T. R. Werner

Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects

Ground-state properties of exotic even-even nuclei with extreme neutron-to-proton ratios are described in the framework of self-consistent mean-field theory with pairing formulated in coordinate space. This theory properly accounts for the influence of the particle continuum, which is particularly important for weakly bound systems. The pairing properties of nuclei far from stability are studied with several interactions emphasizing different aspects, such as the range and density dependence of the effective interaction. Measurable consequences of spatially extended pairing fields are presented, and the sensitivity of the theoretical predictions to model details is discussed. {copyright} {ital 1996 The American Physical Society.}

Spin-orbit and tensor mean-field effects on spin-orbit splitting including self-consistent core polarizations

A new strategy of fitting the coupling constants of the nuclear energy density functional is proposed, which shifts attention from ground-state bulk to single-particle properties. The latter are analyzed in terms of the bare single-particle energies and mass, shape, and spin core-polarization effects. Fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants directly to the f{sub 5/2}-f{sub 7/2} spin-orbit splittings in {sup 40}Ca, {sup 56}Ni, and {sup 48}Ca is proposed as a practical realization of this new program. It is shown that this fit requires drastic changes in the isoscalar spin-orbit strength and the tensor coupling constants as compared to the commonly accepted values, but it considerably and systematically improves basic single-particle properties including spin-orbit splittings and magic-gap energies. Impact of these changes on nuclear binding energies is also discussed.

Mean-field description of ground-state properties of drip-line nuclei: Shell-correction method

A shell-correction method is applied to nuclei far from the beta stability line, and its suitability to describe effects of the particle continuum is discussed. The sensitivity of predicted locations of one- and two-particle drip lines to details of the macroscopic-microscopic model is analyzed.

Point symmetries in the Hartree-Fock approach. I. Densities, shapes, and currents

Three mutually perpendicular symmetry axes of the second order, inversion, and time reversal can be used to construct a double point group denoted by D2h(TD). Properties of this group are analyzed in relation to the symmetry and symmetry-breaking effects within the mean-field (Hartree-Fock) theories, both in even and odd fermion systems. We enumerate space symmetries of local one-body densities, and symmetries of electromagnetic moments, that appear when some or all of the D2h(TD) elements represent self-consistent mean-field symmetries.

Isospin-breaking corrections to superallowed Fermi beta-decay in isospin- and angular-momentum-projected nuclear Density Functional Theory

Background: The superallowed �-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed �-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuclear density functional theory employing two density functionals derived from the density independent Skyrme interaction. Pairing correlations are ignored. Our framework can simultaneously describe various effects that impact matrix elements of the Fermi decay: symmetry breaking, configuration mixing, and long-range Coulomb polarization. Results: The isospin-breaking corrections to the I = 0 + ,T = 1 → I = 0 + ,T = 1 pure Fermi transitions are computed for nuclei from A=10 to A=98 and, for the first time, to the Fermi branch of the I,T = 1/2 → I,T = 1/2 transitions in mirror nuclei from A=11 to A=49. We carefully analyze various model assumptions impacting theoretical uncertainties of our calculations and provide theoretical error bars on our predictions. Conclusions: The overall agreement with empirical isospin-breaking corrections is very satisfactory. Using computed isospin-breaking corrections we show that the unitarity of the CKM matrix is satisfied with a precision better than 0.1%.

Point symmetries in the Hartree-Fock approach. II. Symmetry-breaking schemes

We analyze breaking of symmetries that belong to the double point group

Physics of exotic nuclear states

{D}_{2h}^{\mathrm{TD}}

A ≈ 80 and A ≈ 100 Nuclei Studied Within the Mean Field Approach

(three mutually perpendicular symmetry axes of the second order, inversion, and time reversal). Subgroup structure of the

Shell structure fingerprints of tensor interaction

{D}_{2h}^{\mathrm{TD}}

GLOBAL NUCLEAR STRUCTURE ASPECTS OF TENSOR INTERACTION

group indicates that there can be as many as 28 physically different, broken-symmetry mean-field schemes \char22{} starting with solutions obeying all the symmetries of the