Range Effective Interaction Research Articles

Momentum and density dependence of the isospin part of nuclear mean field and equation of state of asymmetric nuclear matter

Momentum and density dependence of the isospin part of nuclear mean field u τ ( k , ρ ) which is still, in part, the open problem of the old Lane potential is analysed using density dependent finite range effective interactions. The behaviour of u τ ( k = k f , ρ ) around the Fermi momentum k f is found to be related to the density dependence of nuclear symmetry energy J τ ( ρ ) and nucleon effective mass M ∗ ( k = k f , ρ ) / M in symmetric nuclear matter. The momentum dependence of u τ ( k , ρ ) is separated out in terms of a simple functional u τ e x ( k , ρ ) which vanishes at k = k f and involves only the finite range parts of the exchange interactions between pairs of like and unlike nucleons. Depending on the choice of the parameters of these exchange interactions two conflicting trends of momentum dependence are noticed which lead to two opposite types of splitting of neutron and proton effective masses. The equation of state of asymmetric nuclear matter and the high density behaviour of nuclear symmetry energy J τ ( ρ ) are studied by constraining the additional parameters involved on the basis that pure neutron matter should not be predicted to be bound by any reasonable nuclear interaction. Emphasis is also given on the need of experimental data sensitive to the differences between neutron and proton transport properties in highly asymmetric dense nuclear matter and its analysis to constrain the high density behaviour of nuclear symmetry energy as well as to resolve the controversy on the two opposite types of splitting of neutron and proton effective masses.

Counter terms for low momentum nucleon–nucleon interactions

There is much current interest in treating low energy nuclear physics using the renormalization group (RG) and effective field theory (EFT). Inspired by this RG-EFT approach, we study a low-momentum nucleon–nucleon (NN) interaction, V low- k , obtained by integrating out the fast modes down to the scale Λ∼2 fm −1. Since NN experiments can only determine the effective interaction in this low momentum region, our chief purpose is to find such an interaction for complex nuclei whose typical momenta lie below this scale. In this paper we find that V low- k can be highly satisfactorily accounted for by the counter terms corresponding to a short range effective interaction. The coefficients C n of the power series expansion ∑ C n q n for the counter terms have been accurately determined, and results derived from several meson-exchange NN interaction models are compared. The counter terms are found to be important only for the S, P and D partial waves. Scaling behavior of the counter terms is studied. Finally we discuss the use of these methods for computing shell model matrix elements.

Collective excitations far from the valley of stability

Collective Vibrations of nuclei far from the valley of stability are investigated within the quasi-particle random phase approximation based on relativistic Hartree-Bogoliubov theory with non-linear meson couplings. Pairing correlations are described in by a finite range effective particle-particle interaction of Gogny type. The quasi-particle random phase equations are solved in the canonical basis and collective strength distributions are discussed.

Two-body correlations in halo nuclei and effective interactions

Light nuclei with two particles (neutron or proton) or two holes outside a core have been studied in a two-particle RPA model with the Gogny and a zero range density dependent effective interactions. It has been shown that the model is able to consistently describe 6He, 14C, 12Be and 11Li. The case of 12Be, described either as a 10Be-core plus two neutrons or as the core of 14Be, has been discussed in more details and a quasi boson expansion of the ground state wave function has been performed. To get consistent results in the two schemes one has suggested the same inversion of 2s and 1 p 1 2 shells in the n+ 12Be average potential as known in the n+ 10Be one. In the same model, a T=0 neutron-proton zero range effective interaction has been proposed to describe the 1 +, T=0 states in 14N and discussed in 10B.

Folding model study ofα−pscattering: Systematics of elastic scattering, effective interaction, and inelastic excitation ofN*resonances

For a description of elastic and inelastic $\ensuremath{\alpha}\ensuremath{-}p$ scattering exciting ${N}^{*}$ resonances optical potentials and transition potentials were derived by folding nucleon and nucleus mass densities with a variable range effective interaction. For elastic $\ensuremath{\alpha}\ensuremath{-}p$ scattering in forward direction, a reasonable description of essentially all data has been obtained from low energies up to the GeV region. Also, $\ensuremath{\alpha}$ scattering from ${}^{4}\mathrm{He}$ and ${}^{12}\mathrm{C}$ is quite well described with potentials, which indicate that the used folding method is a valid approach for the systems in question. The strong energy dependence of the deduced potentials can be accounted for by a sum of scalar and vector meson-exchange potentials and a soft Pomeron-exchange contribution. The scalar meson-exchange potential falls off rapidly with energy and has a large radius in agreement with theoretical predictions. Consistent with the flavor SU(3) quark model, the vector-meson coupling is rather weak in the central potential, but is strong in the spin-orbit potential, for which a soft Pomeron contribution is negligible. The differences between the deduced $\ensuremath{\alpha}\ensuremath{-}p$ and nucleon-nucleon $(\mathrm{NN})$ potentials are understood; further, an excellent description of the energy dependence of the s-wave $\mathrm{NN}$ amplitudes is obtained in the folding model framework. Distorted wave Born approximation calculations for inelastic $\ensuremath{\alpha}\ensuremath{-}p$ scattering show a t-dependence of the $L=0$ cross section consistent with empirical form factors. Absolute yields for excitation of the resonances ${P}_{11}(1440),$ ${D}_{13}(1520)$ and ${F}_{15}(1680)$ were calculated, using resonance shapes from $\ensuremath{\pi}\ensuremath{-}N$ scattering. A quantitative description of the data at ${E}_{\ensuremath{\alpha}}=4.2\mathrm{GeV}$ is obtained using fluid-dynamical transition densities and strengths exhausting large fractions of scalar energy weighted sum rules. The rather pure scalar (non-spin-isospin-flip) character of these excitations and the observed cross sections are in severe conflict with the constituent quark model. Finally, a prediction is made for $p\ensuremath{-}\ensuremath{\alpha}$ scattering at an incident energy of ${E}_{p}=2.2\mathrm{GeV},$ which yields strongly increased cross sections for ${N}^{*}$ excitations.

Effective interaction range in the spin crossover phenomenon: Wajnflasz and domain models

The importance of cooperative interaction has been pointed out in the spin crossover phenomena. Sorai and co-workers have proposed a so-called domain model, in which the degree of correlation is expressed by a phenomenological parameter characterizing the sharpness of the transition. Wajnflasz has introduced a pioneering statistical model, in which the microscopic interaction and the entropy effect are considered. In the present work, we study the relation between these two models. In particular, we derive the analytical relation between the effective interaction range of the domain model and the microscopic parameters of the Wajnflasz model.

Tomonaga-Luttinger parameters for quantum wires

The low-energy properties of a homogeneous one-dimensional electron system are completely specified by two Tomonaga-Luttinger parameters ${K}_{\ensuremath{\rho}}$ and ${v}_{\ensuremath{\sigma}}.$ In this paper we discuss microscopic estimates of the values of these parameters in semiconductor quantum wires that exploit their relationship to thermodynamic properties. Motivated by the recognized similarity between correlations in the ground state of a one-dimensional electron liquid and correlations in a Wigner crystal, we evaluate these thermodynamic quantities in a self-consistent Hartree-Fock approximation. According to our calculations, the Hartree-Fock approximation ground state is a Wigner crystal at all electron densities and has antiferromagnetic order that gradually evolves from spin-density wave to localized in character as the density is lowered. Our results for ${K}_{\ensuremath{\rho}}$ are in good agreement with weak-coupling perturbative estimates ${K}_{\ensuremath{\rho}}^{\mathrm{pert}}$ at high densities, but deviate strongly at low densities, especially when the electron-electron interaction is screened at long distances. ${K}_{\ensuremath{\rho}}^{\mathrm{pert}}\ensuremath{\sim}{n}^{1/2}$ vanishes at small carrier density n, whereas we conjecture that ${K}_{\ensuremath{\rho}}\ensuremath{\rightarrow}1/2$ when $\stackrel{\ensuremath{\rightarrow}}{n}0,$ implying that ${K}_{\ensuremath{\rho}}$ should pass through a minimum at an intermediate density. Observation of this nonmonotonic dependence could be used to measure the effective interaction range in a realistic semiconductor quantum wire geometry. In the spin sector we find that the spin velocity decreases with increasing interaction strength or decreasing n. Strong correlation effects make it difficult to obtain fully consistent estimates of ${v}_{\ensuremath{\sigma}}$ from Hartree-Fock calculations. We conjecture that ${v}_{\ensuremath{\sigma}}{/v}_{\mathrm{F}}\ensuremath{\propto}{n/V}_{0},$ where ${V}_{0}$ is the interaction strength, in the limit $\stackrel{\ensuremath{\rightarrow}}{n}0.$

Relaxation of excited electrons in a paramagnetic electron gas: The role of spins in screening and scattering

The scattering lifetime of excited electrons close enough to the Fermi surface is investigated using the standard kinetic framework. This framework is implemented by effective, spin-dependent interactions and numerical phase-shift calculations. The nontrivial interplay between wave-mechanical interference effects in scattering and correlations in screening and dressing is discussed. Their role and relative importance are quantified via a comparative theoretical study. fermions ~not necessarily electrons, i.e., nucleons ! interact- ing through central forces is well-known, 7,8 The description is based on the free-space Schrodinger equation. We may suppose—and this will be the actual case in this work—that the spin-dependent part of the two-body effective interaction is proportional to the product s1is2 of two Pauli spin operators. 3,4,8 Generally, the scattering state function must be antisymmetric when all the coordinates of the two fermions ~spatial and spin! are interchanged. The rate of scattering is related 9 to the differential cross section ( ds) which is de- fined in terms ofproperly determined singlet and triplet am- plitudes. At these above circumstances the role of exchange appears as an interference effect in the differential cross section. 8 In the present work we shall investigate in detail the physical aspects of the effective interaction required in an implementation of the kinetic treatment of the relaxation process. 2 The influence of the fermion many-body environ- ment ''around'' our two-particle subsystem results in a short- range effective interaction between them. The scattering should be described, therefore, at least via an in-medium Schrodinger equation. The effective interaction must include electrostatic screening and exchange-correlation-mediated dressing, due to the Coulomb and Pauli correlations. These may affect the scattering characteristics ( ds) in a nontrivial manner in combination with the above-mentioned wave- interference effect. This paper is organized as follows. In Sec. II, we present the theoretical framework for the scattering lifetime, the models for the effective interaction, and the obtained results. These latter are given analytically and numerically in the form of illustrative figures. The results, based on different approximations, are discussed in a comparative way. The last section, Sec. III, is devoted to the conclusions. We shall use atomic units e 2 5\5me51 throughout this work.

Effective interaction between reverse micelles: A study from the potential of mean force at infinite dilution

The effective interaction potential between reverse micelles is computed by adding the potential of mean force at infinite dilution to the direct interaction between micelles. The former is computed from an integral equations approach and the latter is modeled by van der Waals and electrostatic contributions. This model is used to discuss the characteristics of the effective interaction—range, strength, and temperature dependence—deduced in previous work from the effective one-component approach. From a detailed analysis of the various contributions to the effective interaction, it is concluded in agreement with other studies, that the relative long range of the interaction is attributed to electrostatic contributions. The moderate interaction strength is found to result from strong cancellations between direct interactions (short range repulsion plus van der Waals attraction between surfactant films) and indirect ones (“depletion” plus “solvation” effects). In contrast with previous studies which attributed the increase with temperature of the interaction strength only to the extension of surfactant chains (direct interaction), the variation with temperature of the potential of mean force is found to be equally important.

Molecular Dynamic Simulation of Adhesional Release of Particles from Surfaces

The generalized form of the Lennard-Jones soft-sphere pair potential is used to examine the adhesional attachment and release behavior of particles on surfaces for materials of varying “ductility”. Using a two-dimensional simulation, with the repulsive term held constant at m = 12, the attractive term is varied from n = 2 to n = 10 at a constant binding energy to provide a controlled way of changing the effective range of interaction between atoms. Molecular dynamics simulates the placement of particles on a free surface and the subsequent removal of these particles by controlling the displacement of the center of mass. Simulations indicate that the longer-ranged removal forces literally tear out a chunk of the surface by pulling out a tether-like strand connecting the ball and plate. As the forces become shorter range, the size of the region of disturbed material after separation decreases until, at the shortest range, only three atoms are transferred and there is relatively little damage to the system on separation as indicated by the lack of slip steps in the plate. Results are discussed both mechanistically and from the point of view of more traditional approaches to surface force behavior, such as the JKR and DMT models.

Bosonic Clouds with Attractive Interaction Beyond the Local Interaction Approximation

We study the properties of a Bose–Einstein condensed cloud of atoms with negative scattering length confined in a harmonic trap. When a realistic non local (finite range) effective interaction is taken into account, we find that, besides the known low density metastable solution, a new branch of Bose condensate appears at higher density. This state is self–bound but its density can be quite low if the number N of atoms is not too big. The transition between the two classes of solutions as a function of N can be either sharp or smooth according to the ratio between the range of the attractive interaction and the length of the trap. A tight trap leads to a smooth transition. In addition to the energy and the shape of the cloud we study also the dynamics of the system. In particular, we study the frequencies of collective oscillation of the Bose condensate as a function of the number of atoms both in the local and in the non local case. Moreover, we consider the dynamics of the cloud when the external trap is switched off.

Halo structure of 11Li in proton scattering: A folding model description with isospin, density and momentum dependent effective interaction

Recent 11Li+p elastic scattering data at 62, 68.4, and 75 MeV and inelastic scattering data at 68.4 MeV, taken at RIKEN, are analysed with an isospin, density and momentum dependent finite range effective interaction (SBM) and M3Y interaction in a single folding model. The M3Y folded 11Li+p potentials are found to be almost similar to the folded 9Li+p potentials. But the SBM folded 11Li+p potentials are distinctly different, causing small but significant change in the angular distribution. Folded potentials need appreciable reduction factors indicating possible effects of strong breakup channel coupling. No significant change in results is found if 9Li core + Gaussian two-neutron halo density is used instead of the COSM density of 11Li although the radial extent of the latter is much larger. The angular distribution of the recently discovered excited state at 1.3 MeV, well reproduced by the SBM folded potential, is found to be predominantly dipole in nature.

Spin polarised nuclear matter and its application to neutron stars

An equation of state (EOS) of nuclear matter with explicit inclusion of a spin-isospin dependent force is constructed from a finite range, momentum and density dependent effective interaction. This EOS is found to be in good agreement with those obtained from more sophisticated models for unpolarised nuclear matter. Introducing spin degrees of freedom, it is found that it is possible for neutron matter to undergo a ferromagnetic transition at densities realisable in the core of neutron stars. The maximum mass and the surface magnetic field of the neutron star can be fairly explained in this model. Since finding quark matter rather than hadronic matter at the core of neutron stars is a possibility, the proposed EOS is also applied to the study of hybrid stars. It is found using the bag model picture that one can in principle describe both the mass as well as the surface magnetic field of hybrid stars satisfactorily.

Analysing power puzzle of [formula omitted] scattering: consistent analysis with density and momentum dependent finite range effective interaction

The p+ 6Li angular distribution data at E p = 10–136 MeV for both the ground state (1 +) and the first excited state (3 1 +) of 6Li are analysed with a density and momentum dependent finite range effective interaction (SBM) in a single folding model. For the polarised incident protons at E p = 10, 49.75, 65 and 80 MeV, the analyses of the analysing power data are also carried out. For comparison, analyses with the density independent M3Y interaction and pure phenomenological potential are presented. The transition densities are computed from the 6Li(e,e′) data in the Fourier-Bessel series expansion method. The SBM potential along with these experimental density profiles of 6Li gives a reasonable description of both the cross section and the analysing power data. In a coupled channel calculation, the effect of coupling the ground state to the 3 1 + resonant state of 6Li is found to be important at E p = 10 and 24 MeV. The effect of this coupling becomes less significant at higher incident energies where the simple one step distorted wave Born approximation calculations fit the measured cross section data. The puzzling discrepancy observed in the previous analyses of the analysing power data is greatly reduced by the use of the SBM interaction.

Computer simulation of the bias factor in void swelling in metals

In order to obtain information on the bias factor in void swelling in metals, computer simulation in a model lattice has been performed for the interaction between a dislocation, or a dislocation loop and point defects in both fcc (Au) and bcc (Fe) metals. Not only a straight dislocation but also a jogged dislocation was chosen for the calculation of the interaction. In fcc metal, the calculation was made for the interaction between an extended dislocation and point defects. The effective interaction range, L, was determined for all the cases, and from these values the so-called bias factor was obtained as 55 and 19% for fcc (Au) and bcc (Fe) metals, respectively in the case of a straight dislocation. Almost no difference for this range L was seen between a dislocation without a jog and that with a jog. However, sink efficiency is considered to be higher for a jogged dislocation than a straight one. A comparatively small bias factor, about 8%, was obtained for the case of a dislocation loop and point defects in the fcc lattice.

Modelling an infinite nucleonic system. Static and dynamical properties. Study of density fluctuations

For one decade, several fields in physics as well microscopic as macroscopic benefit from the computational particle-models (astrophysics, electronics, fluids mechanics...). In particular, the nuclear matter offers an interesting challenge as many body problem, owing to the quantal nature of its components and the complexity of the in-medium interaction. Using a model derived from semi-classical Vlasov equation and the projection of the Wigner function on a Gaussian coherent states basis (pseudo-particles), static and dynamical properties of nuclear matter are studied, featuring the growing of bulk instabilities in dilute matter. Using different zero and finite range effective interactions, the effect of the model parameters upon the relation total energy - density - temperature and surface energy of the pseudo-particles fluid is pointed out. The dynamical feature is first based upon a model of the 2-body Uehling-Ulhenbeck collisionnal term. A study of the relaxation of a nucleonic system is performed. At last, the pseudo-particle model is used in order to extract time scale for the growing of density fluctuations. This process is supposed to be a possible way to clusterization during heavy nuclei collisions.

Finite range momentum and density dependent effective interaction and analysis of nuclear incompressibility.

Extraction of the nuclear matter incompressibility ${\mathit{K}}_{\mathrm{\ensuremath{\infty}}}$ from the experimental giant monopole resonance (GMR) data via liquid drop type expansion of compression modulus of finite nuclei ${\mathit{K}}_{\mathit{A}}$ is found to be fraught with uncertainties. Hence a realistic finite range effective interaction is constructed that reproduces the bulk properties of nuclear systems as well as the GMR data in the Thomas-Fermi approximation. The nuclear matter incompressibility calculated with this interaction is found to be 226 MeV. A numerical scheme is also proposed which enables us to extract the various coefficients occurring in the expansion of ${\mathit{K}}_{\mathit{A}}$ employing this effective interaction.

Influence of transport mechanism on adsorption of interacting colloid particles

The localized irreversible adsorption of interacting colloid particles on homogeneous liquid/solid interfaces was analysed. The Monte Carlo and Brownian dynamics numerical approaches were used for simulating particle adsorption kinetics as a function of the effective interaction range and the transport mechanism of the particles towards the interface. The theoretical methods were used for interpreting the experimental results obtained in direct microscope observation cells under conditions of electrostatic attraction between particles and interfaces. Monodisperse suspensions of polystyrene and melamine latex particles (in the micrometre size range) were used in these experiments, with mica sheets as the adsorbing surface. It was found that the particle transport mechanism exerts a profound effect on the structure of the adsorbed layer characterized by the pair correlation function. The experimental results were well accounted for by the Brownian dynamics simulation method. The simple random sequential adsorption model often used previously was found to be suitable for moderate flow rates. Our results showed also that the Langmuir model is not appropriate for describing the localized adsorption of particles on homogeneous surfaces.

Thermodynamic instabilities of nuclear matter at finite temperature with finite range effective interactions

A systematic study of the equation of state for symmetric nuclear matter is performed in the framework of a finite-temperature density dependent Hartree-Fock method using the Gogny finite-range effective interaction. Special attention is devoted to the density and temperature dependence of the single-particle spectrum, the effective mass and the momentum distributions. The liquid-gas phase transition and the spinodal lines are discussed, in connection with the breakup of heated nucleus into small clusters that takes place in medium energy heavy ion reactions. The level density parameter, which has been derived by a low temperature expansion of the internal energy, is also discussed. Comparisons with previous calculations using zero range effective interactions are also made.

Liquid 3He: A density functional approach with a finite range interaction

The properties of liquid helium-4 are investigated in a mean field approximation using a novel finite range effective interaction. The surface tension is found in agreement with the experimental value and the surface width equal to 5.7 X.