Binding energies and modelling of nuclei in semiclassical simulations

We study the binding energies of spin–isospin saturated nuclei with nucleon number 8?A?100$8?A?100$ in semiclassical Monte Carlo many-body simulations. The model Hamiltonian consists of (i) nucleon kinetic energy, (ii) a nucleon–nucleon interaction potential, and (iii) an effective Pauli potential which depends on density. The basic ingredients of the nucleon–nucleon potential are a short-range repulsion, and a medium-range attraction. Our results demonstrate that one can always expect to obtain the empirical binding energies for a set of nuclei by introducing a proper density dependent Pauli potential in terms of a single variable, the nucleon number, A. The present work shows that in the suggested procedure there is a delicate counterbalance of kinetic and potential energetic contributions allowing a good reproduction of the experimental nuclear binding energies. This type of calculations may be of interest in further reproduction of other properties of nuclei such as radii and also exotic nuclei.     

Dependence of nuclear Z factor on the chemical potential

A simple microscopic formula is derived for the renormalization factor Z of Green’s function on the basis of the self-consistency relation of many-body theory and the Brueckner method. This formula involves the derivative of the Brueckner G matrix with respect to energy. Based on the analysis of the properties of the G matrix for a slab of nuclear matter, the G matrix is approximately replaced by the off-mass-shell T matrix taken for free NN scattering at a negative energy E equal to the doubled chemical potential μ of the nucleus under consideration. The Z factor thus calculated depends strongly on μ and decreases with |μ|. This effect is important for analyzing the properties of atomic nuclei near the drip line, where μ is zero.     

The many-body problem with an energy-dependent confining potential

We consider systems of N bosons bound by two-body harmonic interactions, whose frequency depends on the total energy of the system. Such energy dependent confining interactions between the bosons yield remarkable properties of the many-body system. As the quantum numbers increase, the total energy cannot exceed a saturation energy, which is independent of the number of particles N. Moreover, the ground state energy increases with N. As a result, the density of states tends rapidly to infinity as N and/or the quantum numbers increase.     

High-frequency magnetic properties and attenuation characteristics for barium ferrite composites

High-frequency magnetic properties and attenuation characteristics for barium-ferrite/epoxy composites have been studied. The methods for increasing μ′ and μ″ and controlling f_R, including ion substitution, doping of small amount of oxides, effect of damping, as well as the modification of particle sizes and shapes, are introduced. The results show that the composites are potential candidates for use as electromagnetic (EM) attenuation materials with low reflectivity and broad bandwidth at 2-18 GHz.     

A new approach to electron-electron interactions in strongly correlated systems at arbitrary spin-polarization and temperature

The uniform electron fluid is the reference model for density functional calculations. Even for this system, many-body perturbation theory, and related methods become questionable when the density parameter r_s exceeds unity. Hence, quantum Monte Carlo (QMC) simulation has been almost the only applicable method. We review a new approach, which uses a mapping of the quantum fluid to a classical Coulomb fluid, based on density-functional concepts. It is applicable at finite temperatures and arbitrary spin polarizations as well, and correctly recovers even the logarithmic terms in the exchange and correlations energies close to T=0. We show by detailed comparison with available QMC data that the method yields accurate pair-distribution functions, spin-dependent energies, static local-field factors, Landau parameter-based quantities like m∗ and g∗, for strongly coupled electron fluids.     

Relation between chemical and ionization potentials in atoms

The chemical potential μ in an atom is calculated by going to infinite distance from the nucleus. Then the kinetic energy contribution to μ is shown to be - I, with I the ionization potential. The potential energy per particle from correlation is obtained for the additional contribution from a local density approximation.     

Fast convergence of path integrals for many-body systems

We generalize a recently developed method for accelerated Monte Carlo calculation of path integrals to the physically relevant case of generic many-body systems. This is done by developing an analytic procedure for constructing a hierarchy of effective actions leading to improvements in convergence of N-fold discretized many-body path integral expressions from 1/N to 1/Np for generic p. In this Letter we present explicit solutions within this hierarchy up to level p=5. Using this we calculate the low lying energy levels of a two particle model with quartic interactions for several values of coupling and demonstrate agreement with analytical results governing the increase in efficiency of the new method. The applicability of the developed scheme is further extended to the calculation of energy expectation values through the construction of associated energy estimators exhibiting the same speedup in convergence.     

The ferromagnetic phase of quark matter in the framework of one gluon exchange and thermodynamics with the density-temperature-dependent particle mass model

In the current work we examine the possibility of ferromagnetism phase of quark matter by using the one gluon exchange interaction and the thermodynamics with the density-temperature-dependent particle masses as well as the normal thermodynamics (with constant masses). We calculate the free energy per particle of the polarized and unpolarized states to discuss the difference between these two phases at various densities and temperatures. In our calculations we assume that the QCD coupling, α_c, is constant (the simple model) or varies with the temperature and the density (the asymptotic freedom); but we keep α_c less than one, because we intend to use the perturbation method to calculate the exchange energy. We also assume that the up and down quarks are massless and do not interact. Only the strange quarks interact with each other via the one gluon exchange interaction. The free and internal energies as well as the effective masses and the pressure are calculated at different densities and temperatures. The results are discussed and a comparison is made with those of Tatsumi. Finally it is shown that the present models do not predict any transition for the strange quark matter to its ferromagnetic phase.     

Variational pair theory of the attractive and extended Hubbard model ind-dimensions

We present a variational approach for treating the Hubbard Hamiltonian in one, two and three dimensions. It is based on 2M-fermion wavefunctions which are allowed to form correlated spin-singlet pairs. Expressions for the ground state energy and correlation functions are derived in terms of general pair coefficient functions. The presented approach offers a convenient starting point for improved variational treatments that allow to include different specific types of pair correlations. We present first applications to the attractive and to the extended Hubbard model using a very simple ansatz for the pair coefficient functions. The ground state energy, chemical potential, order parameter, momentum distribution as well as spin-spin and density-density correlation functions follow from a system of coupled nonlinear equations that has to be solved selfconsistently. All quantities are given for arbitrary band-filling in one, two and three dimensions. Our results are compared with those of other approximations and for the one-dimensional case with the exact results of Krivnov and Ovchinnikov.     

Low integer Landau level filling factors ν and indications for the fractional ν=1/2 in the 2D organic metal κ-(BEDT-TTF)2I3

In the two-dimensional (2D) organic metal κ-(BEDT-TTF)₂I₃ the low integer Landau level filling factors ν=1-4 are observed under specific experimental conditions. In high magnetic fields even the presence of the fractional ν=1/2 is strongly indicated in this multilayer material. These ν are detected by the chemical potential μ, i.e. a thermodynamic quantity, which could be probed under complex fermiological conditions.     

Spin polarization of two-dimensional electron system in parabolic potential

We analyze the ground state of the two-dimensional quantum system of electrons confined in a parabolic potential with the system size around 100 at 0 K. We map the system onto a classical system on the basis of the classical-map hypernetted-chain (CHNC) method which has been proven to work in the integral-equation-based analyses of uniform systems and apply classical Monte Carlo and molecular dynamics simulations. We find that, when we decrease the strength of confinement keeping the number of confined electrons fixed, the energy of the spin-polarized state with somewhat lower average density becomes smaller than that of the spin-unpolarized state with somewhat higher average density. This system thus undergoes the transition from the spin-unpolarized state to the spin polarized state and the corresponding critical value of rs estimated from the average density is as low as rs∼0.4 which is much smaller than the rs value for the Wigner lattice formation. When we compare the energies of spin-unpolarized and spin-polarized states for given average density, our data give the critical rs value for the transition between unpolarized and polarized states around 10 which is close to but still smaller than the known possibility of polarization at rs∼27. The advantage of our method is a direct applicability to geometrically complex systems which are difficult to analyze by integral equations and this is an example.     

Self-consistent calculation of the optical potential and ground-state properties of nuclear matter

On the basis of the Green-function formalism, we performed a self-consistent calculation of the self-energy ∑(k, ω) of a particle interacting with the infinite nuclear medium. The function ∑(k, ω) was mapped out in the energy-momentum plane, and the single-particle energy ω(k), momentum distribution ?(k) and the “on-shell” part of the self-energy, ∑(k, ω(k)), were defined, from which all physical properties followed. In particular we investigated the ground-state properties of nuclear matter in two Λ-approximations of the T-matrix. In one, the intermediate two-particle propagator, Λ₀₀, represented free-particle propagation; in the other, called Λ₁₁, intermediate states included both interacting particles and holes. Pauli principle effects were included in both approximations. The second approximation was expected to be conserving because it included a large part of the rearrangement effects which, we found, contributed ～6 MeV per particle to the average energy and ～28 MeV to the singleparticle energy at zero momentum. The Hugenholtz-van Hove theorem was nearly satisfied, with only 1 MeV separating the chemical potential from the average energy. We also studied, in the Λ₀₀-approximation, the optical potential for the scattering of a particle by a large nucleus; it was directly related to the “on-shell” part of the self-energy. It was found that, below 100 MeV, the real part varied as (?90 + 0.584E) [MeV], and the imaginary part as (2.4 + 0.009 E) [MeV].     

Abnormal nuclear matter and many-body forces

Qualitative aspects of quantum corrections to the Lee-Wick abnormal nuclear matter are studied in terms of many-body forces in the normal nuclear matter implied by the σ-model Lagrangian field theory. Using a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA), we have found that an abnormal nuclear state can be bound or unbound depending upon whether strongly attractive multi-body forces are present or absent in the normal matter. This is in support of our previous result obtained heuristically from some general considerations of quantum corrections. A strongly bound abnormal matter with an equilibrium density of a few times the normal nuclear matter density ρ₀ can be formed if large attractive manybody forces can be accommodated in the normal nuclear matter. However if one accepts the present status of theories of nuclear matter binding energy in which no attractive many-body forces are called for, then the abnormal state can occur only at large densities (perhaps 8 to 10 times ρ₀) and is expected to be unbound by several hundred MeV per particle.     

Simulating the thermal stability and phase changes of small carbon clusters and fullerenes

The thermal stability, phases and phase changes of small carbon clusters and fullerenes are investigated by constant energy Molecular Dynamics simulations performed over a wide range of temperatures, i.e., from to above the melting point of graphitic carbon. The covalent bonds between the carbon atoms in the clusters are represented by the many-body Tersoff potential. The zero temperature structural characteristics of the clusters, i.e., the minimum energy structures as well as the isomer hierarchy can be rationalized in terms of the interplay between the strain energy (due to the surface curvature) and the number of dangling bonds in the cluster. Minimization of the strain energy opposes the formation of cage structures whereas minimization of the number of dangling bonds favors it. To obtain a reliable picture of the processes experienced by carbon clusters as a function of temperature, both thermal and dynamical characteristics of the clusters are carefully analyzed. We find that higher excitation temperatures are required for producing structural transformations in the minimum energy structures than in higher lying isomers. We have also been able to unambiguously identify some structural changes of the clusters occurring at temperatures well below the melting-like transition. On the other hand, the melting-like transition is interrupted before completion, i.e., the thermal decomposition of the clusters (evaporation or ejection of or units) occurs, from highly excited configurations, before the clusters have fully developed a liquid-like phase. Comparison with experiments on the thermal decomposition of and a discussion of the possible implications of our results on the growth mechanisms leading to the formation of different carbon structures are included. Received: 25 March 1998 / Received in final form: 30 October 1998     

Magnetic ordering above room temperature in the sigma-phase of Fe66V34

Magnetic properties of four sigma-phase Fe_100−xV_x samples with 34.4?x?55.1 were investigated by Mössbauer spectroscopy and magnetic measurements in the temperature interval 4.2-300 K. Four magnetic quantities, viz. hyperfine field, Curie temperature, magnetic moment and susceptibility, were determined. The sample containing 34.4 at% V was revealed to exhibit the largest values found up to now for the sigma-phase for average hyperfine field, 〈B〉=12.1 T, average magnetic moment per Fe atom, 〈μ〉=0.89 μ_B, and Curie temperature, T_C=315.3 K. The quantities were shown to be strongly correlated with each other. In particular, T_C is linearly correlated with 〈μ〉 with a slope of 406.5 K/μ_B, as well as 〈B〉 is so correlated with 〈μ〉, yielding 14.3 T/μ_B for the hyperfine coupling constant.     

Influence of surface roughness and contact load on friction coefficient and scratch behavior of thermoplastic olefins

To study the effects of surface roughness and contact load on the friction behavior and scratch resistance of polymers, a set of model thermoplastic olefins (TPO) systems with various surface roughness (R_a) levels were prepared and evaluated. It is found that a higher R_a corresponds to a lower surface friction coefficient (μ_s). At each level of R_a, μ_s gets larger as contact load increases, with a greater increase in μ_s as R_a level increases. It is also observed that with increasing contact load and increasing R_a, the μ_s tend to level off. In evaluating TPO scratch resistance, a lower μ_s would delay the onset of ductile drawing-induced fish-scale surface deformation feature, thereby raising the load required to cause scratch visibility. However, as the contact load is further increased, the μ_s evolves to become scratch coefficient of friction (SCOF) as significant sub-surface deformation and tip penetration occur and material displacement begins, i.e., ploughing. No dependence of R_a and μ_s on the critical load for the onset of ploughing is observed. In this work, the distinction between μ_s and SCOF will be illustrated. Approaches for improving scratch resistance of polymers via control of R_a are also discussed.     

Ground state energy of the electron-hole liquid in type-II (GaAs)m/(AlAs)m quantum wells

The ground state energy of quasi-two-dimensional electron-hole liquid (EHL) at zero temperature is calculated for type-II (GaAs)_m/(AlAs)_m (5≤m≤10) quantum wells (QWs). The correlation effects of Coulomb interaction are taken into account by a random phase approximation of Hubbard. Our EHL ground state energy per electron-hole pair is lower than the exciton energy calculated recently for superlattices, so we expected that EHL is more stable state than excitons at high excitation density. It is also demonstrated that the equilibrium density of EHL in type-II GaAs/AlAs QWs is of one order of magnitude larger than that in type-I GaAs/AlAs QWs.     

Method for solving the many-body bound state nuclear problem

We present a method based on hyperspherical harmonics to solve the nuclear many-body problem. It is an extension of accurate methods used for studying few-body systems to many bodies and is based on the assumption that nucleons in nuclei interact mainly via pairwise forces. This leads to a two-variable integro-differential equation which is easy to solve. Unlike methods that utilize effective interactions, the present one employs directly nucleon-nucleon potentials and therefore nuclear correlations are included in an unambiguous way. Three body forces can also be included in the formalism. Details on how to obtain the various ingredients entering into the equation for the A-body system are given. Employing our formalism we calculated the binding energies for closed and open shell nuclei with central forces where the bound states are defined by a single hyperspherical harmonic. The results found are in agreement with those obtained by other methods.     

Helium-cluster decay widths of molecular states in beryllium and carbon isotopes

⁴He (i.e., α particle) and ⁶He emissions from possible molecular states in beryllium and carbon isotopes have been investigated using a mean-field-type cluster potential. Calculations can reasonably describe the α-decay widths of studied states in beryllium and carbon isotopes, and also ²⁰Ne, compared with experiments. For the nucleus ¹⁰Be, we discussed α-decay widths with different shapes or different decay modes, in order to understand the very different decay widths of two excited states. The widths of ⁶He decays from ¹²Be and α decays from ^13,14C are predicted, which could be useful for future experiments.     

Transport in a flashing ratchet in the presence of anomalous diffusion

Transport of a particle in a flashing ratchet coupled to a non-Ohmic environment with spectrum ∝ω^μ−1 (0<μ<2) is considered. If the temperature is much less than the barrier height of the ratchet potential and the waiting time of the particle in the potential on is long enough, the current J is evaluated approximately by the step periodic number per cycle. The results show that the maximum of peak for J is a non-monotonous function of μ, the optimal μ appears in the region of superdiffusion. The current in the anomalous ratchet is much larger than in the normal one.