Abstract:
we describe the basic mechanisms responsible for nuclear bulk properties and shell formation incorporated in the duflo zuker models. the emphasis is put on explaining why functionals of the occupancies can be so efficient in accounting for data with minimal computational effort.

Abstract:
Se discuten los mecanismos que son responsables para la propiedades nucleares globales y la formación de capas en los modelos Duflo-Zuker. Se enfatiza la importancia de funcionales de las ocupancias para describir los datos experimentales con un esfuerzo computacional mínimo.

Abstract:
It is shown that a very simple three-body monopole term can solve practically all the spectroscopic problems--in the $p$, $sd$ and $pf$ shells--that were hitherto assumed to need drastic revisions of the realistic potentials.

Abstract:
The three main contributions to the nuclear Hamiltonian - monopole, quadrupole and pairing - are analyzed in a shell model context. The first has to be treated phenomenologically, while the other two can be reliably extracted from the realistic interactions. Due to simple scaling properties, the realistic quadrupole and pairing interactions eliminate the tendency to collapse of their conventional counterparts, while retaining their basic simplicity.

Abstract:
It is shown that nuclear level densities in a finite space are described by a continuous binomial function, determined by the first three moments of the Hamiltonian, and the dimensionality of the underlying vector space. Experimental values for $^{55}$Mn, $^{56}$Fe, and $^{60}$Ni are very well reproduced by the binomial form, which turns out to be almost perfectly approximated by Bethe's formula with backshift. A proof is given that binomial densities reproduce the low moments of Hamiltonians of any rank: A strong form of the famous central limit result of Mon and French. Conditions under which the proof may be extended to the full spectrum are examined.

Abstract:
By assuming the existence of a pseudopotential smooth enough to do Hartree-Fock variations and good enough to describe nuclear structure, we construct mass formulae that rely on general scaling arguments and on a schematic reading of shell model calculations. Fits to 1751 known binding energies for N,Z$\geq 8$ lead to RMS errors of 614 keV with 14 parameters and 388 keV with 28 parameters. The latter is easily reduced to a 20 parameter form at 423 keV.

Abstract:
The residual part of the realistic forces ---obtained after extracting the monopole terms responsible for bulk properties--- is strongly dominated by pairing and quadrupole interactions, with important $\sigma\tau\cdot\sigma \tau$, octupole and hexadecapole contributions. Their forms differ from the schematic ones through normalizations that lead to a universal $A^{-1/3}$ scaling for all multipoles. Coupling strengths and effective charges are calculated and shown to agree with the observed values.

Abstract:
By assuming the existence of a pseudopotential smooth enough to do Hartree-Fock variations and good enough to describe nuclear structure, we construct mass formulae that rely on general scaling arguments and on a schematic reading of shell model calculations. Fits to 1751 known binding energies for N,Z$\geq 8$ lead to rms errors of 375 keV with 28 parameters. Tests of the extrapolation properties are passed successfully. The Bethe-Weizs\"acker formula is shown to be the asymptotic limit of the present one(s). The surface energy of nuclear matter turns out to be probably smaller than currently accepted.

Abstract:
A gross estimate of the neutron skin [0.80(5)$(N-Z)/A$ fm] is extracted from experimental proton radii, represented by a four parameter fit, and observed mirror displacement energies (CDE). The calculation of the latter relies on an accurately derived Coulomb energy and smooth averages of the charge symmetry breaking potentials constrained to state of the art values. The only free parameter is the neutron skin itself. The Nolen Schiffer anomaly is reduced to small deviations (rms=127 keV) that exhibit a secular trend. It is argued that with state of the art shell model calculations the anomaly should disappear. Highly accurate fits to proton radii emerge as a fringe benefit.

Abstract:
The first detailed comparison of the low-momentum interaction V_{low k} with G matrices is presented. We use overlaps to measure quantitatively the similarity of shell-model matrix elements for different cutoffs and oscillator frequencies. Over a wide range, all sets of V_{low k} matrix elements can be approximately obtained from a universal set by a simple scaling. In an oscillator mean-field approach, V_{low k} reproduces satisfactorily many features of the single-particle and single-hole spectra on closed-shell nuclei, in particular through remarkably good splittings between spin-orbit partners on top of harmonic oscillator closures. The main deficiencies of pure two-nucleon interactions are associated with binding energies and with the failure to ensure magicity for the extruder-intruder closures. Here, calculations including three-nucleon interactions are most needed. V_{low k} makes it possible to define directly a meaningful unperturbed monopole Hamiltonian, for which the inclusion of three-nucleon forces is tractable.