COLLECTIVE MODES OF EXCITATION IN DEFORMED NEUTRON-RICH Mg ISOTOPES

2010 ◽  
Vol 25 (21n23) ◽  
pp. 1783-1786 ◽  
Author(s):  
KENICHI YOSHIDA
Keyword(s):  
Density Functional ◽  
Random Phase ◽  
Negative Parity ◽  
Giant Resonances ◽  
Energy Density Functional ◽  
Hartree Fock ◽  
Peak Structure ◽  
Dipole Resonance ◽  
Giant Monopole Resonance ◽  
Mg Isotopes

Giant resonances and the pygmy mode in neutron-rich Mg isotopes close to the drip line are investigated by means of the deformed Hartree-Fock-Bogoliubov and quasiparticle random-phase approximations using a Skyrme energy-density functional. It is found that the giant monopole resonance has a two-peak structure due to the deformation. The lower-energy resonance is generated associated with the mixing with the Kπ = 0+ component of the giant quadrupole resonance. We find for the negative-parity excitations that the pygmy dipole resonance appeared just above the threshold has a significant mixing effect among the isovector dipole, isoscalar octupole and compression dipole excitations.

scholarly journals Nuclear structure and the nucleon effective mass: explorations with the versatile KIDS functional

2019 ◽  
Vol 26 ◽  
pp. 104
Author(s):  
P. Papakonstantinou ◽  
H. Gil
Keyword(s):  
Equation Of State ◽  
Effective Mass ◽  
Density Functional ◽  
Compression Modulus ◽  
Dipole Polarizability ◽  
Heavy Nuclei ◽  
Giant Resonances ◽  
Energy Density Functional ◽  
Atomic Nuclei ◽  
Giant Monopole Resonance

The connection from the structure and dynamics of atomic nuclei (finite nuclear system) to the nuclear equation of state (thermodynamic limit) is primarily made through nuclear energy-density functional (EDF) theory. Failure to describe both entities simultaneously within existing EDF frameworks means that we have either seriously misjudged the scope of EDF or not fully taken advantage of it. Enter the versatile KIDS Ansatz, which is based on controlled, order-by-order extensions of the nuclear EDF with respect to the Fermi momentum and allows a direct mapping from a given, immutable equation of state to a convenient Skyrme pseudopotential for applications in finite nuclei. A recent proof-of-principle study of nuclear ground-states revealed the subversive role of the effective mass. Here we summarize the formalism and previous results and present further explorations related to giant resonances. As examples we consider the electric dipole polarizability of 68Ni and the giant monopole resonance (GMR) of heavy nuclei, particularly the fluffiness of 120Sn. We find that the choice of the effective mass parameters and that of the compression modulus affect the centroid energy of the GMR to comparable degrees.

scholarly journals Investigation of the nuclear structure of 84-108Mo isotopes using Skyrme-Hartree-Fock method

2019 ◽  
Vol 13 (26) ◽  
pp. 1-11
Author(s):  
Ali A. Alzubadi
Keyword(s):  
Density Functional ◽  
Good Description ◽  
Mean Field ◽  
Nucleon Nucleon ◽  
Effective Density ◽  
Skin Thickness ◽  
Neutron Skin ◽  
Energy Density Functional ◽  
Charge Densities ◽  
Hartree Fock

Over the last few decades the mean field approach using selfconsistentHaretree-Fock (HF) calculations with Skyrme effectiveinteractions have been found very satisfactory in reproducingnuclear properties for both stable and unstable nuclei. They arebased on effective energy-density functional, often formulated interms of effective density-dependent nucleon–nucleon interactions.In the present research, the SkM, SkM*, SI, SIII, SIV, T3, SLy4,Skxs15, Skxs20 and Skxs25 Skyrme parameterizations have beenused within HF method to investigate some static and dynamicnuclear ground state proprieties of 84-108Mo isotopes. In particular,the binding energy, proton, neutron, mass and charge densities andcorresponding root mean square radius, neutron skin thickness andcharge form factor are calculated by using this method with theSkyrme parameterizations mentioned above. The calculated resultsare compared with the available experimental data. Calculationsshow that the Skyrme–Hartree–Fock (SHF) theory with aboveforce parameters provides a good description on Mo isotopes.

Microscopic description of the fusion excitation function of 32,36S+90,94,96Zr

2020 ◽  
Vol 29 (07) ◽  
pp. 2050046
Author(s):  
M. Rashdan ◽  
T. A. Abdel-Karim
Keyword(s):  
Excitation Function ◽  
Excited States ◽  
Density Functional ◽  
Neutron Density ◽  
Energy Density Functional ◽  
Hartree Fock ◽  
Density Distributions ◽  
Text Interaction ◽  
Good Agreement

The fusion excitation function for the systems [Formula: see text]S+[Formula: see text]Zr is investigated using a microscopic internuclear potential derived from Skyrme energy density functional. The inputs in this approach are the proton and neutron density distributions of the interacting nuclei, which are derived from Skyrme–Hartree–Fock calculations. The SkM[Formula: see text] interaction is used in the calculation of the nuclear densities as well as the internuclear potential. The coupling to low lying inelastic excited states of target and projectile is considered. The role of the neutron transfer is discussed, where it is considered through the CCFULL model calculation. A good agreement with the experimental data is obtained without adjustable parameters.

scholarly journals Microscopic optical potentials within the weak density dependent nucleon-nucleon effective interactions

2017 ◽  
Vol 126 (1C) ◽  
pp. 17
Author(s):  
Nguyễn Như Lê ◽  
Trần Viết Nhân Hào
Keyword(s):  
Density Functional ◽  
Collective Motion ◽  
Nucleon Nucleon ◽  
Energy Density Functional ◽  
Effective Interactions ◽  
Density Dependent ◽  
Hartree Fock ◽  
Optical Potentials ◽  
Weak Density ◽  
Nucleon Nucleon Interaction

<p class="tomtat1">The microscopic optical potentials have been investigated in the framework of the nuclear structure approach based on the energy-density functional approaches. The effective phenomenological nucleon-nucleon interaction SLy5 is consistently used to obtain the Hartree-Fock single particle states, the collective motion at small amplitudes of the target, and the coupling between the particle and phonons. The role of the weak density dependent interaction is showed. </p>

Non-empirical derivation of the parameter in the B88 exchange functional

2009 ◽  
Vol 87 (10) ◽  
pp. 1485-1491 ◽  
Author(s):  
Peter Elliott ◽  
Kieron Burke
Keyword(s):  
Density Functional ◽  
Noble Gas ◽  
Generalized Gradient ◽  
Energy Density Functional ◽  
Empirical Parameter ◽  
Specific Approach ◽  
Hartree Fock ◽  
Large Numbers ◽  
Local Approximations ◽  
Crucial Part

The B88 exchange energy density functional (created by Becke in 1988) is a crucial part of the most popular density functional in use today, B3LYP. B88 contains one empirical parameter which was fitted to Hartree–Fock exchange energies for the noble gas atoms. We show how local approximations to exchange become relatively exact under a very specific approach to the limit of large numbers, but the usual gradient expansion does not. The leading corrections can be captured by generalized gradient approximations, producing a non-empirical derivation of the parameter in B88.

PYGMY DIPOLE RESONANCE AND TWO NEUTRON SEPARATION ENERGIES IN SOFT AND HEAVY NUCLEI

2010 ◽  
Vol 19 (07) ◽  
pp. 1371-1381
Author(s):  
KUTSAL BOZKURT
Keyword(s):  
Mean Field Theory ◽  
Random Phase ◽  
Mean Field ◽  
Nucleon Nucleon ◽  
Tensor Interaction ◽  
Binding Energies ◽  
Heavy Nuclei ◽  
Hartree Fock ◽  
Dipole Resonance ◽  
Pygmy Dipole Resonance

We investigate isovector pygmy dipole resonance (IVPDR) for the case of neutron-rich soft nuclei 68 Ni , and heavy nuclei such as 112 Sn and 208 Pb using effective nucleon–nucleon Skyrme interaction. We use the mean-field theory and employ the random phase approximation (RPA). We observe that our results for the pygmy dipole resonance (PDR) for neutron-rich nuclei are in reasonable agreement with their experimental results. We also predict PDR for very neutron-rich heavy nuclei. We then study two-neutron separation Skyrme energies (S2n) using the Hartree–Fock + BCS with and without tensor interaction in the same nucleus and compare our results with their experimental values. We see that the total binding energies of nuclei 208 Pb are not extremely sensitive to the tensor interaction.

On the shape of spherically averaged Fermi-hole correlation functions in density functional theory. 1. Atomic systems

1989 ◽  
Vol 67 (3) ◽  
pp. 460-472 ◽  
Author(s):  
Vincenzo Tschinke ◽  
Tom Ziegler
Keyword(s):  
Density Functional Theory ◽  
Correlation Function ◽  
Energy Density ◽  
Density Functional ◽  
Exchange Energy ◽  
Energy Density Functional ◽  
Functional Theory ◽  
Atomic Systems ◽  
Hartree Fock ◽  
Fermi Hole

We have compared, for atomic systems, the spherically averaged Fermi-hole correlation function [Formula: see text] in the Hartree–Fock theory with the corresponding function [Formula: see text] employed in local density functional theory. It is shown that, in contrast to [Formula: see text], the function [Formula: see text] behaves qualitatively incorrectly at positions r1 of the reference electron far from the nucleus. Furthermore, we have shown that the qualitatively incorrect behaviour of [Formula: see text] can be remedied by an approximate expansion of [Formula: see text] in powers of s, where s is the inter-electronic distance. However, such an expansion must be conducted in two regions due to the discontinuity of [Formula: see text] as a function of s at the atomic nucleus. Based on the two-region expansion of [Formula: see text] we have developed an alternative approximate density functional expansion [Formula: see text] for the spherically averaged Fermi-hole correlation function. The corresponding exchange energy density functional yields values for the exchange energies of atoms in good agreement with Hartree–Fock results. Keywords: atomic exchange energy, density functional theory, Fermi hole.

scholarly journals Unified Equation of State for Neutron Stars Based on the Gogny Interaction

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1613
Author(s):  
Xavier Viñas ◽  
Claudia Gonzalez-Boquera ◽  
Mario Centelles ◽  
Chiranjib Mondal ◽  
Luis M. Robledo
Keyword(s):  
Equation Of State ◽  
Neutron Stars ◽  
Density Functional ◽  
Mean Field ◽  
Nuclear Interaction ◽  
Energy Density Functional ◽  
Hartree Fock ◽  
The Moment ◽  
Finite Nuclei ◽  
Pairing Field

The effective Gogny interactions of the D1 family were established by D. Gogny more than forty years ago with the aim to describe simultaneously the mean field and the pairing field corresponding to the nuclear interaction. The most popular Gogny parametrizations, namely D1S, D1N and D1M, describe accurately the ground-state properties of spherical and deformed finite nuclei all across the mass table obtained with Hartree–Fock–Bogoliubov (HFB) calculations. However, these forces produce a rather soft equation of state (EoS) in neutron matter, which leads to predict maximum masses of neutron stars well below the observed value of two solar masses. To remove this limitation, we built new Gogny parametrizations by modifying the density dependence of the symmetry energy predicted by the force in such a way that they can be applied to the neutron star domain and can also reproduce the properties of finite nuclei as good as their predecessors. These new parametrizations allow us to obtain stiffer EoS’s based on the Gogny interactions, which predict maximum masses of neutron stars around two solar masses. Moreover, other global properties of the star, such as the moment of inertia and the tidal deformability, are in harmony with those obtained with other well tested EoSs based on the SLy4 Skyrme force or the Barcelona–Catania–Paris–Madrid (BCPM) energy density functional. Properties of the core-crust transition predicted by these Gogny EoSs are also analyzed. Using these new Gogny forces, the EoS in the inner crust is obtained with the Wigner–Seitz approximation in the Variational Wigner–Kirkwood approach along with the Strutinsky integral method, which allows one to estimate in a perturbative way the proton shell and pairing corrections. For the outer crust, the EoS is determined basically by the nuclear masses, which are taken from the experiments, wherever they are available, or by HFB calculations performed with these new forces if the experimental masses are not known.

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