• Introduction • General principles • Examples: quantitative nuclear theory

Nuclear structure approaches for the 21st century

Witek Nazarewicz (UTK/ORNL)

HITES 2012, New Orleans, June 4-7, 2012

• Introduction

• General principles

• Examples: quantitative nuclear theory

o Excellent spectrum of results presented at this meeting!

• Predictive capability

• Computing

• Summary

• A third rate theory forbids

• A second rate theory explains after the fact

• A first rate theory predicts

A. Lomonosov

Happy the man who has been able to discern the cause of things

Virgil, Georgica Theories

Models

•Fundamental aspects (reduction)

• Nature of building blocks

• Nature of fundamental interactions

•Self-organization of building blocks (emergence)

• Nature of composite structures and phases

• Origin of simple patterns in complex systems

The intellectual drivers of nuclear physics today

2007 NSAC Long Range Plan The Frontiers of Nuclear Science

14 questions in 2007 LRP

Similar classification present in nuclear theory:

the choice of building blocks is crucial!

Triple Portrait of Cardinal Richelieu, Philippe de Champaigne (c. 1640), National Gallery, London

microscopic mesoscopic empirical

Nuclear structure Nuclear reactions

Hot and dense quark-gluon matter Hadron structure

Nuclear astrophysics New standard model

Applications of nuclear science Hadron-Nuclear interface

R es ol ut io n

Third Law of Progress in Theoretical Physics by Weinberg:

“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!”

E ff e ct iv e F ie ld T he o ry

DFT collective and

algebraic models

CI ab initio

LQCD

quark

models

11

Li

208

Pb

298

U

Physics of nuclei is demanding

Input

Forces, operators

• rooted in QCD

• insights from EFT

• many-body interactions

• in-medium renormalization

• microscopic functionals

• low-energy coupling constants optimized to data

• crucial insights from exotic nuclei

Many-body dynamics

• many-body techniques o direct schemes

o symmetry-based truncations o symmetry breaking and

restoration

• high-performance computing

• interdisciplinary connections

Open channels

• nuclear structure impacted by couplings to reaction and decay channels

• clustering, alpha decay, and fission still remain major challenges for theory

• continuum shell model, ab-initio reaction theory and microscopic optical model

• unified picture of structure and reactions

Beane et al. PRL 97, 012001 (2006) NN scattering on Lattice

Essential links between hadrons and nuclei: Lattice QCD and EFT

The Nuclear Many-Body Problem

Eigenstate of angular momentum, parity, and

~isospin

coupled integro-differential

equations in 3A dimensions

Interfaces provide crucial clues Interfaces provide

crucial clues

dim ens ion of th e pr oble m

The nuclear landscape as seen by theorists …

High performance computing

provides answers to questions that

neither experiment nor analytic theory can address; hence, it becomes a

third leg supporting the field of

nuclear physics

The ADLB (Asynchronous Dynamic Load-Balancing) version of GFMC was used to make calculations of ¹²C with a complete Hamiltonian (two- and three-nucleon potential 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 ADLB (Asynchronous Dynamic Load-Balancing) version of GFMC was used to make calculations of ¹²C with a complete Hamiltonian (two- and three-nucleon potential 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.

12C in GFMC: Pieper et al.

Epelbaum et al., Phys. Rev. Lett. 106, 192501 (2011)

Lattice spacing 1.97 fm

Examples: Ab Initio

Coupled-cluster method

description of medium-mass open nuclear systems

G. Hagen et al., arXiv:1204.3612 (2012)

½⁺ virtual state

• Strong coupling to continuum for neutron rich calcium isotopes

• Level ordering of states in the gds shell is

contrary to naïve shell model picture

• Strong coupling to continuum for neutron rich calcium isotopes

• Level ordering of states in the gds shell is

contrary to naïve shell model picture

Examples: Configuration Interaction

Ab initio nuclear reactions

 Arrive at a fundamental understanding of nuclear properties from a unified theoretical standpoint rooted in the fundamental forces among nucleons

 Develop theoretical foundations for an accurate description of reactions between light ions in a thermonuclear environment

 Computational tools for addressing fusion reactions that power stars and Earth-based fusion facilities such as the National Ignition Facility (NIF)

 Provide research community with accurate evaluations and uncertainties for nuclear astrophysics and fusion diagnostic

Impact Objectives

Ab initio theory reduces uncertainty due to conflicting data

 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

 “Ab initio theory of light-ion reactions”, by P. Navrátil, S. Quaglioni, and R. Roth, J. Phys. Conf. Ser. 312, 082002 (2011)

 ``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., Phys. Rev. Lett. 107, 122502 (2011)

http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.107.122502

15

• Monte Carlo

• Importance-truncated NCSM

• Symmetry-based truncations

Ab initio symplectic no-core shell model

T Dytrych, K D Sviratcheva, J P Draayer, C Bahri, and J P Vary. J. Phys. G 35, 123101 (2008)

Symplectic Sp(3,R) symmetry-adapted basis

G. Rosensteel and D.J. Rowe, Phys. Rev. Lett. 38, 10 (1977)

first 0+ excited state of 16O first 0+ excited state of 16O

• Effective truncation scheme

• Very promising approach to cluster states

Mass table

Goriely, Chamel, Pearson: HFB-17 Phys. Rev. Lett. 102, 152503 (2009)

dm=0.581 MeV dm=0.581 MeV

Cwiok et al., Nature, 433, 705 (2005)

BE differences

Examples: Nuclear Density Functional Theory

Traditional (limited) functionals

provide quantitative description

The Nuclear Landscape

• Protons and neutrons formed 10^-6s-1s after Big Bang (13.7 billion years ago)

• H, D, He, Li, Be, B formed 3-20 min after Big Bang

• Other nuclei born later in heavy stars and supernovae

Example: Large Scale Mass Table Calculations

 5,000 even-even nuclei, 250,000 HFB runs, 9,060 processors – about 2 CPU hours

 Full mass table: 20,000 nuclei, 12M configurations — full JAGUAR Cray XT5 Skyrme-DFT mass table

0 4 8 12 16 20 24

S

( M e V )

Er

neutron number

80 100 120 140 160

experiment drip line

0 2 4

140 148 156 164

neutron number

0 4 8

58 62 66

proton number

N=76 _{154 162}

S2n (MeV) S2p (MeV)

FRDM HFB-21 SLy4 UNEDF1 UNEDF0 SV-min exp

Er

Description of observables and model-based extrapolation

• Systematic errors (due to incorrect assumptions/poor modeling)

• Statistical errors (optimization and numerical errors)

Erler et al., Nature (2012)

How many protons and neutrons can be bound in a nucleus?

Skyrme-DFT: 6,900±500

Skyrme-DFT: 6,900±500

The limits: Skyrme-DFT Benchmark 2012

0 40 80 120 160 200 240 280

neutron number

0 40 80 120

p ro to n n um b er

to n d r ip line

t w o - n e u t r o n d r i p l i n e

232 240 248 256

n e u t r o n n u m b e r

proton number

90 110

100 Z=50

Z=82

Z=20

N=50

N=82

N=126

N=20

N=184

d r i p l i n e S V - m i n

k n o w n n u c l e i s t a b l e n u c l e i

N=28 Z=28

230 244

N=258

Nuclear Landscape 2012

S 2 n = 2 M e V

Literature: 5,000-12,000

288

~3,000

Asymptotic freedom ?

from B. Sherrill

Erler et al., Nature (2012)

Neutron star crust Neutron star

crust

Astronomical observables Astronomical

observables Nuclear observables

Nuclear observables Many-body

theory Many-body

theory Nuclear

interactions Nuclear interactions

Nuclear matter equation of state

Nuclear matter equation of state

Microphysics (transport,…) Microphysics (transport,…)

Quest for understanding the neutron-rich matter on Earth and in the Cosmos

RNB

facilities

Optimized Functionals Optimized Functionals

Numerical Techniques Numerical Techniques

Large-scale DFT Large-scale DFT

Confrontation with experiment; predictions Confrontation with experiment; predictions

Collective dynamics Collective dynamics

LACM, Fission: the ultimate challenge

Stability of the heaviest nuclei, r-process, advanced fuel cycle, stockpile stewardship…

PRC 78, 014318 (2008)

PRC 85, 024304 (2012) PRC 84, 054321(2011)

PRC 80, 014309 (2009)

PRC 80, 014309 (2009)

Prospects

FRIB GSI RIKEN

TRIUMF NSCL GANIL

ISOLDE

Existing major dedicated facilities

Future major facilities

Radioactive Ion Beam Facilities Worldwide

Experiment provides crucial insights

KORIA

nuclei hadrons

1Teraflop=10¹² flops 1peta=10¹⁵ flops (today)

1exa=10¹⁸ flops (next 10 years)

Theoretical Tools and Connections to Computational Science Theoretical Tools and Connections to Computational Science

Tremendous opportunities

for nuclear theory!

Petaflop-Yrs on Task

Transport in QCD (quenched) Transport in QCD (quenched)

Isotope separator optimization

Isotope separator optimization Energy Recovery LinacEnergy Recovery Linac Nucleon Spin

Nucleon Spin Deuteron Deuteron

Alpha particle Alpha particle

10

1 10 10

Hot and Dense QCD Hot and Dense

QCD

Cold QCD Cold QCD

Nuclear Structure

Nuclear Structure

Nuclear Astrophysics

Nuclear Astrophysics

Accelerator Physics Accelerator

Physics

Excited hadron spectrum Excited hadron spectrum Nuclear force

Nuclear force

Neutron EDM Neutron EDM

10

Gluon distributions Gluon distributions

Light nuclei Light nuclei

Light ion reactions Light ion reactions

Triple a process Triple a process

0n bb rates for ⁴⁸Ca 0n bb rates for ⁴⁸Ca Neutron induced fission Neutron induced fission Weakly bound nuclei

Weakly bound nuclei

Dynamics of neutron star crust Dynamics of neutron star crust

3D supernova 3D supernova Global solar model

Global solar model

Precision nuclear network Precision nuclear network

Precision neutrino network Precision neutrino network Multienergy neutrino transport

Multienergy neutrino transport

QCD critical point QCD critical point High-T limit of QCD EOS

High-T limit of QCD EOS QCD at T>0QCD at T>0 Continuum extrapolated QCD EOS Continuum extrapolated QCD EOS Quarkonium spectroscopy

Quarkonium spectroscopy

Electron-cooling design Electron-cooling design

6D Vlasov 6D Vlasov

from Martin Savage from Martin Savage

Theory is developing new statistical tools to deliver uncertainty

quantification and error analysis for theoretical studies as well as for the assessment of new experimental data. Such technologies are

essential as new theories and computational tools are explicitly intended to be applied to entirely

new nuclear systems and conditions that are not accessible to

experiment.

Future: large multi-institutional efforts involving strong coupling between physics, computer science, and applied math

http://unedf.org/

Happy birthday, Jerry!

• The nuclear many-body problem is very complex, computationally difficult, and interdisciplinary.

• 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

• For reliable model-based extrapolations, we need to improve predictive capability by developing methods to quantify

uncertainties

• Large international coherent theory effort is needed to make progress

• New-generation computers will continue to provide unprecedented opportunities

• Collaboration with computer scientists and applied mathematicians is the key

Summary

Thank You

Thank You

BACKUP

W. Henning

A: 0, …, 1, 1, 2, 4, ²⁰⁸Pb, ∞

…as seen by Jefferson Lab

The Nuclear Landscape

=

A lot of progress is taking place at interfaces

The Nuclear Many-Body Problem

The Nuclear Many-Body Problem

Ab initio theory for light nuclei and nuclear matter

Ab initio: QMC, NCSM, CCM,…

(nuclei, neutron droplets, nuclear matter)

 Quantum Monte Carlo (GFMC)

12C

 No-Core Shell Model ¹⁴F,

14C

 Coupled-Cluster Techniques

17F, ⁵⁶Ni

 Quantum Monte Carlo (GFMC)

12C

 No-Core Shell Model ¹⁴F,

14C

 Coupled-Cluster Techniques

17F, ⁵⁶Ni

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

NN+NNN interactions

NN+NNN interactions

Renormalization Renormalization Ab initio input

Many body method Many body

method

Observables Observables

• Direct comparison with experiment

• Pseudo-data to inform theory

Configuration interaction techniques

• light and heavy nuclei

• detailed spectroscopy

• quantum correlations (lab-system description)

NN+NNN interactions

NN+NNN

interactions RenormalizationRenormalization

Diagonalization

Truncation+diagonalization Monte Carlo

Diagonalization

Truncation+diagonalization Monte Carlo

Observables Observables

• Direct comparison with experiment

• Pseudo-data to inform reaction theory and DFT Matrix elements

fitted to experiment Matrix elements fitted to experiment

Input: configuration space + forces

Method

M. Hjorth-Jensen et al., J. Phys. G 37, 064035 (2010) T. Otsuka et al. Phys. Rev. Lett. 104, 012501 (2010)

Isotopes near ¹⁰⁰Sn flout conventional wisdom

Darby et al., Phys. Rev. Lett. 105, 162502 (2010)

NN+NNN interactions

NN+NNN interactions

Density Matrix Expansion Density Matrix

Expansion Input

Energy Density Functional Energy Density

Functional

Observables Observables

• Direct comparison with experiment

• Pseudo-data for reactions and astrophysics

Density dependent interactions Density dependent

interactions

Fit-observables

• experiment

• pseudo data Fit-observables

• experiment

• pseudo data

Optimization Optimization

DFT variational principle HF, HFB (self-consistency)

Symmetry breaking DFT variational principle HF, HFB (self-consistency)

Symmetry breaking

Symmetry restoration Multi-reference DFT (GCM) Time dependent DFT (TDHFB)

Symmetry restoration Multi-reference DFT (GCM) Time dependent DFT (TDHFB)

Nuclear Density Functional Theory and Extensions

• two fermi liquids

• self-bound

• superfluid (ph and pp channels)

• self-consistent mean-fields

• broken-symmetry generalized product states

Technology to calculate observables

Global properties Spectroscopy

DFT Solvers Functional form Functional optimization Estimation of theoretical errors

Mean-Field Theory Density Functional Theory ⇒

• mean-field one-body densities⇒

• zero-range local densities⇒

• finite-range gradient terms⇒

• particle-hole and pairing channels

• Self-consistency guaranteed via HFB equations

• Time-dependent extension: TDDFT

• Has been extremely successful. A broken- symmetry generalized product state does surprisingly good job for nuclei.

• Broken symmetries imply the existence of

collective degrees of freedom (shape-, pairing-, spin-, isospin-deformations)

• two fermi liquids

• self-bound

• superfluid

• continuum space crucial

Degrees of freedom: nucleonic densities

Electronic DFT: Hohenberg, Kohn (Nobel 1999), Sham…

Bohr-Mottelson, Landau-Migdal, Bogoliubov-Belyaev, Brueckner, Negele-Vautherin, Baranger, Strutinski…

Nuclear DFT:

Neutron Skin!

Nuclear Density Functional Theory

and Extensions

Ab Initio Configuration Interaction

Compound Nucleus Reaction Theory

Excited States

Effective Interaction Ground

State

Reactions

nuclear meson decay

Superallowed Fermi 0⁺ →0⁺ b-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."

0.9999(6)

Towner and Hardy 2010

Impressive experimental effort worldwide

Microscopic calculations of isospin-breaking corrections to superallowed b-decay

W. Satuła et al.,Phys. Rev. Lett 106, 132502 (2011)

Erler et al, Nature (2012)

Exotic topologies of superheavy nuclei: Coulomb frustration

Self-consistent calculations confirm the fact that the “pasta phase” might have a rather complex structure, various shapes can coexist, at the same time significant lattice distortions are likely and the neutron star crust could be on the verge of a disordered phase.

A challenge is to assess stability of such forms

P. Pyykkö: A suggested Periodic Table up to Z ≤ 172, based on Dirac-Fock calculations on atoms and ions, Phys. Chem. Chem. Phys. 13, 161-168 (2011)

“Half of chemistry is still undiscovered. We don't know what it looks like and that's the challenge”

The limit of mass and

charge is still undiscovered.

We don't know what it looks like and that's the challenge.

•Funded for 5 years by DOE (NP/SC, NNSA, ASCR)

•9 universities and 7 national labs

•Junior scientists: 11 students, 19 postdocs/year

• ~50 researchers in



physics



computer science



applied mathematics

•International partners

EXAMPLE: Universal Nuclear Energy Density Functional

• Ab initio structure

• Ab initio functionals

• DFT applications

• DFT extensions

• Reactions

For a popular description of UNEDF, see:

•SciDAC Review Winter 2007

http://www.scidacreview.org/0704/pdf/unedf.pdf

•Nucl. Phys. News 21, No. 2, 24 (2011)

~50 Papers in 2011 so far: 1 Science, 11 PRL

Focus on:

•Predictive power

•Robust extrapolations

•Validation

•Guidance

Focus on:

•Predictive power

•Robust extrapolations

•Validation

•Guidance