Theoretical developments in heavy nuclei

The present-day nuclear structure theory exhibits a great degree of synergy with respect to methods that are used to describe various phenomena in heavy nuclear systems. From few-body methods, through the shell model to mean-field approaches, the bridges are being built between different ways of describing the stable as well as the most exotic nuclei. In the present talk, I give a review of several selected subjects that are currently at the fore front of new developments in this domain of nuclear science.Comment: Plenary talk at the INPC'01, Berkeley, USA, 30 July - 3 August, 2001, 15 LaTeX pages, 16 EPS files with figure

Lipkin translational-symmetry restoration in the mean-field and energy-density-functional methods

Based on the 1960 idea of Lipkin, the minimization of energy of a symmetry-restored mean-field state is equivalent to the minimization of a corrected energy of a symmetry-broken state with the Peierls-Yoccoz mass. It is interesting to note that the "unphysical" Peierls-Yoccoz mass, and not the true mass, appears in the Lipkin projected energy. The Peierls-Yoccoz mass can be easily calculated from the energy and overlap kernels, which allows for a systematic, albeit approximate, restoration of translational symmetry within the energy-density formalism. Analogous methods can also be implemented for all other broken symmetries.Comment: 15 LaTeX pages, 8 eps figures, submitted to Journal of Physics

Mean-Field Calculation Based on Proton-Neutron Mixed Energy Density Functionals

We have performed calculations based on the Skyrme energy density functional (EDF) that includes arbitrary mixing between protons and neutrons. In this framework, single-particle states are generalized as mixtures of proton and neutron components. The model assumes that the Skyrme EDF is invariant under the rotation in isospin space and the Coulomb force is the only source of the isospin symmetry breaking. To control the isospin of the system, we employ the isocranking method, which is analogous to the standard cranking approach used for describing high-spin states. Here, we present results of the isocranking calculations performed for the isobaric analog states in $A = 40$ and $A = 54$ nuclei.Comment: 6 pages, 7 figures, talk given at the 2nd Conference on "Advances in Radioactive Isotope Science 2014" (ARIS 2014), Tokyo, Japan, Jun. 1-6, 201

Fully self-consistent calculations of nuclear Schiff moments

We calculate the Schiff moments of the nuclei 199Hg and 211Ra in completely self-consistent odd-nucleus mean-field theory by modifying the Hartree-Fock-Bogoliubov code HFODD. We allow for arbitrary shape deformation, and include the effects of nucleon dipole moments alongside those of a CP-violating pion-exchange nucleon-nucleon interaction. The results for 199Hg differ significantly from those of previous calculations when the CP-violating interaction is of isovector character.Comment: 7 pages, 2 figure

Ab initio derivation of model energy density functionals

I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results

Hartree-Fock-Bogoliubov Theory of Polarized Fermi Systems

Condensed Fermi systems with an odd number of particles can be described by means of polarizing external fields having a time-odd character. We illustrate how this works for Fermi gases and atomic nuclei treated by density functional theory or Hartree-Fock-Bogoliubov (HFB) theory. We discuss the method based on introducing two chemical potentials for different superfluid components, whereby one may change the particle-number parity of the underlying quasiparticle vacuum. Formally, this method is a variant of non-collective cranking, and the procedure is equivalent to the so-called blocking. We present and exemplify relations between the two-chemical-potential method and the cranking approximation for Fermi gases and nuclei.Comment: 11 RevTeX pages, 4 figures, submitted to Physical Review A, extended versio

On Th229 and time-dependent fundamental constants

The electromagnetic transition between the almost degenerate 5/2+ and 3/2+ states in Th229 is deemed to be very sensitive to potential changes in the fine structure constant alpha. State of the art Hartree-Fock and Hartree-Fock-Bogoliubov calculations are performed to compute the difference in Coulomb energies of the two states which determines the amplification of variations in alpha into variations of the transition frequency. The kinetic energies are also calculated which reflect a possible variation in the nucleon or quark masses. A generalized Hellmann-Feynman theorem is proved including the use of density-matrix functionals. As the two states differ mainly in the orbit occupied by the last unpaired neutron the Coulomb energy difference results from a change in the nuclear polarization of the proton distribution. This effect turns out to be rather small and to depend on the nuclear model, the amplification varies between about -4 x 10^4 and +4 x 10^4. Therefore much more effort must be put into the improvement of the nuclear models before one can draw conclusions from a measured drift in the transition frequency on a temporal drift of fundamental constants. All calculations published so far do not reach the necessary fidelity. PACS 06.20.Jr,21.60.Jz,27.90.+bComment: 13 pages with 3 figure