Jacek Dobaczewski Reading materials: Jacek Dobaczewski:2004 RIA Summer School Jacek Dobaczewski:2005 Ecole Doctorale de Physique, Strasbourg Witek Nazarewicz:2007 Lectures at the University of Knoxville Jacek Dobaczewski: 2008 the 18th Jyväskylä Summer School Jacek Dobaczewski: 2008 Euroschool on Exotic Beams Jacek Dobaczewski: draft of a book (in Polish) Home page:

Jacek Dobaczewski Price of land in Poland per voivodship Energy density functional Price voivodship functional

Jacek Dobaczewski Price of land in Poland per district Energy density functional Price district functional

Jacek Dobaczewski Price of land in Eurpe per country Energy density functional Price country functional

Jacek Dobaczewski Hohenberg-Kohn theorem

Jacek Dobaczewski Hohenberg-Kohn theorem (trivial version)

Jacek Dobaczewski Nuclear Energy Density Functional (physical insight)

Jacek Dobaczewski Hydrogen atom perturbed near the center Relative errors in the S- wave binding energies are plotted versus: (i) the binding energy for the Coulomb theory (ii) the Coulomb theory augmented with a delta function in first-order perturbation theory (iii) the non-perturbative effective theory through a 2, and (iv) the effective theory through a 4.

Jacek Dobaczewski Dimensional analysis - regularization

Jacek Dobaczewski Dimensional analysis – the hydrogen-like atom

Jacek Dobaczewski N 3 LO in the chiral perturbation effective field theory W.C. Haxton, Phys. Rev. C77, (2008)

Jacek Dobaczewski EFT phase-shift analysis np phase parameters below 300 MeV lab. energy for partial waves with J=0,1,2. The solid line is the result at N 3 LO. The dotted and dashed lines are the phase shifts at NLO and NNLO, respectively, as obtained by Epelbaum et al. The solid dots show the Nijmegen multi-energy np phase shift analysis and the open circles are the VPI single-energy np analysis SM99. D.R. Entem and R. MachleidtPhys.Rev. C68 (2003)

Jacek Dobaczewski Indistinguishability principle

Jacek Dobaczewski Fock space

Jacek Dobaczewski Creation and annihilation operators

Jacek Dobaczewski Operators in the Fock space

Jacek Dobaczewski d d n-n distance (fm) n-n potential (MeV) O -O potential (meV) 2 2 O -O distance (nm) 2 2 O -O system 2 2 n-n system (1S 0 ) O2O2 O2O2 n n n-n versus O 2 -O 2 interaction

Jacek Dobaczewski

Jacek Dobaczewski Density matrices

Jacek Dobaczewski Coulomb force – the direct self-consistent potential

Jacek Dobaczewski Coulomb force – the exchange self-consistent potential

Jacek Dobaczewski Nitrogen atom Hydrogen atom Ammonia molecule NH 3 left state right state

Jacek Dobaczewski Ammonia molecule NH 3 Distance of N from the H 3 plane (a.u.) Total energy (a.u.) Symmetry-conserving configuration Symmetry-breaking configurations

Jacek Dobaczewski

225 Ra Experiment R.G. Helmer et al., Nucl. Phys. A474 (1987) 77 Skyrme-Hartree-Fock J. Dobaczewski, J. Engel, Phys. Rev. Lett. 94, (2005) 1/2+ 1/ J z =1/2

Jacek Dobaczewski NH Raratio 0.1 meV55 keV1.8 ×10 -9 T 1/2 (Q.M.)6.6 ps0.012 as5.5 ×10 8 T 1/2 (E.M.)16 ks~5 ns3.2 ×10 12 D 0.76 e×nm~0.1 e× fm7.6×10 -6

Jacek Dobaczewski Nuclear deformation Elongation (a.u.) Total energy (a.u.) Symmetry-conserving configuration Symmetry-breaking configurations

Jacek Dobaczewski Origins of nuclear deformation Elongation (a.u.) Single-particle energy (a.u.) Open-shell system: 8 particles on 8 doubly degenrate levels

Jacek Dobaczewski Hartree-Fock interaction energy

Jacek Dobaczewski mean field one-body densities zero range local densities finite range non-local densities Hohenberg-Kohn Kohn-Sham Negele-Vautherin Landau-Migdal Nilsson-Strutinsky Modern Mean-Field Theory Energy Density Functional j,, J, T, s, F, Nuclear densities as composite fields

Jacek Dobaczewski Direct interaction energy

Jacek Dobaczewski Exchange interaction energy (I)

Jacek Dobaczewski Density matrix in the non-local direction

Jacek Dobaczewski Exchange interaction energy (II)

Jacek Dobaczewski Nuclear densities as composite fields

Jacek Dobaczewski Local energy density: (no isospin, no pairing)

Jacek Dobaczewski Complete local energy density Mean field Pairing E. Perlińska, et al., Phys. Rev. C69 (2004)

Jacek Dobaczewski Mean-field equations

Jacek Dobaczewski Phenomenological effective interactions

Jacek Dobaczewski M.V. Stoitsov, et al., Phys. Rev. C68, (2003)