Nuclear Data Sheets for A = 134

We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional local-density-plus-gradients form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wave-function based methods or by Legendre transform via effective actions. We describe known and unresolved issues for applying these formulations to the nuclear many-body problem and discuss how ab initio approaches can help improve empirical energy density functionals.

Toward ab initio density functional theory for nuclei

Nuclei with large neutron-to-proton ratios have neutron skins, which manifest themselves in an excess of neutrons at distances greater than the radius of the proton distribution. In addition, some drip-line nuclei develop very extended halo structures. The neutron halo is a threshold effect; it appears when the valence neutrons occupy weakly bound orbits. In this study, nuclear skins and halos are analyzed within the self-consistent Skyrme-Hartree-Fock-Bogoliubov and relativistic Hartree-Bogoliubov theories for spherical shapes. It is demonstrated that skins, halos, and surface thickness can be analyzed in a model-independent way in terms of nucleonic density form factors. Such an analysis allows for defining a quantitative measure of the halo size. The systematic behavior of skins, halos, and surface thickness in even-even nuclei is discussed.

Nuclear skins and halos in the mean field theory

The knowledge of the nuclear matrix elements for the neutrinoless double beta decay is fundamental for neutrino physics. In this paper, an innovative technique to extract information on the nuclear matrix elements by measuring the cross section of a double charge exchange nuclear reaction is proposed. The basic point is that the initial- and final-state wave functions in the two processes are the same and the transition operators are similar. The double charge exchange cross sections can be factorized in a nuclear structure term containing the matrix elements and a nuclear reaction factor. First pioneering experimental results for the 40Ca(18O,18Ne)40Ar reaction at 270 MeV incident energy show that such cross section factorization reasonably holds for the crucial 0+ $ \rightarrow$
 0+ transition to 40Args, at least at very forward angles.

Heavy-ion double charge exchange reactions: A tool toward $0 \nu\beta\beta$ nuclear matrix elements

The density matrix expansion is used to obtain a local energy density functional for interactions with a realistic meson exchange structure. Hartree-Fock (HF) equations are derived and applications to infinite matter and finite nuclei are discussed. Using a generalized Slater approximation for the density matrix the HF equations still incorporate the momentum structure of the underlying finite range interaction. For applications a density dependent effective interaction is determined from a $G$ matrix where the density dependence is adjusted to the saturation properties of symmetric nuclear matter. Intending applications to systems far off stability special attention is paid to the low density regime and asymmetric nuclear matter. Results are compared to Skyrme HF calculations. The ground state properties of stable nuclei are well reproduced. The potential of the approach is further exemplified in calculations for $A=100\ensuremath{-}140$ tin isotopes. Extended neutron skins are found beyond ${}^{130}\mathrm{Sn}$ corresponding to solid layers of neutron matter surrounding a core of normal composition.

H. Lenske

Papers

Hartree-Fock calculations in the density matrix expansion approach