Skyrme Hartree-Fock Research Articles

NONRELATIVISTIC LIMIT OF POINT-COUPLING MODEL

The nonrelativistic reduction of the realistic relativistic point-coupling model is performed. The necessity to introduce the nonderivative tensor term is shown. Unfortunately a Galilean-invariant nonrelativistic Hamiltonian density could not be obtained from all terms of the point-coupling model. This fact is due to the nonrelativistic limit of the nonderivative tensor terms which are not Galilean invariant terms in its nonrelativistic forms. The result is compared with that of Skyrme–Hartree–Fock. The role of tensor and nonlinear terms and the average values of the constants in the energy functional of both models are compared and discussed. The nonrelativistic forms of a four-fermion point-coupling model using Hartree and Hartree–Fock approximations are also compared and discussed.

DEFORMATION AND WEAK DECAY OF Λ HYPERNUCLEI

We use the self-consistent mean-field theory to discuss the ground state and decay properties of Λ hypernuclei. We first discuss the deformation of Λ hypernuclei using the relativistic mean-field (RMF) approach. We show that, although most of the hypernuclei have a similar deformation parameter to the core nucleus, the shape of 28 Si is drastically altered, from oblately deformed to spherical, if a Λ particle is added to this nucleus. We then discuss the pionic weak decay of neutron-rich Λ hypernuclei using the Skyrme Hartree-Fock + BCS method. We show that, for a given isotope chain, the decay rate increases as a function of mass number, due to the strong neutron-proton interaction.

Exploration of a modified density dependence in the Skyrme functional

A variant of the basic Skyrme-Hartree-Fock (SHF) functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular momentum). We optimize the new functional with exactly the same adjustment strategy as used in an earlier study with a standard Skyrme functional. This allows direct comparisons of the performance of the new functional relative to the standard one. We discuss various observables: bulk properties of finite nuclei, nuclear matter, giant resonances, super-heavy elements, and energy systematics. The new functional performs at least as well as the standard one, but offers a wider range of applicability (e.g. for projection) and more flexibility in the regime of high densities.

An Investigation for Ground State Features of Some Structural Fusion Materials

Environmental concerns associated with fossil fuels are creating increased interest in alternative non-fossil energy sources. Nuclear fusion can be one of the most attractive sources of energy from the viewpoint of safety and minimal environmental impact. When considered in all energy systems, the requirements for performance of structural materials in a fusion reactor first wall, blanket or diverter, are arguably more demanding or difficult than for other energy system. The development of fusion materials for the safety of fusion power systems and understanding nuclear properties is important. In this paper, ground state properties for some structural fusion materials as 27Al, 51V, 52Cr, 55Mn, and 56Fe are investigated using Skyrme–Hartree–Fock method. The obtained results have been discussed and compared with the available experimental data.

Proton scattering observables from Skyrme–Hartree–Fock densities

Proton and neutron densities from Skyrme–Hartree–Fock (SHF) calculations are used to generate non-local ( g-folding) proton–nucleus optical potentials. They are formed by folding the densities with realistic nucleon–nucleon interactions. The potentials are then used to calculate differential cross sections and spin observables for proton scattering. Good agreement with data has been found, supporting those found previously when using SHF charge densities in analyses of electron scattering data. That agreement was improved by use of (shell model) occupation numbers to constrain the HF iterations. That, in part, is also the case with analyses of proton scattering data. The g-folding method is extended to exotic nuclei by including data for neutron-rich sd-shell nuclei from the inverse kinematics of scattering from hydrogen.

INCOMPRESSIBILITY OF ASYMMETRIC NUCLEAR MATTER

Using an isospin- and momentum-dependent modified Gogny (MDI) interaction, the Skyrme-Hartree-Fock (SHF) approach, and a phenomenological modified Skyrme-like (MSL) model, we have studied the incompressibility K sat (δ) of isospin asymmetric nuclear matter at its saturation density. Our results show that in the expansion of K sat (δ) in powers of isospin asymmetry δ, i.e., K sat (δ) = K0 + K sat ,2δ2 + K sat ,4δ4 + O(δ6), the magnitude of the 4th-order K sat ,4 parameter is generally small. The 2nd-order K sat ,2 parameter thus essentially characterizes the isospin dependence of the incompressibility of asymmetric nuclear matter at saturation density. Furthermore, the K sat ,2 can be expressed as [Formula: see text] in terms of the slope parameter L and the curvature parameter K sym of the symmetry energy and the third-order derivative parameter J0 of the energy of symmetric nuclear matter at saturation density, and we find the higher order J0 contribution to K sat ,2 generally cannot be neglected. Also, we have found a linear correlation between K sym and L as well as between J0/K0 and K0. Using these correlations together with the empirical constraints on K0 and L, the nuclear symmetry energy E sym (ρ0) at normal nuclear density, and the nucleon effective mass, we have obtained an estimated value of K sat ,2 = -370 ± 120 MeV for the 2nd-order parameter in the isospin asymmetry expansion of the incompressibility of asymmetric nuclear matter at its saturation density.

Effect of the Tensor Force on the Charge Exchange Spin-Dipole Excitations ofPb208

The charge exchange spin-dipole (SD) excitations of 208Pb are studied by using a fully self-consistent Skyrme Hartree-Fock plus random phase approximation formalism which includes the tensor interaction. It is found, for the first time, that the tensor correlations have a unique, multipole-dependent effect on the SD excitations; that is, they produce a softening of 1{-} states, but a hardening of 0{-} and 2{-} states. This paves the way to a clear assessment of the strength of the tensor terms. We compare our results with a recent measurement, showing that our choice of tensor terms improves the agreement with experiment. The robustness of our results is supported by the analytic form of the tensor matrix elements.

β-DECAY HALF-LIVES AROUND 78Ni AND 132Sn IN A SELF-CONSISTENT APPROACH

β-decay half-lives around 78 Ni and 132 Sn are studied with proton-neutron Quasiparticle Random Phase Approximation on the basis of Skyrme-Hartree-Fock (SHF) method. We take into account tensor force correlation in calculating the ground and excited states and find it improves the half-life of 132 Sn . However, the Q value is still underestimated. We also discuss that half-lives do not strongly depend on type of particle-particle interaction in isospin T = 0 channel.

EFFECT OF TENSOR INTERACTION ON HEAVY AND SUPERHEAVY NUCLEI

The effect of tensor interaction is discussed on the deformation and the shell structure of heavy and superheavy nuclei within the deformed Skyrme Hartree-Fock+BCS model. The importance of the tensor correlations is shown for the single particle spectra of protons in 249 Bk . The large shell gaps of superheavy nuclei are found at Z = 114 and Z = 120 for protons and N = 184 for neutrons with the spherical shape irrespective of the tensor correlations. It is also shown that Z = 114 and N = 164 shell gaps are more pronounced by the tensor correlations in the case of SLy 5+ T interaction.

Neutron-proton radii inN≈Znuclei

A simple formula is derived that describes how the Coulomb interaction affects the proton radius in nuclei. It determines the difference between neutron and proton radii in nuclei with N approx Z. It also provides an estimate for the difference between the radii of the Z core neutrons and the protons in nuclei with a large neutron excess. The results obtained from the derived formula are compared with radii calculated in a Skyrme Hartree-Fock calculation.

β-decay properties of neutron-rich Zr and Mo isotopes

Gamow-Teller strength distributions, beta-decay half-lives, and beta-delayed neutron emission are investigated in neutron-rich Zr and Mo isotopes within a deformed quasiparticle random-phase approximation. The approach is based on a self-consistent Skyrme Hartree-Fock mean field with pairing correlations and residual separable particle-hole and particle-particle forces. Comparison with recent measurements of half-lives stresses the important role that nuclear deformation plays in the description of beta-decay properties in this mass region.

Calculation of the ground state properties of even-even Sn isotopes

We investigate the ground-state properties of even-even Sn isotopes using the Skyrme-Hartree-Fock (SHF) and Skyrme-Hartree-Fock-Bogolyubov (SHFB) methods with SKM* and SLy4 force parameters. We focus on isotopes of even-even Sn because these isotopes are vital to the structural studies of unstable nuclei taking place at the electron radioactive-ion collider at RIKEN. In the present paper, we calculate the binding energies per particle, the rms nuclear charge radii, the rms nuclear proton density radii, and the rms nuclear neutron density radii, for even-even Sn isotopes, using the SHF and SHFB methods. We compare our results with experimental data and with the results of relativistic mean-field theory. Notably, we fit our calculated binding energies per particle to experimental results, using the aforementioned SHF methods with SKM* and SLy4 parameters

Neutrino propagation in the nuclear ‘pasta phase’ of neutron stars

The mean free path of the neutrino in charged and neutral current reactions is calculated for inhomogeneous nuclear matter which is expected to appear in the inner crust of neutron stars. The relevant cross section depends on Fermi and Gamow–Teller strength distributions, which are derived from the self-consistent Skyrme–Hartree–Fock and a relativistic mean-field calculations. The inhomogeneous nuclear matter, which appears at the boundary between the inner crust and outer core, is described in terms of cubic Wigner–Seitz cells. It allows for a microscopic description of the structures in the so-called pasta phase of nuclear configurations and provides a smooth transition to the limit of homogeneous matter. The influence of the pasta phase, its microscopical structure and geometrical shapes on neutrino propagation are considered.

Asymmetric nuclear matter and neutron skin in an extended relativistic mean-field model

The density dependence of the symmetry energy, instrumental in understanding the behaviour of the asymmetric nuclear matter, is investigated within the extended relativistic mean field (ERMF) model which includes the contributions from the self and mixed interaction terms for the scalar-isoscalar ($\sigma$), vector-isoscalar ($\omega$) and vector-isovector ($\rho$) mesons upto the quartic order. Each of the 26 different parameterizations of the ERMF model employed are compatible with the bulk properties of the finite nuclei. The behaviour of the symmetry energy for several parameter sets are found to be consistent with the empirical constraints on them as extracted from the analyses of the isospin diffusion data. The neutron-skin thickness in the $^{208}$Pb nucleus for these parameter sets of the ERMF model lie in the range of $\sim 0.20 - 0.24$ fm which is in harmony with the ones predicted by the Skyrme Hartree-Fock model. We also investigate the role of various mixed interaction terms which are crucial for the density dependence of the symmetry energy.

Misfits in Skyrme–Hartree–Fock

We address very briefly five critical points in the context of the Skyrme–Hartree–Fock (SHF) scheme: (1) the impossibility of considering it as an interaction, (2) a possible inconsistency of correlation corrections such as, e.g., the centre-of-mass correction, (3) problems of describing the giant dipole resonance (GDR) simultaneously in light and heavy nuclei, (4) deficiencies in the extrapolation of binding energies to super-heavy elements (SHE) and (5) a yet inappropriate trend in fission lifetimes when going to the heaviest SHE. While the first two points have a more formal bias, the other three points have practical implications and wait for solution.

NEW CALCULATION FOR SOME GROUND STATE FEATURES OF 40Ca, 48Ca32S AND 39K NUCLEI

Some ground states features of 32 S , 39 K , 40 Ca and 48 Ca nuclei are investigated using the Hartree–Fock method with the Skyrme SKM * and SLy4 forces calculated in two different code implementations. The calculated total binding energies per particle and root mean square (rms) nuclear charge radii using the Skyrme–Hartree–Fock (SHF) + BCS method are compared with relativistic mean-field (RMF) theory and experimental values. The obtained charge density distributions from these code implementations are compared with the experimental data. Pairing effects are also included in calculations for the same nuclei. Variations of the total binding energies per particle and rms nuclear charge radii were investigated as the last shell nucleons were carried to the upper shell.

Test of the single state dominance hypothesis for the two-neutrino double beta decay

The single state dominance hypothesis for the two-neutrino double-beta decay matrix elements is tested in this work for the double-beta decaying nuclei 100Mo, 116Cd, and 128Te. In addition to this, we analyze the contribution to the double-beta matrix elements from the low-lying intermediate states and from the whole set of intermediate states. We use a proton-neutron QRPA calculation based on a deformed Skyrme Hartree-Fock mean field with pairing correlations, and we compare these results with the half-lives of the double-beta emitters for which we have experimental information.

Calculation of stellar electron-capture cross sections on nuclei based on microscopic Skyrme functionals

A fully self-consistent microscopic framework for the evaluation of nuclear weak-interaction rates at finite temperature is introduced, based on Skyrme functionals. The single-nucleon basis and the corresponding thermal occupation factors of the initial nuclear state are determined in the finite-temperature Skyrme Hartree-Fock model and charge-exchange transitions to excited states are computed using the finite-temperature random-phase approximation (RPA). Effective interactions are implemented self-consistently: Both the finite-temperature single-nucleon Hartree-Fock equations and the matrix equations of RPA are based on the same Skyrme energy density functional. Using a representative set of Skyrme functionals, the model is applied in the calculation of stellar electron-capture cross sections for selected nuclei in the iron mass group and for neutron-rich Ge isotopes.

Fission of heavy Λ hypernuclei with the Skyrme–Hartree–Fock approach

Fission-related phenomena of heavy Λ hypernuclei are discussed with the constraint Skyrme–Hartree–Fock + BCS (SHF + BCS) method, in which a similar Skyrme-type interaction is employed also for the interaction between a Λ particle and a nucleon. Assuming that the Λ particle adiabatically follows the fission motion, we discuss the fission barrier height of U Λ 239 . We find that the fission barrier height increases slightly when the Λ particle occupies the lowest level. In this case, the Λ particle is always attached to the heavier fission fragment. This indicates that one may produce heavy neutron-rich Λ hypernuclei through fission, whose weak decay is helpful for the nuclear transmutation of long-lived fission products. We also discuss cases where the Λ particle occupies a higher single-particle level.

Superdeformed and hyperdeformed states inZ=122isotopes

We calculate the binding energy, root-mean-square radius, and quadrupole deformation parameter for the recent, possibly discovered superheavy element $Z=122$, using the axially deformed relativistic mean-field (RMF) and nonrelativistic Skyrme Hartree-Fock (SHF) formalisms. The calculation is extended to include various isotopes of $Z=122$ element, starting from $A=282$ to $A=320$. We predict highly deformed structures in the ground state for all the isotopes. A shape transition appears at about $A=290$ from a highly oblate to a large prolate shape, which may be considered as the superdeformed and hyperdeformed structures of the $Z=122$ nucleus in the mean-field approaches. The most stable isotope (largest binding energy per nucleon) is found to be $^{302}122$, instead of the experimentally observed $^{292}122$.