Advances in Computational Nuclear Structure

1. Computing Atomic Nuclei Witold Nazarewicz (UTK/ORNL/Warsaw) Colloquium, University of Jyväskylä, October 10, 2008 • Prelude • Introduction • Progress report • Connections and relevance • Computational strategy • Perspectives

2. Prelude

3. Ulm 1482 Homann 1720

4. Some nuclei are more important than others - + - + - + + - + - 149Tb 18F,22Na 225Ra Over the last decade, tremendous progress has been made in techniques to produce and characterize designer nuclei, rare atomic nuclei with characteristics adjusted to specific research needs nuclear structure tests of fundamental laws of nature 45Fe applications astrophysics

5. 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

6. Introduction

7. Nuclear Structure

8. Designer Nuclei in Nuclear Landscape 62Ga 78Ni 134Sn 45Fe 11Li 7H 208Hg 42Si 25O 45Fe 101Sn 149Tb 70Se 42Al 43Al 40Mg 250Fm Novel decay modes 180Hg 95Cd 96Cd 82 126 Extending the limits 82 1228 28 20 50 8 28 Probing existence/changes of the shell structure far from stability 2 20 8 2

9. Nuclear Structure Theory Progress Report

10. 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 • Short-range repulsion: a red herring! • Accurate ab-initio methods allow for interaction tests • Worldwide attack on nuclear energy density functional • Quantitative microscopic nuclear structure • Integrating nuclear structure and reactions • High-performance computing continues to revolutionize microscopic nuclear many-body problem: impossible becomes possible

11. Links to CMP/AMO science!!! number of nuclei < number of processors!

12. 1, 2, 3, 4, 208, ∞

13. Ab initio theory for light nuclei and nuclear matter Ab initio: GFMC, NCSM, CCM (nuclei, neutron droplets, nuclear matter) • Quantum Monte Carlo (GFMC) 12C • No-Core Shell Model 14F • Coupled-Cluster Techniques 56Ni • Faddeev-Yakubovsky • Bloch-Horowitz • … • Input: • Excellent forces based on the phase shift analysis • EFT based nonlocal chiral NN and NNN potentials

14. NN and NNN interactions Effective-field theory (χPT) potentials Vlow-k unifies NN interactions at low energy Bogner, Kuo, Schwenk, Phys. Rep. 386, 1 (2003) • Quality two- and three-nucleon interactions exist • Not uniquely defined (local, nonlocal) • Soft and hard-core N3LO: Entem et al., PRC68, 041001 (2003) Epelbaum, Meissner, et al.

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

16. Coupled Cluster Theory Size Extensive! converged CCSD results for medium-mass nuclei with N3LO Medium-mass nuclei from chiral nucleon-nucleon interactions G. Hagen, T. Papenbrock, D.J. Dean and M. Hjorth-Jensen, Phys. Rev. Lett. 101, 092502 (2008)

18. Mean-Field Theory ⇒ Density Functional Theory • 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.

19. Nuclear DFT: works well for BE differences Nature 449, 1022 (2007) S. Cwiok, P.H. Heenen, WN Nature, 433, 705 (2005) Stoitsov et al., 2008 • Global DFT mass calculations: HFB mass formula: m~700keV

20. Towards spectroscopic-quality nuclear density functional Functional form and error estimation J. Toivanen et FIDIPRO, Phys. Rev. C 78, 034306 (2008) FIDIPRO collaboration

21. Neutron-rich matter and neutron skins Pygmy dipole Furnstahl 2002 skin 208Pb pressure Bulk neutron matter equation of state Constraints on the mass-vs-radius relationship of neutron stars Giant dipole E1 strength GSI 2005

22. Prog. Part. Nucl. Phys. 59, 432 (2007)

23. A remark: physics of exotic nuclei is demanding Interactions Many-body Correlations Open Channels • Interactions • Poorly-known spin-isospin components come into play • Long isotopic chains crucial exotic nuclei • Open channels • Nuclei are open quantum systems • Exotic nuclei have low-energy decay thresholds • Coupling to the continuum important • Virtual scattering • Unbound states • Impact on in-medium Interactions • Configuration interaction • Mean-field concept often questionable • Asymmetry of proton and neutron Fermi surfaces gives rise to new couplings • New collective modes; polarization effects

24. Connections and Relevance

25. Connections to quantum many-body systems Complex Systems • Understanding the transition from microscopic to mesoscopic to macroscopic • Symmetry breaking and emergent phenomena • Pairing in finite systems • Quantum chaos • Open quantum systems • Dynamical symmetries and collective dynamics • Dilute fermion matter: • strongly correlated • very large scattering length (unitary limit) • Low-density neutron matter • Cold fermions in traps

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

27. 2008 Nobel Prize in Physics

28. Superallowed Fermi 0+ 0+-decay studies (testing the unitarity of the Cabibbo-Kobayashi-Maskawa matrix) 62Ga@ TRIUMF (2006-2008) T1/2=116.100(22)ms, BR=99.858(8)% Jyväskylä (2008) BR=99.893(24) 34Ar, 34Cl@TAMU (2006) T1/2=843.8(4) ms,1.5268(5)s 38mK@TRIUMF (2008) BR=99.967(4)% with new symmetry-breaking corrections: with new symmetry-breaking corrections: 46V@ ANL (2005) Q=7052.90(40) keV 46V@ Jyväskylä (2006) Q=7052.72(31) keV Munich tandem (2008) Q=7052.10(31) keV 50Mn,54Co@Jyväskylä (2007) Q=7634.48(7), 8244.54(10) keV 26mAl,42Sc@Jyväskylä (2006) Q=4232.83(13),6426.13(21) keV 26mAl @ISOLDE (2008) Q Half-life Q-value 0.9996(7) Branching Ratio • more cases measured… stay tuned… • Advances in isospin mixing calculations 38mK

29. Computational Strategy

30. Connections to computational science 1Teraflop=1012 flops 1peta=1015 flops (next 2-3 years) 1exa=1018 flops (next 10 years)

31. Universal Nuclear Energy Density Functional http://unedf.org/ • Funded (on a competitive basis) by • Office of Science • ASCR • NNSA • 15 institutions • ~50 researchers • physics • computer science • applied mathematics • foreign collaborators • FIDIPRO • Warsaw • France/Belgium • Japan • 5 years …unprecedented theoretical effort ! [See http://www.scidacreview.org/0704/html/unedf.html by Bertsch, Dean, and Nazarewicz]

33. Example: Large Scale Mass Table Calculations Science scales with processors M. Stoitsov HFB+LN mass table, HFBTHO INCITE award Dean et al. 17.5M hours Even-Even Nuclei • The SkM* mass table contains 2525 even-even nuclei • A single processor calculates each nucleus 3 times (prolate, oblate, spherical) and records all nuclear characteristics and candidates for blocked calculations in the neighbors • Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration) Jaguar Cray XT4 at ORNL All Nuclei • 9,210 nuclei • 599,265 configurations • Using 3,000 processors - about 25 CPU hours see MassExplorer.org

34. Multimodal fission in nuclear DFT • Staszczak, A.Baran, • J. Dobaczewski, W.N.

35. Supernova Modeling Blondin, Mezzacappa, Nature 445, 58 (2007)

36. Strategy… From Ian Thompson

37. (n+AXi) at energy Eprojectile Computational Workflow Eprojectile (UNEDF work) Target A = (N,Z) Ground state Excited states Continuum states TransitionDensities(r) Structure ModelMethods: HF, DFT, RPA, CI, CC, … Transitions Code UNEDF: VNN, VNNN…  Folding Code Veff for scattering Transition Potentials V(r) (Later: density-dependent & non-local) (other work) Deliverables Inelastic production Compound production Coupled ChannelsCode: FRESCO Partial Fusion Theory Hauser-Feshbach decay chains Residues (N’,Z’) Delayed emissions Compound emission Elastic S-matrix elements Voptical Preequilibrium emission Prompt particle emissions Fit Optical Potential Code: IMAGO Global optical potentials KEY: Code Modules UNEDF Ab-initio Input User Inputs/Outputs Exchanged Data Future research UNEDFReaction work

38. Perspectives

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

40. Why us? Why now? There is a zoo of nuclear functionals on the market. What makes us believe we can make a breakthrough? • Solid microscopic foundation • link to ab-initio approaches • limits obeyed (e.g., unitary regime) • Unique opportunities provided by coupling to CS/AM • Comprehensive phenomenology probing crucial parts of the functional • different observables probing different physics • Stringent optimization protocol providing not only the coupling constants but also their uncertainties (theoretical errors) • Unprecedented international effort • Unique experimental data available (in particular: far from stability; link to RNB science) Conclusion: we can deliver a well theoretically founded EDF, of spectroscopic quality, for structure and reactions, based on as much as possible ab initio input at this point in time

41. Conclusions • Exciting science; old paradigms revisited • Interdisciplinary (quantum many-body problem, cosmos,…) • Relevant to society (energy, medicine, national security, …) • Theory gives the mathematical formulation of our understanding and predictive ability • New-generation computers provide unprecedented opportunities • Large coherent international theory effort is needed to make a progress 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. Thank You

42. Backup

43. Charge radii of halo nuclei measured at ANL/TRIUMF/SPIRAL Radioactive Ion Science Timeline Shell structure changes in exotic nuclei 6-He enhanced reaction cross sections at TwinSol Trapped francium at Stony Brook Studies with accelerated 132-Sn and 82-Ge at HRIBF Science Technology/facilities Applications 21-Na -correlations at Berkeley Shell structure of exotic nuclei with knockout reactions at NSCL Charge radius of 6-He at ATLAS 78-Ni lifetime at NSCL Nobel Prize for nucleo-synthesis Relativistic Coulomb excitation of 32-Mg at RIKEN First in-flight fragmentation experiments at Berkeley Direct radiative capture with 21-Na at ISAC-I 38m-K -correlations at TRINAT First application of radiochemistry to inertial fusion target diagnosis 100-Sn discovered at GSI and GANIL Nobel Prize for magic numbers First mass measurement of short-lived nuclei at PS in CERN First accelerated beam experiment (13-N) at LLN Parity violation in beta decay Neutron halos discovered at Berkeley beta-NMR demonstrated at ANL Two-proton emitters discovered at GSI and GANIL BBHF theory of nucleosynthesis Explanation of magic numbers Momentum distribution of halo at RIKEN Invention of PET scanner Z=105 (Db) discovered in Dubna Radiochemistry used to monitor nuclear weapons tests Mössbauer effect Projectile-fisson of 238-U and Z=112 discovered at GSI Measurement of half-life of r-process nucleus Proton emission discovered at Harwell BBHF theory of nucleosynthesis Z=100 (Fm) discovered Z=108 chemistry at GSI Fermi builds controlled fission reactor Acceleration of RIBs at LLN First in-flight separator at Oak Ridge Beta-delayed proton radioactivity discovered at Dubna and McGill Island of inversion at N=20 and shape coexistence in proton-rich Hg at iSOLDE ISOLTRAP Targeted alpha therapy at ISOLDE IGISOL at Jyväskylä Becquerel discovers radioactivity The Curies discover polonium First ISOL experiment in Copenhagen Laser ion source at ISOLDE Neutron-induced fission Isotopic tracer technique by von Hevesy Nobel Prize for magic numbers NSCL Nobel Prize for unified model 6-He produced in Copenhagen Explanation of magic numbers SPIRAL1 RIKEN ISOLDE GSI HRIBF GANIL ISAC-I REX-ISOLDE 1900 1930 1960 2000

44. Based on Pethick & Ravenhall Ann. Rev. Nucl. Part. Sci. 45 (1995) 429

45. Short-range correlations: a red herring

46. Hagen et al, ORNL/UTK Ab initio: Reactions Nollett et al, ANL Coupled Clusters CC GFMC Quaglioni & Navratil, LLNL 2008 No Core Shell Model +Resonating Group Method 11Be: arXiv:0804.1560

47. How many parameters are really needed? Spectroscopic (s.p.e.) Global (masses) Bertsch, Sabbey, and Uusnakki Phys. Rev. C71, 054311 (2005) Kortelainen, Dobaczewski, Mizuyama, Toivanen, arXiv:0803.2291 New optimization strategy and protocol needed

48. Alignment of variables related to neutron skin: =1: full alignment/correlation =0: not aligned P.G. Reinhard W. Nazarewicz in preparation

49. SciDAC 2 Project:Building a Universal Nuclear Energy Density Functional • Understand nuclear properties “for element formation, for properties of stars, and for present and future energy and defense applications” • Scope is all nuclei, with particular interest in reliable calculations of unstable nuclei and in reactions • Order of magnitude improvement over present capabilities • Precision calculations • Connected to the best microscopic physics • Maximum predictive power with well-quantified uncertainties • [See http://www.scidacreview.org/0704/html/unedf.html • by Bertsch, Dean, and Nazarewicz]

50. Construction of the functional Perlinska et al., Phys. Rev. C 69, 014316 (2004) • +isoscalar and isovector densities: • spin, current, spin-current tensor, kinetic, and kinetic-spin • + pairing densities isoscalar (T=0) density isovector (T=1) density p-h density p-p density (pairing functional) Most general second order expansion in densities and their derivatives • Constrained by microscopic theory: ab-initio functionals provide quasi-data! • Not all terms are equally important. Usually ~12 terms considered • Some terms probe specific experimental data • Pairing functional poorly determined. Usually 1-2 terms active. • Becomes very simple in limiting cases (e.g., unitary limit)