Monte-Carlo simulation of transient gel formation and break-up during reversible aggregation

Monte-Carlo simulations of reversible aggregation on a cubic lattice were done by introducing a finite probability (P) of nearest neighbours to form a bond. Depending on the volume fraction of occupied sites (φ) and P we observed different phenomena by monitoring as a function of time the space filling and the distribution of the aggregates and the gel fraction. At smaller values of P the system develops into an equilibrium distribution of aggregates of which the average size increases with increasing φ until above a critical value the system percolates. At larger values of P the system phase separates into two phases with different densities. Above a critical value of φ the system percolates during a finite time. The life time of the gel and the maximum gel fraction were studied as a function of P. Received 1st March 2001 and Received in final form 24 April 2001     

The Al-Pd-Mn quasicrystalline approximant -phase revisited

A detailed investigation of the Fourier space of several Al-Pd-Mn samples with composition Al-72.6 at. %, Pd-22.9 at. %, Mn-4.5 at. % is reported. In the phase diagram of the Al-Pd-Mn ternary alloy, this composition corresponds to the so-called ξ' phase which was described as an icosahedral quasicrystalline approximant. By re-examining the Fourier space by means of X-ray diffraction (powder patterns and single crystal precession patterns), complex structures in close relation with the ξ'-phase have been observed. These long-range order complex structures are described as resulting from a periodic perturbation of the ξ' structure along the c direction. Two states with periodicities c (3 + τ) and c (5 + τ) have been observed in this study (τ: golden mean). Structural models based on periodic arrangements of “defects” layers separating layers of phase are proposed. These two states are certainly intermediate states between the phase and the metastable decagonal quasicrystalline phase. Received 11 April 2002 / Received in final form 24 June 2002 Published online 17 September 2002     

Harmonically trapped ideal quantum gases

We solve the problem of a Bose or Fermi gas in d-dimensions trapped by δ ⩽ d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature T _c if and only if d + δ > 2, along with a jump in the specific heat at T _c if and only if d + δ > 4. Specific heats for both gas types precisely coincide as functions of temperature when d + δ = 2. The trapped system behaves like an ideal free quantum gas in d + δ dimensions. For δ = 0 we recover all known thermodynamic properties of ideal quantum gases in d dimensions, while in 3D for δ = 1, 2 and 3 one simulates behavior reminiscent of quantum wells, wires anddots, respectively. Good agreement is found between experimental critical temperatures for the trapped boson gases ₃₇ ⁸⁷Rb, ₃ ⁷Li, ₃₇ ⁸⁵Rb, ₂ ⁴He, ₁₉ ⁴¹K and the known theoretical expression which is a special case for d = δ = 3, but only moderate agreement for ₁₁ ²⁷Na and ₁ ¹H. Received 17 July 2002 / Received in final form 14 October 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: mdgg@hp.fciencias.unam.mx     

Optimized δ expansion for relativistic nuclear models

The optimized δ-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. This technique is discussed in the λφ⁴ model and then implemented in the Walecka model for the equation of state of nuclear matter. The results obtained with the δ expansion are compared with those obtained with the traditional mean field, relativistic Hartree and Hartree-Fock approximations. Received: 17 March 1997 / Revised version: 27 August 1997     

Charge radius change in the heavy tin isotopes until A = 132 from laser spectroscopy

Laser spectroscopy measurements have been carried out on the very neutron-rich tin isotopes with the COMPLIS experimental setup. Using the 5s ²5p ²³ P ₀ → 5s ²5p6s ³ P ₁ optical transition, hyperfine spectra of ^126-132Sn and ^{125m, 127m, 129m-131m}Sn where recorded for the first time. The variation of the mean-square charge radius ( δ〈r ²〉) between these nuclei and nuclear moments of the isomers and the odd isotopes were thus measured. An odd-even staggering which inverts at A = 130 is clearly observed. This indicates a small appearance of a plateau on the δ〈r ²〉 which has to be confirmed by measuring the isotope shift beyond A = 132. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: leblanc@ipno.in2p3.fr     

A molecular theory of smectic C liquid crystals made of rod-like molecules

Organic compounds exhibiting the smectic C phase are made of rod-like molecules that have dipolar groups with lateral components. We argue that the off-axis character of the lateral dipolar groups can account for tilt in layered smectics (SmC, SmC*, SmI etc.). We develop a mean-field theory of the smectic C phase based on a single-particle potential of the form U _C ∝ sin(2θ)cosφ, consistent with the biaxial nature of the phase, where θ and φ are the polar and azimuthal angles, respectively. The hard-rod interactions that favour the smectic A phase with zero tilt angle are also included. The theoretical phase diagrams compare favourably with experimental trends. Our theory also leads to the following results: i) a first-order smectic C to smectic A transition above some value of the McMillan parameter α, leading to a tricritical point on the smectic C to smectic A transition line and ii) a first-order smectic C to smectic C transition over a very small range of values of the model parameters. We have also extended the theory to include the next higher-order term in the tilting potential and to include the effect of different tilt angles for the molecular core and the chain in the SmC phase. Received 3 August 2002 RID="a" ID="a"Present address: Department of Physics, Vijaya College, R. V. Road, Bangalore - 560 004, India. RID="b" ID="b"e-mail: nvmadhu@rri.res.in     

Atomic coherent states studied by virtue of the EPR entangled state and their Wigner functions

Based on the newly constructed Einstein, Podolsky and Rosen (EPR) entangled state representation we introduce macroscopic classical functions associated with atomic coherent state τ with angular momentum value j. These functions are proportional to the ordinary one-variable Hermite polynomials of order 2j. The corresponding Wigner quasiprobability function for τ in phase space is also derived which turns out to be a two-variable Hermite polynomial H _{2j, 2j}. In so doing, a new classical-quantum correspondence scheme for angular momentum system is established. Received 7 August 2002 / Received in final form 14 December 2002 Published online 24 April 2003 RID="a" ID="a"Work supported by the National Natural Science Foundation of China under grant 10175057. RID="b" ID="b"e-mail: fhym@sjtu.edu.en     

The Z = 82 shell closure in neutron-deficient Pb isotopes

Recent mass measurements show a substantial weakening of the binding-energy difference δ_2p(Z, N) = E(Z - 2, N) - 2E(Z, N) + E(Z + 2, N) in the neutron-deficient Pb isotopes. As δ_2p is often attributed to the size of the proton magic gap, it might be speculated that reduction in δ_2p is related to a weakening of the spherical Z = 82 shell. We demonstrate that the observed trend is described quantitatively by self-consistent mean-field models in terms of deformed ground states of Hg and Po isotopes. Received: 25 October 2001 / Accepted: 28 February 2002     

Polaronic behavior in single- and many-electron Holstein model: A new perturbation approach

A new perturbation approach is developed for single- and many-electron Holstein model in one-, two-, and three-dimension. The results show that this approach has a good agreement with the Migdal theory in the adiabatic regime when the coupling is moderate (λ < 1), but with the Lang-Firsov theory in the antiadiabatic regime ( ω/W≫ 1). In the intermediate region, our approach can describe the transition from a large-polaron Fermi-liquid to the small-polaron, and this transition may be discontinuous in adiabatic regime, which means a phase transition appears in many-electron system. In single-electron case, we eliminate the abrupt transition using the degenerate perturbation theory, and the calculated ground state energy and effective mass are successfully compared with those of previous authors. Besides, the method has the advantage of requiring little computational effort. Received 27 December 2001 / Received in final form 8 April 2002 Published online 31 July 2002     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Dynamical properties of constrained drops

In this communication we analyze the behavior of excited drops contained in spherical volumes. We study different properties of the dynamical systems, i.e. the maximum Lyapunov exponent MLE, the asymptotic distance in momentum space d _∞ and the normalized variance of the maximum fragment. It is shown that the constrained system behaves as undergoing a first-order phase transition at low densities while as a second-order one at high densities. The transition from liquid-like to vapor-like behavior is signaled both by the caloric curves, the thermal response functions and the MLE. The relationship between the MLE, d _∞, and the caloric curve is explored. Received: 28 March 2002 / Accepted: 17 May 2002     

Single-particle quadrupole electromagnetic transitions in p-shell and sd-shell nuclei

Electron scattering Coulomb form factors for the single-particle quadrupole transitions in p-shell and sd-shell nuclei have been studied. Core polarization effects are included through a microscopic theory that includes excitations from the core orbits up to higher orbits with 2ω excitations. The modified surface delta interaction is adopted as a residual interaction. The results are discussed for the ( 1p _1/2 ^-1↦1p _3/2 ^-1) proton transition in ¹⁵N, ( 1d _5/2↦2s _1/2) neutron transition in ¹⁷O and ( 1d _3/2 ^-1↦2s _1/2 ^-1) proton transition in ³⁹K. The inclusion of core polarization effects modifies the form factors markedly and describes the experimental data very well in both the absolute strength and the momentum transfer dependence. Received: 18 April 2002 / Accepted: 1 July 2002 / Published online: 6 March 2003 RID="a" ID="a"e-mail: baguniv@uruklink.net Communicated by A. Molinari     

Scalar mesons and glueball in a quark model allowing for gluon anomalies

This paper is a sequel of a previous one (Scalar mesons in a chiral quark model with glueball, Eur. Phys. J. A 8, 567 (2000)) where an attempt to construct an effective U(3)×U(3)-symmetric meson Lagrangian with a scalar glueball was made. The glueball was introduced by using the dilaton model on the base of scale invariance. The scale invariance breaking because of current quark masses and the scale anomaly of QCD, reproduced by the dilaton potential, was taken into account. However, in the previous paper, the scale invariance breaking because of the terms like h _φφ² and h _σ , where φ and are the pseudoscalar and scalar isosinglets, was not taken into account. These terms are produced by the part of the 't Hooft interaction that is connected with gluon anomalies. Allowing for the scale invariance breaking by these terms has a decisive effect on the quarkonium-glueball mixing and noticeably changes the widths of glueball strong decays. Taking account of this additional source of the scale invariance breaking and its implications are the subject of the present work. It is also shown that in the decay of a glueball into four pions, the channel with two ρ-resonances dominates. Received: 11 January 2001 / Accepted: 25 January 2001     

Carbon clusters for absolute mass measurements at ISOLTRAP

The cyclotron frequencies of singly charged carbon clusters C_n ⁺ (n ≥ 2) were measured with the Penning-trap mass spectrometer ISOLTRAP at ISOLDE/CERN. The present limit of mass accuracy δm/m = 1.2 ^. 10^-8 and the extent of the mass-dependent systematic shift (δm/m)_sys = 1.7(0.6) ^. 10^-10/u ^. (m - m _ref) of the setup were investigated for the first time. In addition, absolute mass measurements by use of pure clusters of the most abundant carbon isotope ¹²C are now possible at ISOLTRAP. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"Present address: CERN, CH-1211 Geneva 23, Switzerland; e-mail: klaus.blaum@cern.ch     

The normal state scattering rate in high- cuprates

A detailed phenomenological model is developed for the normal state transport properties of optimal and overdoped high-T_c cuprates. In particular, an explicit form of scattering rate is identified that may account, qualitatively and quantitatively, for the normal state (magneto)-transport properties of Tl₂Ba₂CuO _{6 + δ} and Bi₂Sr₂CaCu₂O _{8 + δ} across the overdoped side of the phase diagram. The proscribed form of the scattering rate is consistent also with features seen in the photoemission spectroscopy of Bi₂Sr₂CaCu₂O _{8 + δ} and offers a new and intuitive way to understand the evolution of the temperature dependence of the inverse Hall angle in Bi-based cuprates with carrier concentration. Received 5 June 2002 / Received in final form 17 December 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: n.e.hussey@bristol.ac.uk     

Polarization observables in the reaction pn↦dφ

The reaction pn↦dφ is studied within a covariant boson exchange model. The behavior of polarization observables being accessible in forthcoming experiments near threshold is predicted. Received: 13 February 2001 / Accepted: 25 March 2002     

Lifetime of heavy hypernuclei and its implications on the weak ΛN interaction

The lifetime of the Λ-hyperon in heavy hypernuclei measured in proton-Au, -Bi and -U collisions by the COSY-13 Collaboration at COSY-Jülich has been analyzed to yield τ_Λ = (145±11) ps. This value for τ_Λ is compatible with the lifetime extracted from antiproton annihilation on Bi and U targets, albeit much more accurate. Theoretical models based on the meson exchange picture and assuming the validity of the phenomenological ΔI = 1/2 rule predict the lifetime of heavy hypernuclei to be significantly larger (2-3 standard deviations). Such large differences indicate that at least one of the assumptions in these models is not fulfilled. A much better reproduction of the lifetimes of heavy hypernuclei is achieved in the phase space model, if the ΔI = 1/2 rule is discarded in the nonmesonic Λ decay. Received: 8 August 2002 / Accepted: 20 December 2002 / Published online: 25 March 2003 RID="a" ID="a"e-mail: h.stroeher@fz-juelich.de Communicated by Th. Walcher     

Core polarization effects on C4 form factors of sd-shell nuclei

Coulomb form factors of C4 transitions in even-even N = Z sd-shell nuclei ( ²⁰Ne, ²⁴Mg, ²⁸Si and ³²S) are discussed taking into account higher-energy configurations outside the sd-shell model space which are called core polarization effects. Higher configurations are taken into account through a microscopic theory, which allows particle-hole excitations from the 1s and 1p shells core orbits and also from the 2s1d-shell orbits to the higher allowed orbits with excitations up to 4 ω. The effect of core polarization is found essential in both the transition strengths and momentum transfer dependence of form factors, and gives a remarkably good agreement with the measured data with no adjustable parameters. The calculations are based on the Wildenthal interaction for the sd-shell model space and on the modified surface delta interaction (MSDI) for the core polarization effects. Received: 24 January 2002 / Accepted: 29 July 2002 / Published online: 6 March 2003 RID="a" ID="a"e-mail: baguniv@uruklink.net Communicated by P. Schuck     

Magnetic properties of LaNi <Emphasis Type="Bold">1-</Emphasis><Emphasis Type="Bold">x</Emphasis>Mn <Emphasis Type="Bold">x</Emphasis>O <Emphasis Type="Bold">3+δ</Emphasis> perovskites

Magnetic measurements have been carried out in different LaNi_1-xMn_xO _{3 + δ} samples with 0.1 ⩽ x ⩽ 0.9. All these samples show two magnetic anomalies, one at relatively high temperature characteristic of a ferromagnetic ordering and the other at low temperature, typical of magnetic relaxation phenomena. Neutron diffraction patterns indicate that long-range ferromagnetic ordering is only achieved for x ≥ 0.5. Neutron patterns of LaNi_0.5Mn_0.5O _{3 + δ} samples show an ordered arrangement of Ni and Mn atoms in the perovskite lattice. LaNi_0.5Mn_0.5O _{3 + δ} is then, a double perovskite A₂BB'O₆ whereas Ni and Mn atoms are randomly distributed for the rest of the samples. X-ray magnetic circular dichroism experiments confirm the presence of collinear ferromagnetism in LaNi_0.5Mn_0.5O _{3 + δ} . The role of competitive magnetic interactions, structural disorder, magnetic anisotropy and magnetic disaccommodation is also discussed Received 19 July 2002 / Received in final form 23 October 2002 Published online 31 December 2002     

A remark on the large difference between the glueball mass and T<Subscript>c</Subscript> in quenched QCD

The lattice QCD studies indicate that the critical temperature T _c ≃ 260-280 MeV of the deconfinement phase transition in quenched QCD is considerably smaller than the lowest-lying glueball mass m _G ≃ 1500-1700 MeV, i.e., T _c ≪ m _G. As a consequence of this large difference, the thermal excitation of the glueball in the confinement phase is strongly suppressed by the statistical factor e ^-mG/Tc ≃ 0.00207 even near T ≃ T _c. We consider its physical implication, and argue the abnormal feature of the deconfinement phase transition in quenched QCD from the statistical viewpoint. To appreciate this, we demonstrate a statistical argument of the QCD phase transition using the recent lattice QCD data. From the phenomenological relation between T _c and the glueball mass, the deconfinement transition is found to take place in quenched QCD before a reasonable amount of glueballs is thermally excited. In this way, quenched QCD reveals a question “what is the trigger of the deconfinement phase transition ?” Received: 18 November 2002 / Accepted: 4 February 2003 / Published online: 29 April 2003