One-particle exchange in the double folded potential in a semiclassical approximation

The one-particle exchange in the double folded model is analyzed. To this aim the Extended Thomas-Fermi approach to the one-body density matrix is used. The nucleon- nucleon force with Yukawa, Gauss and Coulomb-type form factors are considered. The energy dependence of the exchange part of the double folded potential is investigated and a comparison of the present approach with former ones is carried out.Comment: 22 pages, LateX, and 6 PostScript figures, (submitted to J.of Phys.G

Nuclear incompressibility in the quasilocal density functional theory

We explore the ability of the recently established quasilocal density functional theory for describing the isoscalar giant monopole resonance. Within this theory we use the scaling approach and perform constrained calculations for obtaining the cubic and inverse energy weighted moments (sum rules) of the RPA strength. The meaning of the sum rule approach in this case is discussed. Numerical calculations are carried out using Gogny forces and an excellent agreement is found with HF + RPA results previously reported in literature. The nuclear matter compression modulus predicted in our model lies in the range 210-230 MeV which agrees with earlier findings. The information provided by the sum rule approach in the case of nuclei near the neutron drip line is also discussed.Comment: 10 pages, LaTe

Extended Thomas-Fermi approximation to the one-body density matrix

The one-body density matrix is derived within the Extended Thomas-Fermi approximation. This has been done starting from the Wigner-Kirkwood distribution function for a non-local single-particle potential. The links between this new approach to the density matrix with former ones available in the literature are widely discussed. The semiclassical Hartree-Fock energy at Extended Thomas-Fermi level is also obtained in the case of a non-local one-body Hamiltonian. Numerical applications are performed using the Gogny and Brink-Boeker effective interactions. The semiclassical binding energies and root mean square radii are compared with the fully quantal ones and with those obtained using the Strutinsky averaged method.Comment: 27 pages, LateX, and 2 PostScript figures, (submitted to Nucl. Phys. A

Quasi-Local Density Functional Theory and its Application within Extended Thomas-Fermi Approximation

A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the Extended Thomas-Fermi approximation. Within the framework of this approach the ground-state properties of the doubly magic nuclei are considered. The calculations have been performed using the finite-range Gogny D1S force. The results are compared with the exact Hartree-Fock calculations

Density Functional Theory for a Confined Fermi System with Short-Range Interaction

Effective field theory (EFT) methods are applied to density functional theory (DFT) as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Representative results showing the convergence of Kohn-Sham calculations at zero temperature in the local density approximation (LDA) are compared to Thomas-Fermi calculations and to power-counting estimates.Comment: 36 pages, 20 figures, RevTeX

Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam {\it et al.} to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N$^2$LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a cutoff-dependent coupling {\it constant} arising from zero-range contact interactions and a cutoff-independent coupling {\it function} of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A Mathematica notebook containing the novel density-dependent couplings is provided.Comment: 28 pages, 12 figures. Mathematica notebook provided with submission

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative hbar^2 correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of hbar^4 order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g. 208Pb turns out to be only -6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.Comment: 37 pages, 14 figures, revtex

Semiclassical evaluation of average nuclear one and two body matrix elements

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elements it is shown how the Thomas-Fermi approach can be projected on good parity and also on good angular momentum. For the two-body case the pairing matrix elements are considered explicitly.Comment: 15 pages, REVTeX, 6 ps figures; changed conten