Nuclei far from stability are studied by solving the Hartree-Fock-Bogoliubov (HFB) equations, which describe the self-consistent mean field theory with pairing interaction. Calculations for eveneven nuclei are carried out on a two-dimensional axially symmetric lattice, in coordinate space. The quasiparticle continuum wavefunctions are considered for energies up to 60 MeV. Nuclei near the drip lines have a strong coupling between weakly bound states and the particle continuum. This method gives a proper description of the ground state properties of such nuclei. High accuracy is achieved by representing the operators and wavefunctions using the technique of basis-splines. The detailed representation of the HFB equations in cylindrical coordinates is discussed. Calculations of observables for nuclei near the neutron drip line are presented to demonstrate the reliability of the method.

Using the Hartree-Fock-Bogoliubov (HFB) mean field theory in coordinate space, we investigate ground state properties of the sulfur isotopes from the line of stability up to the two-neutron dripline ( 34−52 S). In particular, we calculate two-neutron separation energies, quadrupole moments, and rms-radii for protons and neutrons. Evidence for shape coexistence is found in the very neutronrich sulfur isotopes. We compare our calculations with results from relativistic mean field theory and with available experimental data. We also study the properties of neutron-rich zirconium ( 102,104 Zr), cerium ( 152 Ce), and samarium ( 158,160 Sm) isotopes which exhibit very large prolate quadrupole deformations.

An important input into reaction theory is the density of states or the level density. Spectral distribution theory (also known as nuclear statistical spectroscopy) characterizes the secular behavior of the density of states through moments of the Hamiltonian. One particular approach is to partition the model space into subspaces and find the moments in those subspaces; a convenient choice of subspaces are spherical shell-model configurations. We revisit these configuration moments and find, for complete 0hω many-body spaces, the following behaviors: (a) the configuration width is nearly constant for all configurations; (b) the configuration asymmetry or third moment is strongly correlated with the configuration centroid; (c) the configuration fourth moment, or excess is linearly related to the square to the configuration asymmetry. Such universal behavior may allow for more efficient modeling of the density of states in a shell-model framework.PACS numbers: 21zc

We consider the secular behavior of shell-model configuration (partial) densities. When configuration densities are characterized by their moments, one often finds large third moments, which can make suitable parameterization of the secular behavior problematic. We review several parameterizations or models, and consider in depth three specific models: Cornish-Fisher, binomial, and modified Breit-Wigner distributions. Of these three the modified Breit-Wigner provides the best secular approximation to exact numerical configuration densities computed via full diagonalization from realistic interactions.Comment: 8 pages, 3 figure