Skyrme Effective Forces Research Articles

About magnetic properties of superfluid neutron matter with spin-triplet anisotropic p-wave pairing in superstrong magnetic fields and at supranuclear densities

Magnetic properties of a dense superfluid neutron matter (relevant to the physics in cores of magnetars, namely the strongly magnetized neutron stars) at supranuclear densities n > n0 (where n0 = 0.17 fm–3 is the saturation nuclear density) with generalized Skyrme effective forces (with three density-dependent terms) and with spin-triplet anisotropic p-wave pairing (similar to 3He-A in magnetic fields, i.e. with spin S = 1 and orbital moment L = 1 of anisotropic Cooper pairs of neutrons) in the presence of a superstrong magnetic field (exceeding the 1017 G) are studied within the framework of the non-relativistic generalized Fermi-liquid theory at zero temperature. The upper limit for the density range of a neutron matter is restricted by the magnitude 3n0 in order to avoid the account of relativistic corrections growing with density. The approximate general formula (valid for any parameterization of the Skyrme forces) is derived here analytically for the magnetic susceptibility (which contains additional correction depending nonlinearly on superstrong magnetic field H and on the density n) of a superfluid neutron matter in the limit of zero temperature. The obtained general formula for magnetic susceptibility is specified for the generalized BSk21 parameterization of the Skyrme forces and figures for corresponding values are plotted on the interval 1.5n0 ≤ n ≤ 3n0 and for superstrong magnetic fields 2⋅1017 G ≤ H ≤ 2⋅1018 G. It is established that the high-density ferromagnetic instability is removed in neutron matter with the generalized Skyrme forces (in particular, with the generalized BSk21 parameterization) not only in normal, but also in superfluid neutron matter with spin-triplet anisotropic p-wave pairing at supranuclear densities and in superstrong magnetic fields.

Potential energy surface and formation of superheavy nuclei with the Skyrme energy-density functional

With the Skyrme energy-density functional theory, the nucleus–nucleus potential is calculated and the potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM*, SkP, SIII, Ska, and SLy4, which correspond to the different equations of state for the isospin symmetry nuclear matter. It is found that the nucleus–nucleus potential is associated with the collision orientation and Skyrme forces. A more repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter, which hinders the formation of superheavy nuclei. The available data in the fusion-evaporation reaction of 48Ca+238U are nicely reproduced with the SkM* parameter by implementing the potential into the dinuclear system model.

A microscopic approach based on particle-vibration coupling: application to charge-exchange transitions and multiplets in odd nuclei

In this contribution, we shall describe a formalism that goes beyond the simple time-dependent mean field and is based on particle-vibration coupling (PVC). Such a formalism has been developed with the idea of being self-consistent. It makes use of Skyrme effective forces, and has been used for several applications. We will focus on charge-exchange transitions, namely we will show that our model describes well both the Gamow-Teller giant resonance width, and the low-lying transitions associated with β -decay. In this latter case, including PVC produces a significant improvement of the half-lives obtained at mean-field level, and leads to a good agreement with experimental data. We will end by discussing particle-phonon multiplets in odd nuclei.

Analytical representations of unified equations of state for neutron-star matter

Context. A unified equation of state (EoS) should describe the crust and the core of a neutron star using the same physical model. The Brussels-Montreal group has recently derived a family of such EoSs based on the nuclear energy-density functional theory with generalized Skyrme effective forces, fitted to the available mass data. At the same time, these forces were constrained to reproduce microscopic calculations of homogeneous neutron matter based on realistic two- and three-nucleon forces. Aims. We represent basic physical characteristics of the latest Brussels-Montreal EoS models by analytical expressions to facilitate their inclusion in astrophysical simulations. Methods. We consider three EoS models, which significantly differ by stiffness: BSk19, BSk20, and BSk21. For each of them we constructed two versions of the EoS parametrization. In the first version, pressure P and gravitational mass density \rho are given as functions of the baryon number density n_b. In the second version, P, \rho, and n_b are given as functions of pseudo-enthalpy, which is useful for two-dimensional calculations of stationary rotating configurations of neutron stars. In addition to the EoS, we derived analytical expressions for several related quantities that are required in neutron-star simulations: number fractions of electrons and muons in the stellar core, nucleon numbers per nucleus in the inner crust, and equivalent radii and shape parameters of the nuclei in the inner crust. Results. We obtain analytical representations for the basic characteristics of the models of cold dense matter, which are most important for studies of neutron stars. We demonstrate the usability of our results by applying them to calculations of neutron-star mass-radius relations, maximum and minimum masses, thresholds of direct Urca processes, and the electron conductivity in the neutron-star crust.

Magnetic Susceptibilities of Dense Superfluid Neutron Matter with Generalized Skyrme Forces and Spin-Triplet Pairing at Zero Temperature

Magnetic properties of a dense superfluid neutron matter (relevant to the physics of neutron star cores) at subnuclear and supranuclear densities (in the range 0.5 < n=n0 < 3.0, where n0 = 0.17 (fm^-3) is the saturation nuclear density) with the so-called generalized Skyrme effective forces BSk18, BSk19, BSk20, BSk21 (containing additional unconventional density-dependent terms) and with spin-triplet p-wave pairing (with spin S = 1 and orbital moment L = 1) in the presence of a strong magnetic field are studied within the framework of the non-relativistic generalized Fermi-liquid theory at zero temperature. The upper limit for the density range of a neutron matter is restricted by the magnitude 3n0 in order to avoid the account of relativistic corrections growing with density. The general formula obtained in [1] (valid for any parametrization of the Skyrme forces) for the magnetic susceptibility of a superfluid neutron matter at zero temperature is specified here for the new BSk18-BSk21 parametrizations of the Skyrme interaction. As is known, all previous conventional Skyrme interactions predict spin instabilities in a normal (nonsuperfluid) neutron matter beyond the saturation nuclear density. It is obtained in the present work that, for the model of superfluid neutron matter with new generalized BSk18-BSk21 parametrizations, such phase transition to the ferromagnetic state occurs neither at subnuclear nor at supranuclear densities. Thus, the high-density ferromagnetic instability is removed in the neutron matter with new generalized Skyrme forces BSk18-BSk21 not only in normal, but also in superfluid states with anisotropic spin-triplet pairing.

Describing of the properties of quadrupole states in a 94Mo nucleus with skyrme interaction

The influence of coupling between simple and complex configurations on the probabilities of E2 and M1 transitions between vibrational quadrupole states is investigated. The finite rank separable approximation for the Skyrme effective forces is used. Properties of the low-energy spectrum for quadrupole excitations in 94Mo nucleus are considered.

Anisotropic pressure in dense neutron matter under the presence of a strong magnetic field

Dense neutron matter with recently developed BSk19 and BSk21 Skyrme effective forces is considered in magnetic fields up to 1020 G at zero temperature. The breaking of the rotational symmetry by the magnetic field leads to the differentiation between the pressures along and perpendicular to the field direction which becomes significant in the fields H>Hth∼1018 G. The longitudinal pressure vanishes in the critical field 1018<Hc≲1019 G, resulting in the longitudinal instability of neutron matter. For the Skyrme force fitted to the stiffer underlying equation of state (BSk21 vs. BSk19) the threshold Hth and critical Hc magnetic fields become larger. The longitudinal and transverse pressures as well as the anisotropic equation of state of neutron matter are determined under the conditions relevant for the cores of magnetars.

The Gamma Decay of the Pygmy Resonance and the Neutron Skin of Nuclei

The Coulomb excitation of the neutron rich 68Ni was measured using it as as secondary radioactive beam at 600 MeV/nucleon impinging on a 197Au target. The dipole strength in the region at around the nucleon binding energy was extracted from the gamma decay measurement. A sizable fraction of "pygmy" dipole strength, energetically located below the giant dipole resonance, is observed in this nucleus. The experimental data is discussed in connection with predictions obtained using different Random Phase Approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data for both 68Ni and 132Sn has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.

Constraints on the symmetry energy and neutron skins from pygmy resonances inNi68andSn132

Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the Pygmy Dipole Resonance (PDR) in 68Ni and 132Sn have been investigated by using different Random Phase Approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.

COMPARISON OF SELF-CONSISTENT SKYRME AND GOGNY CALCULATIONS FOR LIGHT Hg ISOTOPES

The ground-state properties of neutron-deficient Hg isotopes have been investigated by the constrained self-consistent Hartree-Fock-Bogoliubov approach with the Skyrme and Gogny effective forces. In the case of the Skyrme interaction we have also applied the Hartree-Fock+BCS model with the state-dependent δ-pairing interaction. Potential energy surfaces and pairing properties have been compared for the both types of forces.

What can we learn from recent non-relativistic mean field calculations ?

In the present contribution, we discuss the relevance of fully self-consistent HF plus RPA (or HF-BCS plus QRPA) calculations based on Skyrme effective forces, and their impact on our present knowledge of basic properties of the nuclear equation of state, like the incompressibilty and the symmetry energy. Finally, we address the problem whether correlations beyond mean field can alter the picture obtained at the (Q)RPA level. Throghout the paper, the comparison with the results obtained using Gogny forces, or RMF Lagrangians, will be emphasized.

Spin-ordered phase transitions in isospin asymmetric nuclear matter

Spin polarized states in nuclear matter with Skyrme effective forces are studied on the base of a Fermi liquid theory for a wide range of isospin asymmetries and densities. There are a few possible scenarios of spin ordered phase transitions: (a) nuclear matter with SLy4 interaction undergoes at some critical density a phase transition to a spin polarized state with the oppositely directed spins of neutrons and protons; (b) for SkI5 interaction, a spin polarized state with the like-directed neutron and proton spins is formed; (c) nuclear matter with SkI3 interaction under increasing density, at first, undergoes a phase transition to the state with the opposite directions of neutron and proton spins, which goes over at larger density to the state with the same direction of nucleon spins. Spin polarized states at strong isospin asymmetry are accompanied by the long tails in the density profiles of the neutron spin polarization parameter near the critical density, if the energy gain of the transition from the nonpolarized state to a polarized one is the decreasing function of isospin asymmetry (SLy4 force). If the energy gain is increased with isospin asymmetry, there are no long tails in the density distribution of the neutron spin polarization parameter (SkI3, SkI5 forces).

Exploring the extended density-dependent Skyrme effective forces for normal and isospin-rich nuclei to neutron stars

We parameterize the recently proposed generalized Skyrme effective force (GSEF) containing extended density dependence. The parameters of the GSEF are determined by the fit to several properties of the normal and isospin-rich nuclei. We also include in our fit a realistic equation of state for the pure neutron matter up to high densities so that the resulting Skyrme parameters can be suitably used to model the neutron star with the "canonical" mass ($\sim 1.4 M_\odot$). For the appropriate comparison we generate a parameter set for the standard Skyrme effective force (SSEF) using exactly the same set of the data as employed to determine the parameters of the GSEF. We find that the GSEF yields larger values for the neutron skin thickness which are closer to the recent predictions based on the isospin diffusion data. The Skyrme parameters so obtained are employed to compute the strength function for the isoscalar giant monopole, dipole and quadrupole resonances. It is found that in the case of GSEF, due to the the larger value of the nucleon effective mass the values of centroid energies for the isoscalar giant resonances are in better agreement with the corresponding experimental data in comparison to those obtained using the SSEF. We also present results for some of the key properties associated with the neutron star of "canonical" mass and for the one with the maximum mass.

Half-lives of rp-process waiting point nuclei

We give results of microscopic calculations for the half-lives of various proton-rich nuclei in the mass region A = 60-90, which are involved in the astrophysical rp-process, and which are needed as input parameters of numerical simulations in Nuclear Astrophysics. The microscopic formalism consists of a deformed QRPA approach that involves a self-consistent quasiparticle deformed Skyrme Hartree-Fock basis and residual spin-isospin separable forces in both the particle-hole and particle-particle channels. The strength of the particle-hole residual interaction is chosen to be consistent with the Skyrme effective force and mean-field basis, while that of the particle-particle is globally fixed to κ = 0.07 MeV after a judicious choice from comparison to experimental half-lives. We study and discuss the sensitivity of the half-lives to deformation and residual interactions.

Quark Structure and Nuclear Effective Forces

We formulate the quark meson coupling model as a many-body effective Hamiltonian. This leads naturally to the appearance of many-body forces. We investigate the zero range limit of the model and compare its Hartree-Fock Hamiltonian to that corresponding to the Skyrme effective force. By fixing the three parameters of the model to reproduce the binding and symmetry energy of nuclear matter, we find that it allows a very satisfactory interpretation of the Skyrme force.

SKYRME FORCES WITH EXTENDED DENSITY DEPENDENCE

A generalized parameterization of the Skyrme effective force is discussed. Preliminary results are presented for infinite symmetric and asymmetric nuclear matter. In particular, it is shown that an enlarged density dependence based on two terms allows to choose independently the incompressibility and the isoscalar effective mass.

Superfluid states with moving condensate in nuclear matter

Superfluid states of symmetric nuclear matter with finite total momentum of Cooper pairs (nuclear LOFF phase) are studied with the use of Fermi-liquid theory in the model with Skyrme effective forces. It is considered the case of four-fold splitting of the excitation spectrum due to finite superfluid momentum and coupling of T=0 and T=1 pairing channels. It has been shown that at zero temperature the energy gap in triplet-singlet (TS) pairing channel (in spin and isospin spaces) for the SkM$^*$ force demonstrates double-valued behavior as a function of superfluid momentum. As a consequence, the phase transition at the critical superfluid momentum from the LOFF phase to the normal state will be of a first order. Behavior of the energy gap as a function of density for TS pairing channel under increase of superfluid momentum changes from one-valued to universal two-valued. It is shown that two-gap solutions, describing superposition of states with singlet-triplet (ST) and TS pairing of nucleons appear as a result of branching from one-gap ST solution. Comparison of the free energies shows that the state with TS pairing of nucleons is thermodynamically most preferable.

Multi-gap superfluidity in nuclear matter

It is shown that under lowering density or temperature a nucleon Fermi superfluid can undergo a phase transition to a new superfluid state corresponding to superposition of states with singlet-triplet (ST) and triplet-singlet (TS) pairing of nucleons (in spin and isospin spaces). Such states arise as a result of branching from one-gap solution of the self-consistent equations, describing ST pairing of nucleons. The density and temperature dependence of the order parameters for new two-gap solutions is determined in the model with Skyrme effective forces.

Masses and radii of spherical nuclei calculated in various microscopic approaches

The quality of the description of nuclear masses and charge radii, calculated in various microscopic approaches, is studied. The Hartree-Fock-Bogoliubov (HFB), extended Thomas-Fermi model with Strutinski integral (ETFSI), relativistic mean field (RMF), and macroscopic-microscopic (MM) approaches are considered. In the HFB approximation, both finite-range (Gogny) and zero-range (Skyrme) effective forces are used. Spherical even-even nuclei (116 nuclides), from light $(A=16)$ to heavy $(A=220)$ ones, with known experimental mass are chosen for the study. A general result is that the best description of masses of considered nuclei is obtained in the MM and ETFSI approaches, while the best charge radii are obtained within the RMF and ETFSI approximations. The behavior of nuclear masses and radii, when one moves far off the \ensuremath{\beta}-stability line, is also studied.

A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities

In a first paper Skyrme effective forces were revisited in order to improve their isospin properties away from the β stability line. In this paper, these forces are specifically adjusted to reproduce finite nuclei properties. Spin-orbit terms and center of mass correlations are analyzed. New Skyrme parametrizations are proposed and some of their spectroscopic properties are presented, e.g. S 2 n , S 2 p and r.m.s. radii for different isotopic and isotonic series.