Determination of spherical mean field nuclei

For the purpose of fitting nuclear mean-field models, we search for those spherical nuclei which are well reproduced by a mean-field description. To that end, we investigate the correlation energies for isotopic and isotonic chains of semi-magic nuclei. We find that isotonic chains provide the best pool of data. Motivation Self-consistent nuclear mean-field models are a widely used tool for a high quality description of nuclear structure and low-energy dynamics throughout the whole nuclear landscape (perhaps excluding the lightest elements), for a recent review see [1]. The form of the underlying energy functionals can be deduced from rather general arguments (e.g., low momentum expansion). The parameters of a model need to be adjusted phenomenologically. This is usually done by a fit to a selection of nuclei. Spherical nuclei are preferred for technical reasons. It is desirable that the chosen fit nuclei are well described within a mean-field approach, i.e. the correlation energy stemming from softness against deformation and from low-lying quadrupole modes is small. Semi-magic nuclei are usually supposed to meet these both conditions. It is the aim of this contribution to explore the amount of correlation effects in the chains of semi-magic nuclei. Formal framework We concentrate here on the Skyrme-Hartree-Fock model (SHF). The correlations are computed with the techniques as explained in detail in [2, 3]. The potential energy surface (PES) for deformation is determined by constrained Hartree-Fock (CHF) using the quadrupole operator as constraint. The quadrupole collective mass and related zeropoint energies are computed by self-consistent cranking. This information from microscopic calculations determines the collective Hamiltonian for quadrupole motion. The ground-state solution of the collective Schrödinger equation provides the correlation energy associated with lowlying collective quadrupole modes. Results and discussion Figure 1 shows the correlations energy as computed with the Skyrme parameterization SkI3 [4] for a broad selection of semi-magic nuclei. The horizontal lines mark the intended uncertainties on the energies. Nuclei which stay Supported by the BMBF 06 ER 124 -4 -2 0 2 20 40 60 80 100 120 E c o rr = E c o ll E M F [ M e V ]