It's found that the Kaiser effect is not strictly satisfied in heteregeneous materials. Received: 23 January 1998 / Revised: 20 April 1998 / Accepted: 17 June 1998     

Temperature dependence of the anisotropic electrodynamics in the ladder compounds

The optical reflectivity as a function of temperature of the title compound for x =0, 5 and 12 has been measured over a broad spectral range from 4 meV up to 12 eV. Our findings suggest a very anisotropic dynamics of the charge excitation spectrum when measuring along or perpendicular to the ladders. Moreover, a metal-insulator transition develops at low temperatures, leading to a suppression of Drude spectral weight in the far and mid-infrared spectral range. We identify this behaviour as a consequence of the localization effects for small Ca substitution, and of the possible formation of a charge density wave condensate for large Ca substitution. Received: 18 June 1998 / Accepted: 17 July 1998     

A new construction for spinor wave equations

The construction of discrete scalar wave propagation equations in arbitrary inhomogeneous media was recently achieved by using elementary dynamical processes realizing a discrete counterpart of the Huygens principle. In this paper, we generalize this approach to spinor wave propagation. Although the construction can be formulated on a discrete lattice of any dimension, for simplicity we focus on spinors living in 1+1 space-time dimensions. The Dirac equation in the Majorana-Weyl representation is directly recovered by incorporating appropriate symmetries of the elementary processes. The Dirac equation in the standard representation is also obtained by using its relationship with the Majorana-Weyl representation. Received: 3 November 1997 / Received in final form: 9 February 1998 / Accepted: 16 February 1998     

Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interaction U, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When (the one particle localization length), this mixing results in weak chaos accompanied by multifractal wave functions and critical spectral statistics, as in the one particle problem at the mobility edge or in certain pseudo-integrable billiards. In one dimension, a local interaction can only yield this weak chaos but can never drive the two particle system to full chaos with Wigner-Dyson statistics. Received: 22 May 1998 / Received in final form: 24 August 1998 / Accepted: 4 September 1998