Angular-momentum projection of cranked symmetry-unrestricted Slater determinants

We report on development of a new feature of the code HFODD, allowing for the angular-momentum projection of cranked symmetry-unrestricted Slater determinants. After a brief overview of the main theoretical building blocks and formalism, we present several preliminary applications. In particular, we discuss the case of a well-deformed rotational band in 156Gd, and we show the emergence of uncompensated poles in the overlap kernels calculated in an odd-A nucleus 155Eu.Comment: 9 pages, 5 figures, submitted to International Journal of Modern Physics

High-spin intruder states in the fp shell nuclei and isoscalar proton-neutron correlations

We perform a systematic shell-model and mean-field study of fully-aligned, high-spin f_{7/2}^{n} seniority isomers and d_{3/2}^{-1} f_{7/2}^{n+1} intruder states in the A~44 nuclei from the lower-fp shell. The shell-model calculations are performed in the full sdfp configuration space allowing 1p-1h cross-shell excitations. The self-consistent mean-field calculations are based on the Hartree-Fock approach with the Skyrme energy density functional that reproduces empirical Landau parameters. While there is a nice agreement between experimental and theoretical relative energies of fully-aligned states in N>Z nuclei, this is no longer the case for the N=Z systems. The remaining deviation from the data is attributed to the isoscalar proton-neutron correlations. It is also demonstrated that the Coulomb corrections at high spins noticeably depend on the choice of the energy density functional.Comment: 4 pages. submitted to Phys. Rev. Let

The nuclear energy density functional formalism

The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a {\it Hamiltonian-based} picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel $E[g',g]$ at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. "mean-field", derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a {\it mathematically} meaningful fashion even if $E[g',g]$ does {\it not} derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making {\it any} reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a {\it physical} standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.Comment: 64 pages, 8 figures, submitted to Euroschool Lecture Notes in Physics Vol.IV, Christoph Scheidenberger and Marek Pfutzner editor