Neutrino mean free path in hot neutron matter with skyrme interactions

Collective excitations of 3He clusters

Collective excitations of3He clusters are studied by treating the cluster as a quantum liquid drop. We have used the Random-Phase Approximation sum rules technique within a Density Functional Formalism. Results forL=2 to 10 surface modes and theL=0 volume mode are presented.

The response of metal clusters toq- andL-dependent external fields

We have calculated the static polarizability and mean excitation energy of metal clusters submitted toq-andL-dependent external fields ofjL(qr)YL0(Ω) type. Use has been made of an Extended Random-Phase Approximation which includes exchange and correlation effects within a local model, and of the spherical jellium model to describe the neutralizing positive background.

Partial wave decomposition of the N3LO equation of state

By means of a partial wave decomposition, we separate their contributions to the equation of state of symmetric nuclear matter for the N3LO pseudo-potential. In particular, we show that although both the tensor and the spin-orbit terms do not contribute to the equation of state, they give a non-vanishing contribution to the separate (JLS) channels.

Magic numbers, excitation levels, and other properties of small neutral 4He clusters (Nor = 50).

The ground-state energies and the radial and pair distribution functions of neutral 4He clusters are systematically calculated by the diffusion Monte Carlo method in steps of one 4He atom from 3 to 50 atoms. In addition the chemical potential and the low-lying excitation levels of each cluster are determined with high precision. These calculations reveal that the "magic numbers" observed in experimental 4He cluster size distributions, measured for free jet gas expansions by nondestructive matter-wave diffraction, are not caused by enhanced stabilities. Instead they are explained in terms of an enhanced growth due to sharp peaks in the equilibrium concentrations in the early part of the expa…

Variational Study of3HeDroplets

We report variational calculations of energies of ${}^{3}{\mathrm{He}}_{N}$ droplets ( $20\ensuremath{\le}N\ensuremath{\le}40$), using Aziz atom-atom interactions. The trial wave function has a simple structure, combining two- and three-body correlation functions coming from a translationally invariant configuration-interaction description, superimposed to a Jastrow-type correlated wave function with backflow. We find that the smallest bound drop has $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}35$ atoms, and that for each $N$ the minimum energy states have the highest spin values.

Extended Skyrme pseudopotential deduced from infinite nuclear matter properties

We discuss the contributions to the equation of state for the NlLO Skyrme pseudopotential (l = 2,3). We show that by adding fourth- and sixth-order gradient terms, it is possible to fairly reproduce the spin/isospin decomposition of an equation of state obtained from ab initio methods. Moreover, by inspecting the partial-wave decomposition of the equation of state, we show for the first time a possible way to add explicit constraints on the sign of the tensor terms of the Skyrme interaction.

Dipole surface plasmon in K+N clusters

Abstract The technique of sum rules has been used to investigate the dipole surface plasmon for K + N clusters within a Density Functional Theory and the spherical jellium model. The role played by non-local effects is discussed comparing the results obtained from different functionals. Band-structure and core-polarization effects have been phenomenologically included in the calculation by means of an electron effective mass and a dielectric constant. Comparison with recent experimental data is presented.

Diffraction of neutral helium clusters: evidence for "magic numbers".

The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.

Shell structure in mixed3He−4Hedroplets

Due to the immiscibility of ${}^{3}\mathrm{He}$ into ${}^{4}\mathrm{He}$ at very low temperatures, mixed helium droplets consist of a core of ${}^{4}\mathrm{He}$ atoms coated by a ${}^{3}\mathrm{He}$ layer whose thickness depends on the number of atoms of each isotope. When these numbers are such that the centrifugal kinetic energy of the ${}^{3}\mathrm{He}$ atoms is small and can be considered as a perturbation to the mean-field energy, a novel shell structure arises, with magic numbers different from these of pure ${}^{3}\mathrm{He}$ droplets. If the outermost shell is not completely filled, the valence atoms align their spins up to the maximum value allowed by the Pauli principle.

Continued fraction approximation for the nuclear matter response function

A continued fraction approximation is used to calculate the Random Phase Approximation (RPA) response function of nuclear matter. The convergence of the approximation is assessed by comparing it with the numerically exact response function obtained with a typical effective finite-range interaction used in nuclear physics. It is shown that just the first order term of the expansion can give reliable results at densities up to the saturation density value.

Neutron Fermi liquids under the presence of a strong magnetic field with effective nuclear forces

Landau's Fermi liquid parameters are calculated for non-superfluid pure neutron matter in the presence of a strong magnetic field at zero temperature. The particle-hole interactions in the system, where a net magnetization may be present, are characterized by these parameters in the framework of a multipolar formalism. We use either zero- or finite-range effective nuclear forces to describe the nuclear interaction. Using the obtained Fermi liquid parameters, the contribution of a strong magnetic field on some bulk magnitudes such as isothermal compressibility and spin susceptibility is also investigated.

Radiative muon capture and the value of gP in nuclei

Abstract Radiative muon capture by nuclei is analyzed by means of sum rule techniques, providing a total photon yield calculated with RPA precision. The measured yields relative to the ordinary muon capture rate are well reproduced for the nuclei 12C, 16O and 40Ca using a value of the pseudoscalar weak coupling constant gP enhanced by only 25% with respect to its canonical value. Therefore, the large renormalization of gP claimed up to now must be reconsidered.

Mg impurity in helium droplets.

Within the diffusion Monte Carlo approach, we have determined the structure of isotopically pure and mixed helium droplets doped with one magnesium atom. For pure 4He clusters, our results confirm those of M. Mella et al. [J. Chem. Phys. 123, 054328 (2005)] that the impurity experiences a transition from a surface to a bulk location as the number of helium atoms in the droplet increases. Contrarily, for pure 3He clusters Mg resides in the bulk of the droplet due to the smaller surface tension of this isotope. Results for mixed droplets are presented. We have also obtained the absorption spectrum of Mg around the 3s3p 1P_1 <-- 3s2 1S_0 transition.

LiquidHe4andHe3at negative pressure

The critical pressures {ital P}{sub {ital c}} at which liquid {sup 4}He and {sup 3}He each become macroscopically unstable are determined from two kinds of microscopic calculations that reproduce the equation of state. The behavior of the sound velocity {ital c} around this critical pressure is analyzed, and the critical exponent in {ital c}{proportional to}({ital P}{minus}{ital P}{sub {ital c}}){sup {nu}} is found to be {nu}=1/4. A comparison with empirical analysis is also done.

Disappearance of zero sound in asymmetric nuclear matter

Abstract We investigate the thermal RPA response of asymmetric nuclear matter interacting through a Skyrme interaction. For every spin-isospin channel, the evolution of the zero sound as a function of both neutron excess and temperature is analyzed.

Two-body contributions to the effective mass in nuclear effective interactions

Starting from general expressions of well-chosen symmetric nuclear matter quantities derived for both zero- and finite-range effective theories, we derive the contributions to the effective mass. We first show that, independently of the range, the two-body contribution is enough to describe correctly the saturation mechanism but gives an effective mass value around $m^*/m \simeq 0.4$. Then, we show that the full interaction (by instance, an effective two-body density-dependent term on top of the pure two-body term) is needed to reach the accepted value $m^*/m \simeq 0.7-0.8$.

COLLECTIVE SPIN EXCITATIONS OF ALKALI-METAL CLUSTERS

The response function of alkali-metal clusters, modeled as jellium spheres, to dipole (L=1) and quadrupole (L=2) spin-dependent fields is obtained within the time-dependent local-spin-density approximation of density-functional theory. We predict the existence of low-energy spin modes of surface type, which are identified from the strength function. Their collectivity and evolution with size are discussed.

Extended Thomas - Fermi expansion from nuclear linear response

The coefficients of the successive orders of the extended Thomas - Fermi expansion of the kinetic energy density are obtained to the leading order in the density inhomogeneities. This is done by comparing the corresponding static polarizability with the exact value in two cases: a non-interacting nuclear infinite system and symmetric nuclear matter with a Skyrme interaction.

Effects of spin-orbit interaction on nuclear response and neutrino mean free path

PTH; The effects of the spin-orbit component of the particle-hole interaction on nuclear response functions and neutrino mean free path are examined. A complete treatment of the full Skyrme interaction in the case of symmetric nuclear matter and pure neutron matter is given. Numerical results for neutron matter are discussed. It is shown that the effects of the spin-orbit interaction remain small, even at momentum transfer larger than the Fermi momentum. The neutrino mean free paths are marginally affected.

Structure and energetics of mixed4He-3He drops

Using a finite-range density functional, we have investigated the energetics and structural features of mixed helium clusters. The possibility of doping the cluster with a molecule of sulfur hexafluoride is also considered. It is seen that the repulsion introduced by the impurity strongly modifies the properties of the smallest drops. Although only a qualitative comparison is possible, the gross features displayed by our calculations are in agreement with recent experimental findings. {copyright} {ital 1997} {ital The American Physical Society}

Linear response of homogeneous nuclear matter with energy density functionals

Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin-orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe-Salpeter equation for the particle-hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin-isospin strength functions are analyzed for varying conditions…

Infinite matter properties and zero-range limit of nonrelativistic finite-range interactions

We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin-orbit terms from the spin-isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin-orbit of the M3Y interaction is not compatible with lo…

Extended Skyrme Equation of State in asymmetric nuclear matter

We present a new equation of state for infinite systems (symmetric, asymmetric, and neutron matter) based on an extended Skyrme functional that has been constrained by microscopic Brueckner-Bethe-Goldstone results. The resulting equation of state reproduces the main features of microscopic calculations very accurately and is compatible with recent measurements of two times Solar-mass neutron stars. We provide all necessary analytical expressions to facilitate a quick numerical implementation of quantities of astrophysical interest.

Response functions for infinite fermion systems with velocity dependent interactions

Response functions of infinite Fermi systems are studied in the framework of the self-consistent random phase approximation (RPA). Starting from an effective interaction with velocity and density dependence, or equivalently from a local energy density functional, algebraic expressions for the RPA response function are derived. Simple formulae for the energy-weighted and polarizability sum rules are obtained. The method is illustrated by applications to nuclear matter and liquid 3 He. In nuclear matter, it is shown that existing Skyrme interactions give spin-isospin response functions close to those calculated with finite range interactions. The different renormalization of longitudinal and …

Translationally invariant treatment of pair correlations in nuclei: I. Spin and isospin dependent correlations

We study the extension of our translationally invariant treatment of few-body nuclear systems to heavier nuclei. At the same time we also introduce state-dependent correlation operators. Our techniques are tailored to those nuclei that can be dealt with in $LS$ coupling, which includes all nuclei up to the shell closure at $A=40$. We study mainly $p$-shell nuclei in this paper. A detailed comparison with other microscopic many-body approaches is made, using a variety of schematic nuclear interactions. It is shown that our methodology produces very good energies, and presumably also wave functions, for medium mass nuclei.

Multipole response of $^3$He clusters

Ground state properties of normal 3He drops have been studied using either a correlated wave function in conjunction with a realistic potential of Aziz type1) or a mean-field description based on an effective potential 2,3). In general, an overall good agreement between both methods has been found. The second one has the advantage of being rather easily applicable to both static and dynamic calculations, although being less fundamental than the first one. In this work we are concerned with the description of the collective modes of normal 3He drops within the self-consistent Random-Phase Approximation (RPA), in which the same effective interaction is used to generate both the mean-field and…

Response of asymmetric nuclear matter to isospin-flip probes

Abstract We investigate the RPA response of asymmetric nuclear matter to external fields which induce charge exchange between nucleons, both at zero and finite temperature. Closed expressions are obtained for the RPA response in each spin channel when the nucleon–nucleon interaction is of the Skyrme type. Exchange terms are fully taken into account. We consider the transferred momentum, asymmetry and temperature as the relevant parameters of our study. Special emphasis is given to the role of neutron excess in relation to the collective states at low momentum.

WITHDRAWN: Linear Response Theory with finite-range interactions

Core polarization phenomena in pion-nucleus charge-exchange reactions above the delta resonance.

Density functional study of two-dimensionalHe4clusters

Binding energies and density profiles of two-dimensional systems of liquid He-4 with different geometries are studied by means of a zero-range density functional adjusted to reproduce the line tension obtained in a previous diffusion Monte Carlo calculation (lambda_{DMC}=0.121 K/A). It is shown that this density functional provides accurate results for the binding energy of large clusters with a reasonable computational effort.

Jastrow-Correlated Configuration-Interaction Description of Light Nuclei

This work describes recent progress of the UMIST-VALENCIA collaboration on the ab initio study of ground states of light nuclei using realistic forces. The method presented here constructs trial variational wave functions by superimposing a central Jastrow correlation on a state-dependent translationally invariant linearly correlated state, with very promising results.

Translationally invariant treatment of pair correlations in nuclei - II. Tensor correlations

We study the extension of our translationally invariant treatment of few-body nuclear systems to include tensor forces and correlations. It is shown that a direct application of our method is not as successful for realistic V6 interactions as our previous results for V4 potentials suggested. We investigate the cause in detail for the case of $^4$He, and show that a combination of our method with that of Jastrow-correlated wave functions seems to be a lot more powerful, thereby suggesting that for mildly to strongly repulsive forces such a hybrid procedure may be an appropriate description.

Linear response theory and neutrino mean free path using Brussels-Montreal Skyrme functionals

The Brussels-Montreal Skyrme functionals have been successful in describing properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predic…

Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms

The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry, and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.

A diffusion Monte Carlo study of small para-Hydrogen clusters

Abstract An improved Monte Carlo diffusion model is used to calculate the ground state energies and chemical potentials of parahydrogen clusters of three to forty molecules, using two different p-H2-p-H2 interactions. The improvement is due to three-body correlations in the importance sampling, to the time step adjustment and to a better estimation of statistical errors. In contrast to path-integral Monte Carlo results, this method predicts no magic clusters other than that with thirteen molecules.

Minimal mass size of a stable He-3 cluster

The minimal number of 3He atoms required to form a bound cluster has been estimated by means of a Diffusion Monte Carlo procedure within the fixed-node approximation. Several importance sampling wave functions have been employed in order to consider different shell-model configurations. The resulting upper bound for the minimal number is 32 atoms.

Tools for incorporating a D-wave contribution in Skyrme energy density functionals

International audience; The possibility of adding a D-wave term to the standard Skyrme effective interaction has been widely considered in the past. Such a term has been shown to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential. The aim of the present article is to provide the necessary tools to incorporate this term in a fitting procedure: first, a mean-field equation written in spherical symmetry in order to describe spherical nuclei and second, the response function to detect unphysical instabilities. With these tools it will be possible to build a new fitting procedure to determine the coupling constants of the new functional.

Nuclear response functions in homogeneous matter with finite range effective interactions

The question of nuclear response functions in a homogeneous medium is examined. A general method for calculating response functions in the random phase approximation (RPA) with exchange is presented. The method is applicable for finite-range nuclear interactions. Examples are shown in the case of symmetric nuclear matter described by a Gogny interaction. It is found that the convergence of the results with respect to the multipole truncation is quite fast. Various approximation schemes such as the Landau approximation, or the Landau approximation for the exchange terms only, are discussed in comparison with the exact results.

Linear Response Theory with finite-range interactions

International audience; This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle–hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle–hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle–hole interactio…

Toward a density functional description of liquid pH2.

A finite-temperature density functional approach to describe the properties of parahydrogen in the liquid-vapor coexistence region is presented. The first proposed functional is zero-range, where the density-gradient term is adjusted so as to reproduce the surface tension of the liquid-vapor interface at low temperature. The second functional is finite-range and, while it is fitted to reproduce bulk pH2 properties only, it is shown to yield surface properties in good agreement with experiments. These functionals are used to study the surface thickness of the liquid-vapor interface, the wetting transition of parahydrogen on a planar Rb model surface, and homogeneous cavitation in bulk liquid…

Neutrino mean free path in neutron matter with Brussels-Montreal Skyrme functionals

We calculate the neutrino mean free path in cold neutron matter with some modern Brussels-Montreal functionals. The three typical functionals used in this article produce quite different results implying a possible impact on the cooling mechanism of neutron stars.

Bulk-plasmon dispersion relations in metals

En utilisant une technique de la regle de somme dans l'approximation de la phase aleatoire etendue, on examine la relation de dispersion des plasmons en volume, en introduisant les effets de la correlation et de l'echange dans le modele du jellium. Les resultats obtenus sont compares aux resultats experimentaux. On souligne le role cle que jouent les effets de la correlation et de l'echange dans l'amelioration de l'accord entre la theorie et l'experience. On calcule egalement la polarisabilite statique en fonction de 9. Les formules peuvent etre facilement modifiees pour incorporer les effets de la structure de bandes (a travers une masse effective electronique intrabande) et les effets de …

Excitation spectra of aHe3impurity onHe4clusters

The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of a single $^{3}\mathrm{He}$ atom bound to a cluster with $N$ $^{4}\mathrm{He}$ atoms, with the aim of establishing the most adequate filling ordering of single-fermion orbits to the mixed clusters with a large number of $^{3}\mathrm{He}$ atoms. The resulting ordering looks like the rotational spectrum of a diatomic molecule, being classified only by the angular momentum of the level, although vibrational-like excitations appear at higher energies for sufficiently large $N$.

Nuclear liquid-gas phase transition and supernovae evolution

It is shown that the large density fluctuations appearing at the onset of the first order nuclear liquid-gas phase transition can play an important role in the supernovae evolution. Due to these fluctuations, the neutrino gas may be trapped inside a thin layer of matter near the proto-neutron star surface. The resulting increase of pressure may induce strong particle ejection a few hundred milliseconds after the bounce of the collapse, contributing to the revival of the shock wave. The Hartree-Fock+RPA scheme, with a finite-range nucleon-nucleon effective interaction, is employed to estimate the effects of the neutrino trapping due to the strong density fluctuations, and to discuss qualitat…

Thermal effects on small para-hydrogen clusters

A brief review of different quantum Monte Carlo simulations of small (p-H2)N clusters is presented. The clusters are viewed as a set of N structureless p-H2 molecules, interacting via an isotropic pairwise potential. Properties as superfluidity, magic numbers, radial structure, excitation spectra, and abundance production of (p-H2)N clusters are discussed and, whenever possible, a comparison with 4HeN droplets is presented. All together, the simulations indicate that temperature has a paradoxical effect of the properties of (p-H2)N clusters, as they are solid-like at high T and liquid-like at low T, due to quantum delocalization at the lowest temperature. © 2010 Wiley Periodicals, Inc. Int …

Stability chart of small mixed4He−3Heclusters

A stability chart of mixed ${}^{4}\mathrm{He}$ and ${}^{3}\mathrm{He}$ clusters has been obtained by means of the diffusion Monte Carlo method, using both the Aziz HFD-B and the Tang-Toennies-Yiu atom-atom interaction. The investigated clusters contain up to eight ${}^{4}\mathrm{He}$ atoms and up to 20 ${}^{3}\mathrm{He}$ atoms. One single ${}^{4}\mathrm{He}$ binds 20 ${}^{3}\mathrm{He}$ atoms, and two ${}^{4}\mathrm{He}$ bind 1, 2, 8, and more than 14 ${}^{3}\mathrm{He}$ atoms. All clusters with three or more ${}^{4}\mathrm{He}$ atoms are bound, although the combinations ${}^{4}{\mathrm{He}}_{3}^{3}{\mathrm{He}}_{9,10,11}$ and ${}^{4}{\mathrm{He}}_{4}^{3}{\mathrm{He}}_{9}$ are metastable. …

Spurious finite-size instabilities in nuclear energy density functionals: Spin channel

Background: It has been recently shown that some Skyrme functionals can lead to nonconverging results in the calculation of some properties of atomic nuclei. A previous study has pointed out a possible link between these convergence problems and the appearance of finite-size instabilities in symmetric nuclear matter (SNM) around saturation density. Purpose: We show that the finite-size instabilities not only affect the ground-state properties of atomic nuclei, but they can also influence the calculations of vibrational excited states in finite nuclei. Method: We perform systematic fully-self consistent random phase approximation (RPA) calculations in spherical doubly magic nuclei. We employ…

Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry

International audience; We present the development of the extended Skyrme N2LO pseudopotential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behavior of the solutions at the origin. Finally, a fitting procedure for such an N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.

Cavitation in 3He-4he Liquid Mixtures

Phase transitions under equilibrium conditions are experimentally well determined and take place in the coexistence regime. However, phase transitions do not always occur under equilibrium conditions. As the new phase forms, the free energy of the system is lowered, but the original phase can be held in a metastable state close to the equilibrium transition point. Although they are internally stable, in each case there exists another configuration that has a lower thermodynamical potential. The metastable state is separated from the stable state by a thermodynamic barrier. Due to statistical fluctuations in density or concentration, this barrier can be overcome as the result of the formatio…

Translationally-Invariant Coupled-Cluster Method for Finite Systems

The translational invariant formulation of the coupled-cluster method is presented here at the complete SUB(2) level for a system of nucleons treated as bosons. The correlation amplitudes are solution of a non-linear coupled system of equations. These equations have been solved for light and medium systems, considering the central but still semi-realistic nucleon-nucleon S3 interaction.

Microscopic and translationally-invariant calculations with tensor forces and tensor correlations

In this paper we discuss an approach to the ab initio study of ground states of light nuclei using realistic forces. The method constructs trial variational wavefunctions by superimposing state-dependent translationally-invariant pair correlations on a state-independent Jastrow-correlated wavefunction, with very promising results.

Effect of three-body forces on response functions in infinite neutron matter

International audience; We study the impact of three-body forces on the response functions of cold neutron matter. These response functions are determined in the random phase approximation (RPA) from a residual interaction expressed in terms of Landau parameters. Special attention is paid to the non-central part, including all terms allowed by the relevant symmetries. Using Landau parameters derived from realistic nuclear two- and three-body forces grounded in chiral effective field theory, we find that the three-body term has a strong impact on the excited states of the system and in the static and long-wavelength limit of the response functions for which a new exact formula is established.

Neutrino propagation and spin zero sound in hot neutron matter with Skyrme interactions

We present microscopic calculations of neutrino propagation in hot neutron matter above nuclear density within the framework of the Random Phase Approximation . Calculations are performed for non- degenerate neutrinos using various Skyrme effective interactions. We find that for densities just above nuclear density, spin zero sound is present at zero temperature for all Skyrme forces considered. However it disappears rapidly with increasing temperature due to a strong Landau damping. As a result the mean-free path is given, to a good approximation, by the mean field value. Because of the renormalization of the bare mass in the mean field, the medium is more transparent as compared to the fr…

RPA susceptibility of asymmetric nuclear matter at finite temperatures with Skyrme interactions

Abstract We investigate the thermal RPA response of asymmetric nuclear matter interacting through various Skyrme interactions characterized by the value of the effective nucleon mass. Our study concentrates on the evolution of collective states according to the variations of the transferred momentum, temperature and asymmetry ratio. The differences and similarities between the roles of neutron excess and of thermal excitation are discussed. It is shown that the limit of meaningful nuclear asymmetries, namely Y close to 1/3, must be reached in order to observe sizable effects in the structure patterns, a fact that brings support to calculations of dynamical response that resort to symmetric …

A density functional for liquid3He

We present a density functional for the description of liquid3He properties at zero temperature in a mean field approximation. Its basic ingredients are a zero-range, particle- and spin-density dependent effective interaction of Skyrme type, and a long-range effective interaction of Lennard-Jones type supplemented with a weighted density approximation similar to the one used in the study of classical fluids, to phenomenologically account for short range correlations. After fixing the value of its parameters, the functional yields a good description of the equation of state and Landau parameters (spin symmetric and spin antisymmetric as well) from saturation to solidification densities. The …

Nuclear matter response function with a central plus tensor Landau interaction

We present a method to obtain response functions in the random phase approximation (RPA) based on a residual interaction described in terms of Landau parameters with central plus tensor contributions. The response functions keep the explicit momentum dependence of the RPA, in contrast with the traditional Landau approximation. Results for symmetric nuclear matter and pure neutron matter are presented using Landau parameters derived from finite-range interactions, both phenomenological and microscopic. We study the convergence of response functions as the number of Landau parameters is increased.

Thermal nucleation of cavities in liquid helium at negative pressures

We have investigated the nucleation rate at which cavities are formed in $^{4}\mathrm{He}$ and $^{3}\mathrm{He}$ at negative pressures due to thermal fluctuations. To this end, we have used a density functional that reproduces the He liquid-gas interface along the coexistence line. The inclusion of thermal effects in the calculation of the barrier against nucleation results in a sizable decrease of the absolute value of the tensile strength above 1.5 K.

Cavitation of electron bubbles in liquid parahydrogen

Within a finite-temperature density functional approach, we have investigated the structure of electron bubbles in liquid parahydrogen below the saturated vapour pressure, determining the critical pressure at which electron bubbles explode as a function of temperature. The electron-parahydrogen interaction has been modelled by a Hartree-type local potential fitted to the experimental value of the conduction band-edge for a delocalized electron in pH(2). We have found that the pressure for bubble explosion is, in absolute value, about a factor of two smaller than that of the homogeneous cavitation pressure in the liquid. Comparison with the results obtained within the capillary model shows t…

High-quality variational wave functions for small4Heclusters

We report a variational calculation of ground state energies and radii of ${}^{4}{\mathrm{He}}_{N}$ droplets $(3l~Nl~40),$ using the Aziz HFD-B (HE) atom-atom interaction. The trial wave function has a simple structure, combining two- and three-body correlation functions coming from a translationally invariant configuration-interaction description, and Jastrow-type short-range correlations. The calculated ground state energies differ by around 2% from the diffusion Monte Carlo results.

Improved Skyrme forces for Hartree-Fock seniority calculations

Abstract The relationship between Skyrme parameters and physical quantities in nuclear matter is discussed in detail and bounds for some parameters are derived. Improved density-dependent two-body Skyrme forces are obtained by a least-squares fit of all the parameters simultaneously to a large set of data, including nuclear matter, mass formula and Landau parameters, and data of finite nuclei. Special attention is paid to the pairing properties of the interaction. These forces are used to perform self-consistent calculations in spherical closed-shell nuclei and Ca open-shell isotopes, within the Hartree-Fock seniority method. Good agreement with experimental data is obtained.

Nucleation and cavitation in parahydrogen

We have used a density functional approach to investigate thermal homogeneous nucleation and cavitation in parahydrogen. The effect of electrons as seeds of heterogeneous cavitation in liquid parahydrogen is also discussed within the capillary model. (C) 2011 Elsevier B.V. All rights reserved.

Partial wave decomposition of finite-range effective tensor interaction

We perform a detailed analysis of the properties of the finite-range tensor term associated with the Gogny and M3Y effective interactions. In particular, by using a partial-wave decomposition of the equation of state of symmetric nuclear matter, we show how we can extract their tensor parameters directly from microscopic results based on bare nucleon-nucleon interactions. Furthermore, we show that the zero-range limit of both finite-range interactions has the form of the next-to-next-to-next-leading-order (N3LO) Skyrme pseudopotential, which thus constitutes a reliable approximation in the density range relevant for finite nuclei. Finally, we use Brueckner-Hartree-Fock results to fix the te…

Instabilities of infinite matter with effective Skyrme-type interactions

The stability of the equation of state predicted by Skyrme-type interactions is examined. We consider simultaneously symmetric nuclear matter and pure neutron matter. The stability is defined by the inequalities that the Landau parameters must satisfy simultaneously. A systematic study is carried out to define interaction parameter domains where the inequalities are fulfilled. It is found that there is always a critical density $\rho_{cr}$ beyond which the system becomes unstable. The results indicate in which parameter regions one can find effective forces to describe correctly finite nuclei and give at the same time a stable equation of state up to densities of 3-4 times the saturation de…

Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms II: Charge Exchange

International audience; We present the formalism of linear response theory both at zero and finite temperature in the case of asymmetric nuclear matter excited by an isospin flip probe. The particle-hole interaction is derived from a general Skyrme functional that includes spin-orbit and tensor terms. Response functions are obtained by solving a closed algebraic system of equations. Spin strength functions are analyzed for typical values of density, momentum transfer, asymmetry, and temperature. We evaluate the role of statistical errors related to the uncertainties of the coupling constants of the Skyrme functional and thus determine the confidence interval of the resulting response functi…

Does the Gogny interaction need a third Gaussian?

International audience; By considering infinite matter constraints only, we suggest in this paper that the Gogny interaction should benefit from a third Gaussian in its central part. A statistical analysis is given to select the possible ranges which are compatible with these constraints and which minimize a $\chi^2$ function.

High temperature giant dipole and isoscalar resonances

We present a systematic study of the Giant Dipole Resonance (GDR) at high temperatures (T≧4 MeV) in the framework of a semiclassical approximation that uses them1 andm3 RPA sum rules to estimate the GDR mean energy. We focus on the evolution withT of the collective nature of the GDR and of theL=0, 2, 3 and 4 isoscalar resonances. We find that the GDR remains particularly collective at highT, suggesting that it might be possible to observe it experimentally even at temperatures close to the maximum one a nucleus can sustain.

Skyrme effective pseudopotential up to next-to-next-to leading order

The explicit form of the next-to-next-to-leading order ((NLO)-L-2) of the Skyrme effective pseudopotential compatible with all required symmetries and especially with gauge invariance is presented in a Cartesian basis. It is shown in particular that for such a pseudopotential there is no spin-orbit contribution and that the D-wave term suggested in the original Skyrme formulation does not satisfy the invariance properties. The six new (NLO)-L-2 terms contribute to both the equation of state and the Landau parameters. These contributions to symmetric nuclear matter are given explicitly and discussed.

Fitting N$^{3}$LO pseudopotentials through central plus tensor Landau parameters

Landau parameters determined from phenomenological finite-range interactions are used to get an estimation of next-to-next-to-next-to-leading order ((NLO)-L-3) pseudo-potentials parameters. The parameter sets obtained in this way are shown to lead to consistent results concerning saturation properties. The uniqueness of this procedure is discussed, and an estimate of the error induced by the truncation at (NLO)-L-3 is given.

Dipole surface plasmon in large K N + clusters

The dipole surface plasmon forK N + clusters is analyzed using the RPA sum-rule technique within a semiclassical Density Functional Theory and the spherical jellium model. The theoretical frequencies are blue shifted as compared to the experimental ones. The discrepancies between theory and experiment are reduced when considering non-local energy contributions in the density functional and phenomenologically including atomic lattice effects by means of an electron effective mass and a static dielectric constant.

Elementary excitations in superfluidH3e-H4emixtures

We have studied the dynamic structure function of superfluid $^{3}\text{H}\text{e-}^{4}\text{H}\text{e}$ mixtures at zero temperature as a function of pressure and $^{3}\text{H}\text{e}$ concentration. Results obtained in the full random-phase approximation (RPA) plus density-functional theory and in a generalized Landau-Pomeranchuk approach are presented and compared with experiment. Analytic expressions for several sum rules of the dynamic structure functions have been determined, and have been used to obtain average energies of the collective excitations. In the RPA approach, the dispersion relation of the collective modes shows typical features of level repulsion between zero-soundlike …