Nuclear Structure Theory, Introduction Witold Nazarewicz (UTK/ORNL)

1. Nuclear Structure Theory, Introduction Witold Nazarewicz (UTK/ORNL) International Workshop on Nuclear Physics NITheP, Stellenbosch, May 16-21, 2011 100 years after… • Introduction • Science Challenges • Novel analytic theory • Importance of RNB data • High performance computing • Predictive capability and extrapolability • Perspectives

2. The intellectual drivers of nuclear physics today (overarching questions) • How did the matter that makes up the visible universe come into being and how does it evolve? • Nature of building blocks (quarks+gluons, hadrons, nuclei, atoms,…) • Cosmic evolution of the visible matter • How do the building blocks of subatomic matter organize themselves and what phenomena emerge as they do so? • Nature of composite structures and phases • Origin of simple patterns in complex systems? • How have forces hidden from view shaped the properties of matter? • In search of the New Standard Model • The nucleus as a laboratory for testing fundamental symmetries • How can we best use the unique properties of nuclei and technologies developed in nuclear physics to benefit society? • Unique opportunities for applications • Public must be properly compensated for supporting what is fundamentally an intellectual enterprise.

3. Resolution Hot and dense quark-gluon matter Hadron structure Hadron-Nuclear interface Nuclear structure Nuclear reactions Effective Field Theory Nuclear astrophysics New standard model Applications of nuclear science

4. The Nuclear Many-Body Problem Eigenstate of angular momentum, parity, and ~isospin Barrett coupled integro-differential equations in 3A dimensions

5. dimension of the problem Interfaces provide crucial clues number of nuclei < number of processors!

6. Recent years: very successful period for theory of nuclei • many new ideas leading to new understanding • high-quality calculations • new-generation data from Radioactive Nuclear Beam facilities • large-scale computing transforms the nuclear many-body problem • Lattice QCD offers crucial insights and bridges hadrons with nuclei • Effective Field Theory/Renormalization Group provides missing links • The nucleon-based description works down to ~0.5 fm • Accurate ab-initio methods allow for interaction tests • Worldwide attack on the nuclear energy density functional • Quantitative microscopic nuclear structure • Integrating nuclear structure and reactions • Some of the most interesting physics outcomes will be at the interfaces: • QCD to forces to structure • Fruitful interactions with quantum chemistry • Structure and reactions with nuclear astrophysics

7. A realistic nuclear force force: schematic view Nuclear force • Nucleon r.m.s. radius ~0.86 fm • Comparable with interaction range • Half-density overlap at max. attarction • VNN not fundamental (more like inter-molecular van der Waals interaction) • Since nucleons are composite objects, three-and higher-body forces are expected.

8. nucleon-nucleon interactions Anderson Effective-field theory potentials Renormalization group (RG) evolved nuclear potentials Vlow-k unifies NN interactions at low energy N3LO: Entem et al., PRC68, 041001 (2003) Epelbaum, Meissner, et al. Bogner, Kuo, Schwenk, Phys. Rep. 386, 1 (2003)

9. three-nucleon interactions Calci Three-body forces between protons and neutrons are analogous to tidal forces: the gravitational force on the Earth is not justthe sum of Earth-Moon and Earth-Sun forces (if one employs point masses for Earth, Moon, Sun) The computational cost of nuclear 3-body forces can be greatly reduced by decoupling low-energy parts from high-energy parts, which can then be discarded. Recently the first consistent Similarity Renormalization Group softening of three-body forces was achieved, with rapid convergence in helium. With this faster convergence, calculations of larger nuclei are possible!

10. Ab initio theory for light nuclei and nuclear matter Ab initio: QMC, NCSM, CCM,… (nuclei, neutron droplets, nuclear matter) • Input: • Excellent forces based on the phase shift analysis and few-body data • EFT based nonlocal chiral NN and NNN potentials • SRG-softened potentials based on bare NN+NNN interactions Ab initio input NN+NNN interactions Many body method Renormalization • Quantum Monte Carlo (GFMC) 12C • No-Core Shell Model 14F, 14C • Faddeev-Yakubovsky • Lattice EFT 12C (Hoyle) • Coupled-Cluster Techniques 17F, 56Ni • Fermionic Molecular Dynamics • … Observables • Direct comparison with experiment • Pseudo-data to inform theory Feldmeier, Roth

11. GFMC: S. Pieper, ANL 1-2% calculations of A = 6 – 12 nuclear energies are possible excited states with the same quantum numbers computed

12. Lattice EFT Hoyle state in 12C Epelbaum et al., Phys. Rev. Lett. 106, 192501 (2011) Nuclear Coupled Cluster Theory Medium-mass nuclei from chiral nucleon-nucleon interactions Hagen et al., Phys. Rev. Lett. 101, 092502 (2008) Hjorth-Jensen, Physics 4, 38 (2011)

13. Strongly paired fermions: Cold atoms and neutron matter an=-18.5 fm, re=2.7 fm pairing gap s-wave part of AV18 Gezerlis and Carlson, Phys. Rev. C 77, 032801(R) (2008)

14. Configuration interaction techniques • light and heavy nuclei • detailed spectroscopy • quantum correlations (lab-system description) Input: configuration space + forces Method NN+NNN interactions Renormalization Diagonalization Truncation+diagonalization Monte Carlo Matrix elements fitted to experiment Observables • Direct comparison with experiment • Pseudo-data to inform reaction theory and DFT

15. Nuclear shell model One-body Hamiltonian Residual interactioni • Construct basis states with good (Jz, Tz) or (J,T) • Compute the Hamiltonian matrix • Diagonalize Hamiltonian matrix for lowest eigenstates • Number of states increases dramatically with particle number • Can we get around this problem? Effective interactions in truncated spaces (P-included, finite; Q-excluded, infinite) • Residual interaction (G-matrix) depends on the configuration space. Effective charges • Breaks down around particle drip lines Rotureau

16. Average one-body Hamiltonian 120Sn Unbound states Coulomb barrier Discrete (bound) states 0 eF eF Surface region n p Flat bottom

17. 54 nucleonic shells of the nucleus electronic shells of the atom 5p 4d 5s 36 4p 3d 4s 18 3p 3s 10 ? N Z magic nuclei (closed shells) noble gases (closed shells) 2p 2s 126 3p1/2 2f5/2 1i13/2 3p3/2 1h9/2 2f7/2 82 2d3/2 1h11/2 3s1/2 1g7/2 2d5/2 50 1g9/2

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

19. Isotopes near 100Sn flout conventional wisdom Darby et al., Phys. Rev. Lett. 105, 162502 (2010) M. Hjorth-Jensen et al., J. Phys. G 37, 064035 (2010) T. Otsuka et al. Phys. Rev. Lett. 104, 012501 (2010)

21. Mean-Field Theory ⇒ Density Functional Theory Dobaczewski • Nuclear DFT • two fermi liquids • self-bound • superfluid • mean-field ⇒ one-body densities • zero-range ⇒ local densities • finite-range ⇒ gradient terms • particle-hole and pairing channels • Has been extremely successful. A broken-symmetry generalized product state does surprisingly good job for nuclei.

22. Nuclear Density Functional Theory and Extensions Input Dobaczewski NN+NNN interactions Density Matrix Expansion Density dependent interactions Energy Density Functional Optimization • Fit-observables • experiment • pseudo data DFT variational principle HF, HFB (self-consistency) Symmetry breaking Litvinova Rodriguez, Stetcu Symmetry restoration Multi-reference DFT (GCM) Time dependent DFT (TDHFB) Observables • two fermi liquids • self-bound • superfluid (ph and pp channels) • self-consistent mean-fields • broken-symmetry generalized product states • Direct comparison with experiment • Pseudo-data for reactions and astrophysics

23. Nuclear Density Functional Theory: applications Traditional (limited) functionals provide quantitative description BE differences Mass table dm=0.581 MeV Goriely, Chamel, Pearson: HFB-17 Phys. Rev. Lett. 102, 152503 (2009) Cwiok, Heenen, WN, Nature, 433, 705 (2005)

24. Microscopic calculations of isospin-breaking corrections to superallowed b-decay W. Satuła et al.,Phys. Rev. Lett 106, 132502 (2011) with new symmetry-breaking corrections: Superallowed Fermi 0+ →0+-decay studies Kobayashi and Maskawa: … for "the discovery of the origin of broken symmetry, which predicts the existence of at least three families of quarks in nature." Impressive experimental effort worldwide 0.9999(6) nuclear meson decay Towner and Hardy 2010

25. Characterization of phases ground state, excitations, collective modes • In bulk matter • In finite systems (quantum phase transitions) Characterization of individual phases is the first step towards understanding the phase diagram. The characterization of transitions between phases, critical points, triple points… is a true challenge!

26. Collective models (geometric, algebraic) Mesoscopic perspective Collective Bohr Hamiltonian SU(3) Model Interacting Boson Model • Identification of crucial degrees of freedom, many-body symmetries, and scale separation • Focus on certain states, properties, and simple patterns • Phenomenological description of massive amounts of data provides crucial insights • The challenge is to relate these models to microscopic theory Casten, Papenbrock, van Kolck

27. Nuclear Open Quantum Systems Bertulani Complex-energy Shell Model Gamow Shell Model Ab-initio description of nuclear reactions scattering, fusion “First measurements of the differential cross sections for the elastic n-2H and n-3H scattering at 14.1 MeV using an Inertial Confinement Facility”, by J.A. Frenje et al., to be submitted • The n-3H elastic cross section for 14 MeV neutrons, important for understanding how the fuel is assembled in an implosion at NIF, was not known precisely enough. Nuclear theory was asked to help. • Delivered evaluated data with required 5% uncertainty and successfully compared to measurements using an Inertial Confinement Facility • A unification of structure and reaction aspects of weakly-bound or unbound nuclei based on the open quantum system formalism • Many phenomena (threshold effects, exceptional points, channel coupling…) are generic (atoms, molecules, nanotubes, quantum dots, microwave cavities,…)

28. Physics of rare isotopes is demanding Interactions Many-body Correlations Open Channels • Interactions • Poorly-known spin-isospin components come into play • Long isotopic chains crucial First Law: “The conservation of Information” (You will get nowhere by churning equations) … garbage in, garbage out… 11Li 45Fe 298U 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!” Second Law: “Do not trust arguments based on the lowest order of perturbation theory • Open channels • Nuclei are open quantum systems • Exotic nuclei have low-energy decay thresholds • Coupling to the continuum important • Many body correlations • Mean-field concept often questionable • Asymmetry of proton and neutron Fermi surfaces gives rise to new couplings Weinberg’s Laws of Progress in Theoretical Physics From: “Asymptotic Realms of Physics” (ed. by Guth, Huang, Jaffe, MIT Press, 1983)

29. Computational Strategy

30. Theoretical Tools and Connections to Computational Science 1Teraflop=1012 flops 1peta=1015 flops (today) 1exa=1018 flops (next 10 years) Tremendous opportunities for nuclear theory!

31. Transport in QCD (quenched) QCD critical point Hot and Dense QCD Quarkonium spectroscopy QCD at T>0 High-T limit of QCD EOS Continuum extrapolated QCD EOS Alpha particle Nucleon Spin Cold QCD Nuclear force Gluon distributions Deuteron Neutron EDM Excited hadron spectrum Nuclear Structure Light nuclei 0n bb rates for 48Ca Weakly bound nuclei Light ion reactions Neutron induced fission Triple a process Dynamics of neutron star crust Nuclear Astrophysics Global solar model Precision nuclear network Multienergy neutrino transport Precision neutrino network 3D supernova Accelerator Physics Isotope separator optimization Energy Recovery Linac Electron-cooling design 6D Vlasov 10-1 1 10 102 103 Petaflop-Yrs on Task Martin Savage

32. GFMC/ADLB application to 12C The load balancing version of GFMC was used to make calculations of 12C with a complete Hamiltonian (two- and three-nucleon potentials -- AV18+IL7) on 32,000 processors of the Argonne BGP. These are believed to be the best converged ab initio calculations of 12C ever made. The computed binding energy is 93.5(6) MeV compared to the experimental value of 92.16 MeV and the point rms radius is 2.35 fm vs 2.33 from experiment. The figure compares the computed 12C density with that extracted from electron-scattering experiments. Lusk, Pieper, Butler, SciDAC Review 17, Spring 2010

33. Multimodal fission in nuclear DFT • Staszczak et al. • Phys. Rev. C 80, 014309 (2009) Two-dimensional total energy surface for 258Fm in the plane of two collective coordinates: elongation, Q20, and reflection-asymmetry, Q30. Dashed lines show the fission pathways. The symmetry-unrestricted DFT calculations were performed at ORNL on a Cray XT3/XT4 Jaguar supercomputer systems. The novel features include the implementation of the modified Broyden’s method to solve self-consistent equations involving over 7,000,000 variables and the use of the Augmented Lagrangian Method to solve the optimization problem with many constraints.

34. Quality Control Integral to modern nuclear theory is the verification of methods and codes, the estimation of uncertainties, and assessment. • Verification and Validation • Cross-check of different methods and codes • Benchmarking • Uncertainty Quantification and • Error Analysis • Tools for correlation analysis to estimate errors and significance • Uncertainty analysis • Assessment • Development and application of statistical tools • Analysis of experimental data significance P.G. Reinhard and WN, Phys. Rev. C 81, 051303 (R) (2010)

35. Quest for understanding the neutron-rich matter on Earth and in the Cosmos Wambach RNB facilities Nuclear matter equation of state Nuclear observables Nuclear interactions Many-body theory Neutron star crust Astronomical observables Microphysics (transport,…)

36. Summary • The nuclear many-body problem is very complex, computationally difficult • With a fundamental picture of nuclei based on the correct microphysics, we can remove the empiricism inherent today, thereby giving us greater confidence in the science we deliver and predictions we make • We need to improve predictive capability by developing methods to quantify uncertainties • Large international coherent theory effort is needed to make progress • Strong coupling to experiment and RNB science in particular. Crucial role of large infrastructures • New-generation computers will continue to provide unprecedented opportunities • Impossible becomes possible • Collaboration with computer scientists and applied mathematicians is the key Guided by data on short-lived nuclei, we are embarking on a comprehensive study of all nuclei based on the most accurate knowledge of the strong inter-nucleon interaction, the most reliable theoretical approaches, and the massive use of the computer power available at this moment in time. The prospects look good.

37. Backup

38. Hadronic many-body problem Low-lying Hadron Spectrum: LQCD Mass from nothing: DCSB Dürr et al., Science 322, 1224 (2008) DSE and Lattice NN scattering Beane et al. PRL 97, 012001 (2006)

39. Shell structure: a moving target Old paradigms revisited. Crucial input for theory N=20 N=28 Shell energy NSCL GANIL GSI RIBF ANL M. Bender et al. Phys. Lett. B 515, 42–48 (2001)

40. Quality Control Integral to this project is the verification of methods and codes, the estimation of uncertainties, and assessment. • Verification and Validation • Cross-check of different methods and codes • Benchmarking • Uncertainty Quantification and • Error Analysis • Tools for correlation analysis to estimate errors and significance • Uncertainty analysis • Assessment • Development and application of statistical tools • Analysis of experimental data significance Earlier fit (some masses from systematics) Final fit

41. Nuclei: open quantum systems N-2 Z+1 N-2 Z+1 N-1 Z+1 N-1 Z+1 N Z+1 N Z+1 N+1 Z+1 N+1 Z+1 N+2 Z+1 N+2 Z+1 N-2 Z N-1 Z N Z N+1 Z N+2 Z N-2 Z N-1 Z N Z N+1 Z N+2 Z N-2 Z-1 N-1 Z-1 N Z-1 N+1 Z-1 N+2 Z-1 N-2 Z-1 N-1 Z-1 N Z-1 N+1 Z-1 N+2 Z-1 open quantum systems interactions correlations many-body techniques