Nuclear Structure – Current Directions A Thematic Overview R. F. Casten

Temperature T c Quarks and Gluons Critical Point? Color Super- Conductor ? Early Universe Neutron stars Lattice QCD Hadrons Nucleon Nuclei Net Baryon Density

QCD Vacuum Bare Nucleon-Nucleon Interactions Mean Field Models Collective models Neutron Number Proton Number Shell Model(s) Microscopic Ab Initio (GFMC...) Quark-Gluon Interactions Effective Interactions QCD Vacuum

Distance Energy many body systems effective NN force heavynuclei few body systems free NN force fewbody nucleonQCD quarksgluons vacuum quark-gluonsoupQCD relativistic heavy ions electronscattering radioactivebeams The Nuclear Many-Body Problem Energy, Distance, Complexity

The study of nuclei is a forefront area of science that links the Standard Model, QCD phenomena, many-body systems, and the cosmos. Goal: a comprehensive description of nuclei and their reactions Nuclear structure and reactions go beyond nuclei per se: –Understanding the quantum many-body problem at variousdistance/energy scales –Testing the fundamental laws of nature –Understanding stellar evolution and the origin of the elements –Society (national security, energy, medicine…) Both theory and experiment are needed. The Nucleus: an integral part of nuclear science

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?

Overarching goal: This has been a lofty and ambitious goal in nuclear science for over fifty years “Unified” does not mean that there is a single theoretical method that will work in all cases –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 “nuclei” ranging from the deuteron to neutron stars 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 by an underlying use of the constituents and the interactions between them Nuclear Structure Theory

The New Frontiers of Physics with Exotic Nuclei We can customize our system – fabricate “any” nucleus (designer nuclei) controlling the number of constituent protons and neutrons to isolate and amplify specific physics or interactions Four Frontiers 1.Proton Rich Nuclei 2.Neutron Rich Nuclei 3.Heaviest Nuclei 4.Evolution of structure within these boundaries Terra incognita — huge gene pool of nuclei A new era in Nuclear Structure Physics

neutrons protons rp process Crust processes neutron-Star KS s-processs-process r process stellar burning p process Supernova E 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? 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) U Nova T Pyxidis Masses and drip lines Nuclear reaction rates Weak decay rates Electron capture rates Neutrino interactions Equation of State Fission processes Nuclear Input (experiment and theory)

Themes and challenges of Modern Science Complexity out of simplicity How the world, with all its apparent complexity and diversity can be constructed out of a few elementary building blocks and their interactions Simplicity out of complexity How the world of complex systems can display such remarkable regularity and simplicity Understanding the nature of the physical universe Manipulating nature for the benefit of mankind Nuclei: Two-fluid, many-body, strongly-interacting, quantal systems provide wonderful laboratories for frontier research in all four areas

Nuclear collective motion What is the origin of ordered motion of complex nuclei? Complex systems often display astonishing simplicities. Nuclei are no exception. How is it that a heavy nucleus, with hundreds of rapidly moving nucleons, can exhibit collective motion.

Protons, neutrons — fermions j = half-integer (orbital + intrinsic) Pauli Principle: At most 2j + 1 particles in a given orbit Phonons — bosons Two views of nuclear structure Single-particle motionBulk collective motion Single-particle excitations Macroscopic shape with residual interactions of nuclear matter

r = |r i - r j |  V ij r UiUi Microscopy, mean field, shell structure Clusters of levels  shell structure Pauli Principle (≤ 2j+1 nucleons in orbit with ang. mom. j)  magic numbers, inert cores, valence nucleons Many-body  few-body: each body counts. Addition of 2 neutrons in a nucleus with 150 can drastically alter structure  =  nl, E = E nl H.O. E = ħ  (2n+l) E (n,l) = E (n-1, l+2) E (2s) = E (1d)

Independent Particle Motion (particles in a box) Mottleson Importance of shell gaps, magic numbers, and shell structure is not just a matter of details but fundamental to our understanding of one of the most basic features of nuclei– independent particle motion. If we don’t understand the basic quantum levels of nucleons in the nucleus, we don’t understand nuclei. Many aspects: Changing magic numbers, intruder orbits, residual interactions, correlations, collectivity, binding (e.g., drip lines, superheavies), and regularities. Perhaps counter-intuitively, the emergence of specific forms of nuclear collectivity depends on independent particle motion (and the Pauli Principle).

Pairing (in nuclei and nuclear matter)  Unique nuclear features: surface effects/finite size, kinds of Cooper pairs,  Essential for existence of weakly-bound nuclei; continuum scattering  Various density regimes of strength  Crucial for many-body dynamics, skin modes, pair localization  Connection to other fields (BECs, CSC) Manifestations: Energy gaps in even-even nuclei; Compression of levels in odd-A nuclei Odd-even mass differences Moments of inertia and rotational motion Quenching of Coriolis coupling Structural evolution in an Ising context; H = H sph + H Coll : Sph.-Def. Competition Structural singularities in N = Z nuclei

p-n interactions Empirical R 4/2 First direct correlation of empirical p-n interaction strengths with empirical growth rates of collectivity Strongest along diagonal where highest p-n overlaps occur

Approaches to nuclear structure Ab initio Configuration interaction Density Functional Theory Theoretical approaches overlap and need to be bridged Roadmap Collective and Algebraic Models

Approaches to Nuclear Structure Microscopic – Approximate solutions to real nuclei Effective Interactions Ab initio, No core, Monte Carlo Density Functional Theory Enormously complex, numerically intensive. However, revolutionary advances, greatly enhanced ability to predict wide variety of nuclei  promise of a comprehensive theory Macroscopic – Exact solutions to ideal nuclei Geometric symmetries. Simple patterns, quantum nos., Selection rules Analytic, Intuitive understanding -- WHAT symmetries? Challenge to microscopy – Why THESE symmetries, which nuclei, why in THESE nuclei? C o m p l e m e n t a r i t y

Ab initio: GFMC, NCSM, CCM (nuclei, neutron droplets, nuclear matter) S. Pieper, ANL 1-2% calculations of A = 6 – 12 nuclear energies are possible excited states with the same quantum numbers computed NN NNN

Density Functional Theory Asymptotic Freedom ( for theorists )

New Features in Weakly Bound Nuclei New form of matter – low density, diffuse, spatially extended, nearly pure neutron matter Density (log) Radius (fm) p-n core n-skin Normal nuclear density V (r) r Halo Nuclei 11 Li Spatially extended wave functions V (r) r Diffuse Normal potential Altered shell structure

Possible Changes in Structure for Skin Nuclei 82 1g N=5 N=4 2d 3s 1h 2f 3p g 9/2 g 7/2 d 5/2 d 3/2 s 1/2 h 11/2 p 3/2 h 9/2 p 1/2 i 13/ 2 f 5/2 f 7/ g 9/2 g 7/2 d 5/2 d 3/2 s 1/2 h 11/2 h 9/2 f 5/2 f 7/2 p 3/2 p 1/2 harmonic oscillator harmonic oscillator very diffuse surface neutron drip line very diffuse surface neutron drip line no spin orbit exotic nuclei/ hypernuclei no spin orbit exotic nuclei/ hypernuclei around the valley of  -stability around the valley of  -stability J. Dobaczewski and W. Nazarewicz

SUPERHEAVIES

Complementarity of macroscopic and microscopic approaches. Why do certain nuclei exhibit specific symmetries and not others? Why these specific evolutionary trajectories? What unknown regularities appear along the Arc? What will happen far from stability? Classifying Structure -- The Symmetry Triangle of Collective Behavior Sph. Deformed E(5) X(5) Dynamical Symmetries, Phase Transitions, Critical Point Symmetries, Order and Chaos Landau Theory

Neutron “skins” near the neutron drip line Outer regions of low density nearly pure neutron matter Skins and Skin Modes p p nn

Stopped Beam Experiments (Traps) (Traps) ISOL Target/Ion Extraction Reaccelerated Beam Experiments Experiments SecondAcceleratorSecondAccelerator Fast Beam Experiments Exotic Ion Beam Exotic Ions Exotic Ion Exotic Ion Beam Beam High Energy Proton Driver High Energy Proton Driver Fragmentation Target and Ion Separator Exotic Ions High Energy Heavy Ion Driver High Energy Heavy Ion Driver Intense Proton Beam Intense Stable Ion Beam GasStoppingGasStopping Production and use of Exotic Isotopes

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

Exotic Nuclei Paradigm-Changing Discovery Potential Complexity – Simplicity Comprehensive Understanding of Atomic Nuclei Links to nano-science, high energy physics, and the cosmos Applications

Jargon  Key to conference is communication Biggest bottleneck to communication is jargon. Examples (some may shock you): –Jlab: Partons, generalized parton distributions, the sea, quantitative relation of Q 2 to size, Bjorken x… –RIA: island of inversion, yrast states, gamma vibrations, intruder states, K quantum number, B(E2) values, density functional theory…

Thanks to many from whom I have stolen slides, especially Witek Have a great Workshop !!!