1 Nuclear Structure’07: Exciting, Broad, Relevant Witold Nazarewicz (Tennessee) Introduction Progress report Connections Relevance Perspectives

Bordone, 1528 Schenk, Valk, 1700 Mercator, 1648

Introduction

4 Nuclear science is entering a new era of discovery in understanding how nature works at the most basic level and in applying that knowledge in useful ways. National Academy 2007 RISAC Report Nuclear structure. A FRIB would offer a laboratory for exploring the limits of nuclear existence and identifying new phenomena, with the possibility that a more broadly applicable theory of nuclei will emerge. FRIB would investigate new forms of nuclear matter such as the large neutron excesses occurring in nuclei near the neutron drip line, thus offering the only laboratory access to matter made essentially of pure neutrons; a FRIB might lead to breakthroughs in the ability to fabricate the super- heavy elements with larger neutron numbers that are expected to exhibit unusual stability in spite of huge electrostatic repulsion. Nuclear astrophysics. A FRIB would lead to a better understanding of key issues by creating exotic nuclei that, until now, have existed only in nature’s most spectacular explosion, the supernova. A FRIB would offer new glimpses into the origin of the elements, which are produced mostly in processes very far from nuclear stability and which are barely within reach of present facilities. A FRIB would also probe properties of nuclear matter important to theories of neutron-star crusts.

Weinberg’s Laws of Progress in Theoretical Physics From: “Asymptotic Realms of Physics” (ed. by Guth, Huang, Jaffe, MIT Press, 1983) 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!” Nuclear Structure

Overarching goal: –Self-bound, two-component quantum many-fermion system –Complicated interaction based on QCD with at least two- and three- nucleon components –We seek to describe the properties of finite and bulk nucleonic matter ranging from the deuteron to neutron stars and nuclear matter; including strange matter –We want to be able to extrapolate to unknown regions Theory of Nuclei To arrive at a comprehensive and unified microscopic description of all nuclei and low-energy reactions from the the basic interactions between the constituent protons and neutrons There is no “one size fits all” theory for nuclei, but all our theoretical approaches need to be linked. We are making great progress in this direction.

Questions and challenges

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

No shell closure for N=8 and 20 for drip-line nuclei; new shells at 14, 16, 32… Phys. Rev. Lett. 99, (2007) Nature 449, 1022 (2007)

number of nuclei ~ number of processors!

Ab initio: GFMC, NCSM, CCM (nuclei, neutron droplets, nuclear matter) GFMC: S. Pieper, ANL 1-2% calculations of A = 6 – 12 nuclear energies are possible excited states with the same quantum numbers computed  Quantum Monte Carlo (GFMC) 12 C  No-Core Shell Model 13 C  Coupled-Cluster Techniques 40 Ca  Faddeev-Yakubovsky  Bloch-Horowitz  …  Quantum Monte Carlo (GFMC) 12 C  No-Core Shell Model 13 C  Coupled-Cluster Techniques 40 Ca  Faddeev-Yakubovsky  Bloch-Horowitz  … Input: Excellent forces based on the phase shift analysis EFT based nonlocal chiral NN and NNN potentials The nucleon-based description works to <0.5 fm deuteron’s shape

Diagonalization Shell Model (CI) (medium-mass nuclei reached;dimensions 10 9 !) Honma, Otsuka et al., PRC69, (2004) and ENAM’04 Martinez-Pinedo ENAM’04

13

A remark: physics of exotic nuclei is demanding Interactions Poorly-known spin-isospin components come into play Long isotopic chains crucial Interactions Many-body Correlations Open Channels 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

S. Cwiok, P.H. Heenen, W. Nazarewicz Nature, 433, 705 (2005) Large-scale Calculations Stoitsov et al., PRL 98, (2007) Global DFT mass calculations: HFB mass formula:  m~700keV Taking advantage of high-performance computers

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

The nucleus is a correlated open quantum many-body system Environment: continuum of decay channels `Alignment’ of w.b. state with the decay channel 16 O Spectra and matter distribution modified by the proximity of scattering continuum Thomas-Ehrmann effect 13 C 7 13 N /2  C+n 12 C+p 1/2  3/2 

G. Hagen et al., nucl-th/ P. Navratil et al., PRC 73, (2006) K. Nollett et al., nucl-th/ CC NCSM GFMC GSM

Connections

neutrons protons rp process Crust processes n-Star s-processs-process r process stellar burning p process 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? Time (s) X-ray burst Frequency (Hz) Nova 4U T Pyxidis KS

21 Understanding the transition from microscopic to mesoscopic to macroscopic Quantum Chaos and the Random Matrix Theory Superconductivity Loosely bound and open systems Dynamical symmetries and Quantum Phase Transitions Coulomb frustration Fermionic sign problem Connections to complex many-body systems !

femto…femto… Physics of Nuclei subfemto…subfemto… Origin of NN interaction Many-nucleon forces Effective fields nano…nano… Quantum many- body physics In-medium interactions Symmetry breaking Collective dynamics Phases and phase transitions Chaos and order Dynamical symmetries Structural evolution Giga…Giga… Nuclear Astrophysics 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?

Relevance

Nuclear Science Applications LRP’07 report

Atom Trap Trace Analysis: 81 Kr dating MRI of inhaled polarized 129 Xe by a human

Advanced Fuel Cycles neutron-reaction cross sections from eV to 10 MeV the full range of (n,f), (n,n’), (n,xn), (n  ) reactions heavy transuranics, rare actinides, and some light elements (iron, sulfur) Quantified nuclear theory error bars Cross sections input to core reactor simulations (via data evaluation) BETTER CROSS SECTIONS AFFECT both SAFETY and COST of AFC reactors. Science Based Stockpile Stewardship Radiochemical analysis from days of testing: inference on device performance shows final products but not how they came to be. Typical example Yttrium charged particle out reaction. LESS THAN 10% of cross sections in region measured. Theory with quantifiable error bars is needed. Relevance of Nuclear Theory… Addressing national needs AFC workshop proceedings: The Stewardship Science Academic Alliance program workshop: These two examples point to the relevance of Nuclear Theory to OTHER programs of national interest. Quantifiable theory error bars is a key desire. Room for large-scale computing (SciDAC)

Perspectives

Long Range Plan Recommendations for Nuclear Science 1.We recommend completion of the 12 GeV Upgrade at Jefferson Lab. The Upgrade will enable new insights into the structure of the nucleon, the transition between the hadronic and quark/gluon descriptions of nuclei, and the nature of confinement. 2.We recommend construction of the Facility for Rare Isotope Beams, FRIB, a world-leading facility for the study of nuclear structure, reactions and astrophysics. Experiments with the new isotopes produced at FRIB will lead to a comprehensive description of nuclei, elucidate the origin of the elements in the cosmos, provide an understanding of matter in the crust of neutron stars, and establish the scientific foundation for innovative applications of nuclear science to society. 3.We recommend a targeted program of experiments to investigate neutrino properties and fundamental symmetries. These experiments aim to discover the nature of the neutrino, yet unseen violations of time-reversal symmetry, and other key ingredients of the new standard model of fundamental interactions. Construction of a Deep Underground Science and Engineering Laboratory is vital to US leadership in core aspects of this initiative. 4.The experiments at the Relativistic Heavy Ion Collider have discovered a new state of matter at extreme temperature and density—a quark-gluon plasma that exhibits unexpected, almost perfect liquid dynamical behavior. We recommend implementation of the RHIC II luminosity upgrade, together with detector improvements, to determine the properties of this new state of matter.

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

RIBF Radioactive Ion Beam Facilities Timeline NSCL HRIBF FRIB ISOLDE ISAC-II SPIRAL2 SIS FAIR RARF ISAC-I In Flight ISOL Fission+Gas Stopping Beam on target SPIRAL

Young talent Focused effort Large collaborations Data from terra incognita High-performance computing Interaction with computer scientists What is needed/essential? unedf.org

Jaguar Cray XT4 at ORNL No. 2 on Top500 11,706 processor nodes Each compute/service node contains 2.6 GHz dual-core AMD Opteron processor and 4 GB/8 GB of memory Peak performance of over 119 Teraflops 250 Teraflops after Dec.'07 upgrade 600 TB of scratch disk space 1Teraflop=10 12 flops 1peta=10 15 flops (next 2-3 years) 1exa=10 18 flops (next 10 years) Connections to computational science

33 Example: Large Scale Mass Table Calculations Science scales with processors  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)  The even-even calculations define 250,754 configurations in odd-A and odd-odd nuclei assuming 0.5 MeV threshold for the blocking candidates  Using 10,000 processors - about 24 CPU hours Even-Even Nuclei Odd and odd-odd Nuclei M. Stoitsov, HFB+LN mass table, HFBTHO

34 At the end of the run: 2032 converge for up to 500 iterations 404 converge up to 1000 iterations 123 converge up to 2000 iterations 152 converge up to 6000 iterations 26 do not converge A typical run for the whole even-even mass chart contains about 2731 different bound nuclear states which identify the ground states of 1527 even-even nuclei.

35 Linear mixing Broyden M=3 Broyden M=7 194 Rn, HFB+LN, N sh =20 Sly4 + mixed   pairing Broyden Mixing Error Number of iterations

A. Staszczak, J. Dobaczewski, W. Nazarewicz, in preparation Bimodal fission in nuclear DFT nucl-th/ S. Umar and V. Oberacker Phys. Rev. C 76, (2007) TDHF description of heavy ion fusion

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

Conclusions Exciting science; old paradigms revisited Interdisciplinary (quantum many-body problem, cosmos,…) Relevant to society (national security, energy, medicine…) Theory gives the mathematical formulation of our understanding and predictive ability Experiment provides insights and verification New-generation computers provide unprecedented opportunities The study of nuclei makes the connection between the Standard Model, complex systems, and the cosmos 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

Backup

Different deformabilities! Shell effects in metastable minima seem to be under control P.H. Heenen et al., Phys. Rev. C57, 1719 (1998) Important data needed to fix the deformability of the NEDF: absolute energies of SD states absolute energies of HD states Advantages: large elongations weak mixing with ND structures Example: Surface Symmetry Energy Microscopic LDM and Droplet Model Coefficients: P.G. Reinhard et al. PRC 73, (2006)

Nuclear DFT Global properties, global calculations * Global DFT mass calculations: HFB mass formula:  m~700keV Taking advantage of high-performance computers M. Stoitsov et al. S. Goriely et al., ENAM’04

Cold gases, BEC’s, neutron matter

43 Connections to complex many-body systems Dilute Fermions with large/infinite scattering length [impact in nuclear, cold-atom physics, condensed matter and astrophysics (neutron star crust, cooling)] PRL 91, (2003) 172 citations EOS, pairing gap near unitarity predicted at T=0 and T>0 PRL 96, (2006) 43 citations DFT description: PRA 74, (R) (2006) EFT/RG treatment of cold atoms: cond-mat/ Pairing in asymmetric Fermi gasses: PRL 97, (2006) Coupled cluster theory, method of moments [impact in nuclear physics and quantum chemistry] PRL 92, (2004) DMRG approach to nuclei and open quantum systems Rep. Prog. Phys. 67, 513 (2004) Description of weakly-bound and unbound states of many-Fermion systems PRL 97, (2006) Shell model with random interactions [quantum chaos,quantum dots] PRL 93, (2004); PRB 72, (2005); PRB 74, (2006) Quantum phase transitions in mesoscopic systems [impact in nuclear, cold-atom, molecular physics] PRL 92, (2004); NPA 757, 360 (2005) Applications of SM and DFT to atomic physics: PRA66, (2002) Pairing correlations in ultra-small metallic grains (studies of the static-to-dynamic crossover): RMP 76, 643 (2004) !