Microscopic determination of the nuclear incompressibility within the non-relativistic framework

The nuclear incompressibility $K_\infty$ is deduced from measurements of the Isoscalar Giant Monopole Resonance (ISGMR) in medium-heavy nuclei, and the resulting value turns out to be model dependent. Since the considered nuclei have neutron excess, it has been suggested that the model dependence is due to the different behaviour of the symmetry energy in different models. To clarify this issue, we make a systematic and careful analysis based on new Skyrme forces which span a wide range of values for $K_\infty$, for the value of the symmetry energy at saturation and for its density dependence. By calculating, in a fully self-consistent fashion, the ISGMR centroid energy in $^{208}$Pb we reach, for the first time within the non-relativistic framework, three important conclusions: (i) the monopole energy, and consequently the deduced value of $K_\infty$, depend on a well defined parameter related to the shape of the symmetry energy curve and called $K_{sym}$; (ii) Skyrme forces of the type of SLy4 predict $K_\infty$ around 230 MeV, in agreement with the Gogny force (previous estimates using Skyrme interactions having been plagued by lack of full self-consistency); (iii) it is possible to build forces which predict $K_\infty$ around 250 MeV, although part of this increase is due to our poor knowledge of the density dependence and effective mass.Comment: 19 pages, 8 figures. Submitted to PR

Monopole giant resonances and nuclear compressibility in relativistic mean field theory

Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field (RMF) theory. Excitation energies and the structure of eigenmodes are determined from a Fourier analysis of dynamical monopole moments and densities. The generator coordinate method, with generating functions that are solutions of constrained RMF calculations, is also used to calculate excitation energies and transition densities of giant monopole states. Calculations are performed with effective interactions which differ in their prediction of the nuclear matter compression modulus K_nm. Both time-dependent and constrained RMF results indicate that empirical GMR energies are best reproduced by an effective force with K_nm \approx 270 MeV.Comment: 30 pages of LaTeX, 18 PS-figure

Generator Coordinate Calculations for the Breathing-Mode Giant Monopole Resonance in Relativistic Mean Field Theory

The breathing-mode giant monopole resonance (GMR) is studied within the framework of the relativistic mean-field theory using the Generator Coordinate Method (GCM). The constrained incompressibility and the excitation energy of isoscalar giant monopole states are obtained for finite nuclei with various sets of Lagrangian parameters. A comparison is made with the results of nonrelativistic constrained Skyrme Hartree-Fock calculations and with those from Skyrme RPA calculations. In the RMF theory the GCM calculations give a transition density for the breathing mode, which resembles much that obtained from the Skyrme HF+RPA approach and also that from the scaling mode of the GMR. From the systematic study of the breathing-mode as a function of the incompressibility in GCM, it is shown that the GCM succeeds in describing the GMR energies in nuclei and that the empirical breathing-mode energies of heavy nuclei can be reproduced by forces with an incompressibility close to $K = 300$ MeV in the RMF theory.Comment: 27 pages (Revtex) and 5 figures (available upon request), Preprint MPA-793 (March 1994

Far-infrared edge modes in quantum dots

We have investigated edge modes of different multipolarity sustained by quantum dots submitted to external magnetic fields. We present a microscopic description based on a variational solution of the equation of motion for any axially symmetric confining potential and multipole mode. Numerical results for dots with different number of electrons whose ground-state is described within a local Current Density Functional Theory are discussed. Two sum rules, which are exact within this theory, are derived. In the limit of a large neutral dot at B=0, we have shown that the classical hydrodynamic dispersion law for edge waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size effects are taken into account.Comment: We have changed some figures as well as a part of the tex

Neutron density distributions for atomic parity nonconservation experiments

The neutron distributions of Cs, Ba, Yb and Pb isotopes are described in the framework of relativistic mean-field theory. The self-consistent ground state proton and neutron density distributions are calculated with the relativistic Hartree-Bogoliubov model. The binding energies, the proton and neutron radii, and the quadrupole deformations are compared with available experimental data, as well as with recent theoretical studies of the nuclear structure corrections to the weak charge in atomic parity nonconservation experiments.Comment: 16 pages, RevTex, 11 eps figs, submitted to Phys. Rev.

Far-infrared edge modes in quantum dots

We have investigated edge modes of different multipolarity sustained by quantum dots submitted to external magnetic fields. We present a microscopic description based on a variational solution of the equation of motion for any axially symmetric confining potential and multipole mode. Numerical results for dots with different number of electrons whose ground-state is described within a local Current Density Functional Theory are discussed. Two sum rules, which are exact within this theory, are derived. In the limit of a large neutral dot at B=0, we have shown that the classical hydrodynamic dispersion law for edge waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size effects are taken into account.Comment: We have changed some figures as well as a part of the tex

Isospin-mixing corrections for fp-shell Fermi transitions

Isospin-mixing corrections for superallowed Fermi transitions in {\it fp}-shell nuclei are computed within the framework of the shell model. The study includes three nuclei that are part of the set of nine accurately measured transitions as well as five cases that are expected to be measured in the future at radioactive-beam facilities. We also include some new calculations for $^{10}$C. With the isospin-mixing corrections applied to the nine accurately measured $ft$ values, the conserved-vector-current hypothesis and the unitarity condition of the Cabbibo-Kobayashi-Maskawa (CKM) matrix are tested.Comment: 13 pages plus five tables. revtex macro

NUCLEAR GIANT RESONANCES IN COORDINATE SPACE - A SEMICLASSICAL DENSITY FUNCTIONAL APPROACH

Dans le cadre d'une description semiclassique de résonnances géantes nucléaires (GR) en utilisant la force SkM* et les fonctionnelles ETF complètes à l'ordre 4 en 4 , nous présentons des modes propres monopolaires (0+) isoscalaires (I=0) et isovectorielles (I=1) en bon accord avec l'expérience, ainsi que la variation de quelques énergies GR typiques en fonction de la température.We discuss the semiclassical description of nuclear giant resonances (GR) using a realistic Skyrme force (SkM*) and complete ETF density functionals. We present monopole (0+) eigenmodes of isoscalar (I=0) and isovector (I=1) type, which are in good agreement with experiment, and the corresponding m1 and m3 sum rules. We also present the temperature dependence of some typical GR energies (0+, I=0,1 ; 1-, I=1 ; 2+, I=0) in 208Pb