Nuclear Structure – Current Directions

A Thematic Overview

R. F. Casten

Tem

per

atu

re

Tc

Quarks and Gluons

Critical Point?

Color Super-Conductor ?

Ea

rly

Un

ive

rse

Neutron stars

Lattice QCD

Hadrons

Nucleon

Nuclei

Net Baryon Density

QCD Vacuum

1001 5 10 50

1

10

100

Bare Nucleon-Nucleon Interactions

Mean Field ModelsCollective models

Neutron Number

Pro

ton

Num

ber

Shell Model(s)

MicroscopicAb Initio(GFMC...)

Quark-Gluon Interactions

EffectiveInteractions

QCD

QCDVacuum

Distance

Energy

many body systemsmany body systemseffective NN forceeffective NN force

heavyheavynucleinuclei

few body systemsfew body systemsfree NN forcefree NN force

fewfewbodybody

nucleonnucleonQCDQCD

quarksquarksgluonsgluons

vacuumvacuum

quark-gluonquark-gluonsoupsoupQCDQCD

relativi

stic

relativi

stic

heavy io

nsheav

y ions

electronelectron

scatteri

ngscat

tering

radioact

iveradi

oactive

beamsbeams

The Nuclear Many-Body ProblemEnergy, 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

The Nucleus: an integral part of nuclear science

femto…femto…femto…femto…

Physicsof Nuclei

subfemto…subfemto…subfemto…subfemto… •Origin of NN interaction•Many-nucleon forces•Effective fields

nano…nano…nano…nano…

Quantum ma

ny-

body physi

cs

•In-medium interactions•Symmetry breaking•Collective dynamics•Phases and phase transitions•Chaos and order•Dynamical symmetries•Structural evolution

Giga…Giga…Giga…Giga…

NuclearAstrophysics

•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

Nuclear Structure Theory

The New Frontiersof 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 p

roce

ss

rp p

roce

ss

Crust

proces

ses

Crust

proces

sesneutron-Star

KS 1731-260

s-pro

cess

s-pro

cess

s-pro

cess

s-pro

cess

r processr processr processr process

stellar burning

stellar burning

p proces

s

p proces

s

p proces

s

p proces

s

Supernova

E0102-72.3

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

331

330

329

328

327

Fre

quen

cy (

Hz )

10 15 20

4U1728-34

Nova

T Pyxidis

Masses and drip linesNuclear reaction ratesWeak decay ratesElectron capture ratesNeutrino interactionsEquation of StateFission 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.

0 10000

50000

100000

150000

200000

counts

energy (keV)

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 structureSingle-particle motion Bulk collective motion

Single-particle excitations Macroscopic shapewith residual interactions of nuclear matter

r = |ri - rj|

Vij

r

Ui

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 = EnlH.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 nucleiOdd-even mass differencesMoments of inertia and rotational motionQuenching of Coriolis coupling

Structural evolution in an Ising context; H = Hsph + HColl : Sph.-Def. Competition

Structural singularities in N = Z nuclei

p-n interactions

Empirical R4/2

First direct correlation of empirical p-n

interactionstrengths with

empiricalgrowth ratesof collectivity

Strongest along diagonal where

highest p-n overlaps occur

Approaches to nuclear structureApproaches to nuclear structure

Ab initio

Configuration interaction

Density Functional Theory

Theoretical approaches overlap and need to be bridged

Theoretical approaches overlap and need to be bridged

Roadmap

Collective andAlgebraic 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?

Complementarity

Ab initio: GFMC, NCSM, CCM(nuclei, neutron droplets, nuclear matter)

S. Pieper, ANL1-2% calculations of A = 6 – 12 nuclear energies are possibleexcited states with the same quantum numbers computed

NN

NNN

Density Functional Theory

Asymptotic Freedom (for theorists)

New Features in Weakly Bound Nuclei

0 10 20

New form of matter – low density, diffuse, spatially

extended, nearly pure neutron matter

Den

sit

y (l

og

)

Radius (fm)

p-ncore

n-skin

Normal nuclear density

V (r)

r

Halo Nuclei

11Li

Spatially extended wave functions

V (r)

r

Diffuse

Normal potential

Altered shell structure

Possible Changes in Structure for Skin Nuclei

8282

1g

N=5

N=4 2d

3s

1h

2f3p

g9/

2

g7/

2d5/

2

d3/

2s1/

2

h11/

2

p3/

2h9/

2

p1/

2i13/

2

f5/2

f7/2

5050

126126

g9/

2

g7/

2

d5/

2

d3/

2s1/

2

h11/

2

h9/

2f5/2

f7/2

p3/

2

p1/

2

harmonicoscillato

r

harmonicoscillato

r

very diffusesurface

neutron drip line

very diffusesurface

neutron drip line

no spinorbitexotic nuclei/

hypernuclei

no spinorbitexotic nuclei/

hypernuclei

around thevalley of

-stability

around thevalley 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 Classifying Structure -- The Symmetry Triangle of Collective BehaviorCollective Behavior

Sph.

Def

orm

ed

E(5)

X(5)

Dynamical Symmetries, Phase Transitions, Critical Point Symmetries, Order and Chaos

Landau Theory

Neutron “skins” near the neutron drip lineOuter regions of low density nearly pure neutron matter

Skins and Skin Modes

pp

nnnn

Stopped Beam Stopped Beam Experiments Experiments

(Traps)(Traps)

Stopped Beam Stopped Beam Experiments Experiments

(Traps)(Traps)

ISOL ISOL Target/Ion Target/Ion ExtractionExtraction

ISOL ISOL Target/Ion Target/Ion ExtractionExtraction

ReacceleratReaccelerated Beamed Beam

ExperimentsExperiments

ReacceleratReaccelerated Beamed Beam

ExperimentsExperiments

SecondSecondAcceleratoAccelerato

rr

SecondSecondAcceleratoAccelerato

rr

Fast Beam Fast Beam ExperimentsExperimentsFast Beam Fast Beam ExperimentsExperimentsExotic Ion BeamExotic Ion Beam

Exotic Ion BeamExotic Ion Beam

Exotic Exotic IonsIons

Exotic Exotic IonsIons

Exotic Exotic IonIon BeamBeam

Exotic Exotic IonIon BeamBeam

High Energy High Energy Proton Proton DriverDriver

High Energy High Energy Proton Proton DriverDriver

FragmentatioFragmentation Target and n Target and

Ion Ion SeparatorSeparator

FragmentatioFragmentation Target and n Target and

Ion Ion SeparatorSeparator

Exotic Exotic IonsIons

Exotic Exotic IonsIons

High Energy High Energy Heavy Ion Heavy Ion DriverDriver

High Energy High Energy Heavy Ion Heavy Ion DriverDriver

Intense Intense Proton BeamProton Beam

Intense Intense Proton BeamProton Beam

Intense Intense Stable Ion Stable Ion

BeamBeam

Intense Intense Stable Ion Stable Ion

BeamBeam

Gas Gas StoppinStoppin

gg

Gas Gas StoppinStoppin

gg

Production and use of Exotic Isotopes

RIBF

Radioactive Ion Beam Facilities Timeline

20002000 20052005 20102010 20152015 20202020

CARIBU@ATLAS

NSCL

HRIBF

RIF

ISOLDE

ISAC-II

SPIRAL2

SIS FAIR

RARF

ISAC-I

In FlightISOLFission+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 Q2 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 !!!