liczba neutronów N

1. Mapa nuklidów liczba protonów Z liczba neutronów N

2. Perspektywy Teorii Struktury Jądra Atomowego A.D. 2007 Witold Nazarewicz Warszawa, Maj 2007 • Wstęp • Współczesne teorie struktury jądra atomowego (“bottom-up”) • Efektywne oddziaływania międzynukleonowe • Podejścia ‘ab initio’ • Mieszanie konfiguracji (model powłokowy) • Jądrowy funkcjonał gęstości • Ruch kolektywny jąder atomowych (“top-down”) • Perspektywy • Fizyka jąder egzotycznych • Unifikacja teorii struktury i reakcji jądrowych • Astrofizyka jądrowa • Zastosowania • Podsumowanie

3. SGR (fakty, daty…) 1936 ur. Warszawa 1957-1958 zastępca asystenta w IFT UW 1958-1960 asystent w IFT UW 1960-1966 st. asystent w IFT UW 1966-1968 adiunkt w IFT UW 1968-1974 st. wykładowca w IFT UW 1974-1983 adiunkt w IFT UW 1983-1990 docent w IFT UW 1990-1993 profesor nadzw. w IFT UW (profesura 1991) 1993-2006 profesor zwyczajny w IFT UW 2007- profesor zwyczajny, emerytowany, IFT UW Kierownik Studium Wieczorowego Fizyki UW, 1968-1973 Prodziekan Wydziału Fizyki UW, 1982-1984 Zastępca dyrektora IFT UW, 1987-1993 Dyrektor IFT UW, 1993-2005 Sekretarz Generalny PTF, 1987-1991 Teoria jądra atomowego, teoria wielu ciał… Nauczyciel… 7.11.1979

5. Energy Scales in Nuclear Physics QCD scale 1000 MeV g g g g g g g g g g g  _ _ _ _ d d d d d u u u u u d quarks in bags quarks and gluons pion p+ ~140 MeV neutron protons and neutrons baryons and mesons pion-mass scale deuteron ~3 MeV p n  100 MeV nucleonic fields collective coordinates N-binding scale 10 MeV collective ~1 MeV

6. Distance heavy nuclei Energy few body quarks gluons vacuum quark-gluon soup QCD nucleon QCD few body systems free NN force many body systems effective NN force The Nuclear Many-Body Problem Energy, Distance, Complexity Different degrees-of-freedom radioactive beams electron scattering relativistic heavy ions

7. superheavy nuclei proton drip line neutron drip line Nuclear Landscape 126 stable nuclei 82 r-process known nuclei terra incognita 50 protons 82 rp-process neutron stars 28 20 50 8 28 neutrons 2 20 8 2

8. How do protons and neutrons make stable nuclei and rare isotopes? What is the origin of simple patterns in complex nuclei? What is the equation of state of matter made of nucleons? What are the heaviest nuclei that can exist? When and how did the elements from iron to uranium originate? How do stars explode? What is the nature of neutron star matter? How can our knowledge of nuclei and our ability to produce them benefit the humankind? Life Sciences, Material Sciences, Nuclear Energy, Security Questions that Drive the Field Physics of nuclei Nuclear astrophysics Applications of nuclei

9. Recent years: very successful period for theory of nuclei • many new ideas leading to new understanding • new theoretical frameworks • exciting developments • high-quality calculations • The nucleon-based description works to <0.5 fm • Effective Field Theory/Renormalization Group provides missing links • Accurate ab-initio methods allow for interaction tests • Quantitative microscopic nuclear structure • Integrating nuclear structure and reactions • High-performance computing continues to revolutionize microscopic nuclear many-body problem: impossible becomes possible

10. Weinberg’s Laws of Progress in Theoretical Physics From: “Asymptotic Realms of Physics” (ed. by Guth, Huang, Jaffe, MIT Press, 1983) First Law: “The conservation of Information” (You will get nowhere by churning equations) Second Law: “Do not trust arguments based on the lowest order of perturbation theory” Third Law: “You may use any degrees of freedom you like to describe a physical system, but if you use the wrong ones, you’ll be sorry!”

11. The interaction Effective-field theory (χPT) potentials Vlow-k: can it describe low-energy observables? • Quality two- and three-nucleon interactions exist • Not uniquely defined (local, nonlocal) • The challenge is: • to understand their origin • to understand how to use them in nuclei Bogner, Kuo, Schwenk, Phys. Rep. 386, 1 (2003) N3LO: Entem et al., PRC68, 041001 (2003) Epelbaum, Meissner, et al.

12. Ab initio Configuration interaction Density Functional Theory Bottom-up approaches to nuclear structure Roadmap Theoretical approaches overlap and need to be bridged

13. Ab initio: GFMC, NCSM, CCM (nuclei, neutron droplets, nuclear matter) • Quantum Monte Carlo (GFMC) 12C • No-Core Shell Model 13C • Coupled-Cluster Techniques 16O • Faddeev-Yakubovsky • Bloch-Horowitz • … • Input: • Excellent forces based on the phase shift analysis • EFT based nonlocal chiral NN and NNN potentials deuteron’s shape GFMC: S. Pieper, ANL 1-2% calculations of A = 6 – 12 nuclear energies are possible excited states with the same quantum numbers computed The nucleon-based description works to <0.5 fm

14. Diagonalization Shell Model (CI) (medium-mass nuclei reached;dimensions 109!) Honma, Otsuka et al., PRC69, 034335 (2004) and ENAM’04 Martinez-Pinedo ENAM’04

15. Configuration Interaction • One valence shell CI works great, but… 1024 is not an option!!! • Smarter solutions are needed • Monte Carlo Shell Model • Density Matrix Renormalization Group • Factorization schemes Challenges: Configuration space Effective interactions and operators Open channels

16. Old paradigms, universal ideas, are not correct First experimental indications demonstrate significant changes No shell closure for N=8 and 20 for drip-line nuclei; new shells at 14, 16, 32… Near the drip lines nuclear structure may be dramatically different.

17. Modern Mean-Field Theory = Energy Density Functional mean-field ⇒ one-body densities zero-range ⇒ local densities finite-range ⇒ gradient terms particle-hole and pairing channels • Hohenberg-Kohn • Kohn-Sham • Negele-Vautherin • Landau-Migdal • Nilsson-Strutinsky

18. Towards the Universal Nuclear Energy Density Functional Walter Kohn: Nobel Prize in Chemistry in 1998 isoscalar (T=0) density isovector (T=1) density isoscalar spin density Local densities and currents + pairing… isovector spin density current density spin-current tensor density kinetic density kinetic spin density Example: Skyrme Functional Total ground-state HF energy

22. Nuclear DFT From Qualitative to Quantitative! S. Cwiok, P.H. Heenen, W. Nazarewicz Nature, 433, 705 (2005) • Deformed Mass Table in one day! • HFB mass formula: m~700keV • Good agreement for mass differences

23. DFT Correlation Term: Beyond Mean Field nuclear collective dynamics • Variety of phenomena: • symmetry breaking and quantum corrections • LACM: fission, fusion, coexistence • phase transitional behavior • new kinds of deformations • Significant computational resources • required: • Generator Coordinate Method • Projection techniques • Imaginary time method (instanton techniques) • QRPA and related methods • TDHFB, ATDHF, and related methods • Challenges: • selection of appropriate degrees of freedom • simultaneous treatment of symmetry • coupling to continuum in weakly bound systems • dynamical corrections; fundamental theoretical problems. • rotational, vibrational, translational • particle number • isospin

25. What are the missing pieces? Density Functional Theory

26. What is the origin of ordered motion of complex nuclei? Complex systems often display astonishing simplicities. Nuclei are no exception. It is astonishing that a heavy nucleus, consisting of hundreds of rapidly moving protons and neutrons can exhibit collective motion, where all particles slowly dance in unison.

27. molecules Rotational Transitions ~ 10 meV Vibrational Transitions ~ 100 meV Electronic Transitions ~ 1 eV nuclei Rotational Transitions ~ 0.2-2 MeV Vibrational Transitions ~ 0.5-12 MeV Nucleonic Transitions ~ 7 MeV Nuclear collective motion Nuclear collective motion is hardly adiabatic

28. E fission/fusion exotic decay heavy ion coll. Q0 Q E shape coexistence Q1 Q2 Q

31. n p Skins and Skin Modes

32. Z. Phys. A322, 271 (1985) Marago et al, BEC of 87Rb Phys. Rev. Lett. 84, 2056 (2000)

33. Contact with Experiment…

34. The nucleus is a correlated open quantum many-body system Environment: continuum of decay channels Thomas-Ehrmann effect 4946 12C+n 3/2 3685 3502 3089 1/2 2365 1943 12C+p 1/2 13C7 13N6 Unique geometries of light nuclei due to the threshold effects Spectra and matter distribution modified by the proximity of scattering continuum

36. Resonant (Gamow) states Unbound states 0 Discrete (bound) states eF eF n p outgoing solution complex pole of the S-matrix • Gamow, Z. Phys. 51, 204 (1928) • Siegert, Phys. Rev. 36, 750 (1939) • Humblet and Rosenfeld, Nucl. Phys. 26, 529 (1961) Rigged Hilbert space formulation of SM : Gamow Shell Model (2002) (Gelfand triple, nested Hilbert space, equipped Hilbert space) links the distribution and square-integrable aspects of functional analysis.

37. Rigged Hilbert space formulation Caen-Tennessee-Warsaw One-body basis N. Michel et al, PRL 89 (2002) 042502 R. Id Betan et al, PRL 89 (2002) 042501 N. Michel et al, PRC 70 (2004) 064311 G. Hagen et al, PRC 71 (2005) 044314 J. Rotureau et al., DMRG Phys. Rev. Lett. 97, 110603 (2006) non-resonant continuum bound, anti-bound, and resonance states Michel et al.:Virtual states not included explicitly in the GSM basis Phys. Rev. C 74, 054305 (2006)

39. RIA intensities (nuc/s) Mass known > 1012 102 1010 10-2 Half-life known nothing known 10-6 106 Supernova E0102-72.3 n-Star KS 1731-260 How does the physics of nuclei impact the physical universe? • What is the origin of elements heavier than iron? • How do stars burn and explode? • What is the nucleonic structure of neutron stars? X-ray burst p process s-process 4U1728-34 331 Frequency (Hz) 330 r process 329 328 327 10 15 20 Time (s) rp process Nova Crust processes T Pyxidis stellar burning protons neutrons

40. Future major facilities Existing major dedicated facilities NSCL GSI GANIL TRIUMF HRIBF RIKEN ISOLDE FRIB Radioactive Ion Beam Facilities Worldwide

41. QCD • Origin of NN interaction • Many-nucleon forces • Effective fields subfemto… nano… Complex Systems Giga… Cosmos femto… Physics of Nuclei Quantum many-body physics Nuclear Astrophysics • In-medium interactions • Symmetry breaking • Collective dynamics • Phases and phase transitions • Chaos and order • Dynamical symmetries • Structural evolution • Origin of the elements • Energy generation in stars • Stellar evolution • Cataclysmic stellar events • Neutron-rich nucleonic matter • Electroweak processes • Nuclear matter equation of state • How does complexity emerge from simple constituents? • How can complex systems display astonishing simplicities? How do nuclei shape the physical universe?

42. The study of nuclei is a forefront area of science. It is this research that makes the connection between the Standard Model, QCD phenomena, many-body systems, and the cosmos. Nuclear structure and reactions are important for not just nuclei: Understanding the quantum many-body problem Testing the fundamental laws of nature Understanding stellar evolution and how the elements were made Society (national security, energy, medicine…) Theory and experiment are both needed to achieve this goal Theory gives the mathematical formulation of our understanding and predictive ability Experiment provides verification Wszystkiego Najlepszego Grzegorzu!