Pairing gaps from nuclear mean-field models

We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei.Comment: 17 pages, 8 figures. Accepted for publication in EPJ

Consequences of the center-of-mass correction in nuclear mean-field models

We study the influence of the scheme for the correction for spurious center-of-mass motion on the fit of effective interactions for self-consistent nuclear mean-field calculations. We find that interactions with very simple center-of-mass correction have significantly larger surface coefficients than interactions for which the center-of-mass correction was calculated for the actual many-body state during the fit. The reason for that is that the effective interaction has to counteract the wrong trends with nucleon number of all simplified schemes for center-of-mass correction which puts a wrong trend with mass number into the effective interaction itself. The effect becomes clearly visible when looking at the deformation energy of largely deformed systems, e.g. superdeformed states or fission barriers of heavy nuclei.Comment: 12 pages LATeX, needs EPJ style files, 5 eps figures, accepted for publication in Eur. Phys. J.

Conservation Properties in the Time-Dependent Hartree Fock Theory

We discuss the conservation of angular momentum in nuclear time-dependent Hartree-Fock calculations for a numerical representation of wave functions and potentials on a three-dimensional cartesian grid. Free rotation of a deformed nucleus performs extremely well even for relatively coarse spatial grids. Heavy ion collisions produce a highly excited compound system associated with substantial nucleon emission. These emitted nucleons reach the bounds of the numerical box which leads to a decrease of angular momentum. We discuss strategies to distinguish the physically justified loss from numerical artifacts.Comment: 4 page

Potential energy surfaces of superheavy nuclei

We investigate the structure of the potential energy surfaces of the superheavy nuclei 258Fm, 264Hs, (Z=112,N=166), (Z=114,N=184), and (Z=120,N=172) within the framework of self-consistent nuclear models, i.e. the Skyrme-Hartree-Fock approach and the relativistic mean-field model. We compare results obtained with one representative parametrisation of each model which is successful in describing superheavy nuclei. We find systematic changes as compared to the potential energy surfaces of heavy nuclei in the uranium region: there is no sufficiently stable fission isomer any more, the importance of triaxial configurations to lower the first barrier fades away, and asymmetric fission paths compete down to rather small deformation. Comparing the two models, it turns out that the relativistic mean-field model gives generally smaller fission barriers.Comment: 8 pages RevTeX, 6 figure

Projection and ground state correlations made simple

We develop and test efficient approximations to estimate ground state correlations associated with low- and zero-energy modes. The scheme is an extension of the generator-coordinate-method (GCM) within Gaussian overlap approximation (GOA). We show that GOA fails in non-Cartesian topologies and present a topologically correct generalization of GOA (topGOA). An RPA-like correction is derived as the small amplitude limit of topGOA, called topRPA. Using exactly solvable models, the topGOA and topRPA schemes are compared with conventional approaches (GCM-GOA, RPA, Lipkin-Nogami projection) for rotational-vibrational motion and for particle number projection. The results shows that the new schemes perform very well in all regimes of coupling.Comment: RevTex, 12 pages, 7 eps figure

Systematics of collective correlation energies from self-consistent mean-field calculations

The collective ground-state correlations stemming from low-lying quadrupole excitations are computed microscopically. To that end, the self-consistent mean-field model is employed on the basis of the Skyrme-Hartre-Fock (SHF) functional augmented by BCS pairing. The microscopic-macroscopic mapping is achieved by quadrupole-constrained mean-field calculations which are processed further in the generator-coordinate method (GCM) at the level of the Gaussian overlap approximation (GOA). We study the correlation effects on energy, charge radii, and surface thickness for a great variety of semi-magic nuclei. A key issue is to work out the influence of variations of the SHF functional. We find that collective ground-state correlations (GSC) are robust under change of nuclear bulk properties (e.g., effective mass, symmetry energy) or of spin-orbit coupling. Some dependence on the pairing strength is observed. This, however, does not change the general conclusion that collective GSC obey a general pattern and that their magnitudes are rather independent of the actual SHF parameters.Comment: 13 pages, 13 figure

The Skyrme energy functional and low lying 2+ states in Sn, Cd and Te isotopes

We study the predictive power of Skyrme forces with respect to low lying quadrupole spectra along the chains of Sn, Cd, and Te isotopes. Excitation energies and B(E2) values for the lowest quadrupole states are computed from a collective Schroedinger equation which as deduced through collective path generated by constraint Skyrme-Hartree-Fock (SHF) plus self-consistent cranking for the dynamical response. We compare the results from four different Skyrme forces, all treated with two different pairing forces (volume versus density-dependent pairing). The region around the neutron shell closure N=82 is very sensitive to changes in the Skyrme while the mid-shell isotopes in the region N<82 depend mainly on the adjustment of pairing. The neutron rich isotopes are most sensitive and depend on both aspects

Information content of the weak-charge form factor

Parity-violating electron scattering provides a model-independent determination of the nuclear weak-charge form factor that has widespread implications across such diverse areas as fundamental symmetries, nuclear structure, heavy-ion collisions, and neutron-star structure. We assess the impact of precise measurements of the weak-charge form factor of ${}^{48}$Ca and ${}^{208}$Pb on a variety of nuclear observables, such as the neutron skin and the electric-dipole polarizability. We use the nuclear Density Functional Theory with several accurately calibrated non-relativistic and relativistic energy density functionals. To assess the degree of correlation between nuclear observables and to explore systematic and statistical uncertainties on theoretical predictions, we employ the chi-square statistical covariance technique. We find a strong correlation between the weak-charge form factor and the neutron radius, that allows for an accurate determination of the neutron skin of neutron-rich nuclei. We determine the optimal range of the momentum transfer $q$ that maximizes the information content of the measured weak-charge form factor and quantify the uncertainties associated with the strange quark contribution. Moreover, we confirm the role of the electric-dipole polarizability as a strong isovector indicator. Accurate measurements of the weak-charge form factor of ${}^{48}$Ca and ${}^{208}$Pb will have a profound impact on many aspects of nuclear theory and hadronic measurements of neutron skins of exotic nuclei at radioactive-beam facilities.Comment: 10 pages, 4 figure

Appearance of the Single Gyroid Network Phase in Nuclear Pasta Matter

Nuclear matter under the conditions of a supernova explosion unfolds into a rich variety of spatially structured phases, called nuclear pasta. We investigate the role of periodic network-like structures with negatively curved interfaces in nuclear pasta structures, by static and dynamic Hartree-Fock simulations in periodic lattices. As the most prominent result, we identify for the first time the {\it single gyroid} network structure of cubic chiral $I4_123$ symmetry, a well known configuration in nanostructured soft-matter systems, both as a dynamical state and as a cooled static solution. Single gyroid structures form spontaneously in the course of the dynamical simulations. Most of them are isomeric states. The very small energy differences to the ground state indicate its relevance for structures in nuclear pasta.Comment: 7 pages, 4 figure

Spin-Excitation Mechanisms in Skyrme-Force Time-Dependent Hartree-Fock

We investigate the role of odd-odd (with respect to time inversion) couplings in the Skyrme force on collisions of light nuclei, employing a fully three-dimensional numerical treatment without any symmetry restrictions and with modern Skyrme functionals. We demonstrate the necessity of these couplings to suppress spurious spin excitations owing to the spin-orbit force in free translational motion of a nucleus but show that in a collision situation there is a strong spin excitation even in spin-saturated systems which persists in the departing fragments. The energy loss is considerably increased by the odd-odd terms