1 Jacek Dobaczewski Reading materials: Jacek Dobaczewski:2004 RIA Summer School http://www.fuw.edu.pl/~dobaczew/RIA.Summer.Lectures/slajd01.html Jacek Dobaczewski:2005 Ecole Doctorale de Physique, Strasbourg http://www.fuw.edu.pl/~dobaczew/Strasbourg/slajd01.html Witek Nazarewicz:2007 Lectures at the University of Knoxville http://www.phys.utk.edu/witek/NP622/NuclPhys622.html Jacek Dobaczewski: 2008 the 18th Jyväskylä Summer School http://www.fuw.edu.pl/~dobaczew/JSS18/JSS18.html Jacek Dobaczewski: 2008 Euroschool on Exotic Beams http://www.fuw.edu.pl/~dobaczew/Euroschool/Euroschool.html Jacek Dobaczewski:1986-2005 draft of a book (in Polish) http://www.fuw.edu.pl/~dobaczew/Czesc057d.pdf Home page: http://www.fuw.edu.pl/~dobaczew/

2 Jacek Dobaczewski Price of land in Poland per voivodship Energy density functional 245 647 Price voivodship functional 654 763 295 580 446 842 631 356 549 548 490 287 623 362

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

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

5 Jacek Dobaczewski Hohenberg-Kohn theorem

6 Jacek Dobaczewski Hohenberg-Kohn theorem (trivial version)

7 Jacek Dobaczewski Nuclear Energy Density Functional (physical insight)

8 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.

9 Jacek Dobaczewski Dimensional analysis - regularization

10 Jacek Dobaczewski Dimensional analysis – the hydrogen-like atom

11 Jacek Dobaczewski N 3 LO in the chiral perturbation effective field theory W.C. Haxton, Phys. Rev. C77, 034005 (2008)

12 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) 041001

13 Jacek Dobaczewski Indistinguishability principle

14 Jacek Dobaczewski Fock space

15 Jacek Dobaczewski Creation and annihilation operators

16 Jacek Dobaczewski Operators in the Fock space

17 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

18 Jacek Dobaczewski http://www.phy.anl.gov/theory/research/forces.html

19 Jacek Dobaczewski Density matrices

20 Jacek Dobaczewski Coulomb force – the direct self-consistent potential

21 Jacek Dobaczewski Coulomb force – the exchange self-consistent potential

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

23 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

24 Jacek Dobaczewski

25 225 Ra Experiment R.G. Helmer et al., Nucl. Phys. A474 (1987) 77 Skyrme-Hartree-Fock J. Dobaczewski, J. Engel, Phys. Rev. Lett. 94, 232502 (2005) 1/2+ 1/2- 55 0 J z =1/2

26 Jacek Dobaczewski NH 3 225 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

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

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

29 Jacek Dobaczewski Hartree-Fock interaction energy

30 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

31 Jacek Dobaczewski Direct interaction energy

32 Jacek Dobaczewski Exchange interaction energy (I)

33 Jacek Dobaczewski Density matrix in the non-local direction

34 Jacek Dobaczewski Exchange interaction energy (II)

35 Jacek Dobaczewski Nuclear densities as composite fields

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

37 Jacek Dobaczewski Complete local energy density Mean field Pairing E. Perlińska, et al., Phys. Rev. C69 (2004) 014316

38 Jacek Dobaczewski Mean-field equations

39 Jacek Dobaczewski Phenomenological effective interactions

40 Jacek Dobaczewski M.V. Stoitsov, et al., Phys. Rev. C68, 054312 (2003)