• Introduction • General principles • Examples: quantitative nuclear theory; predictive capability • Realities of high- performance computing • Summary

• Introduction

• General principles

• Examples: quantitative nuclear theory;

predictive capability

• Realities of high-

performance computing

• Summary

Computational nuclear structure in the eve of exascale

Witek Nazarewicz (UTK/ORNL)

Physics Colloquium, GSI, April 22, 2014

• A first rate theory predicts

• A second rate theory forbids

• A third rate theory explains after the facts

Alexander I. Kitaigorodskii

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

Virgil, Georgica Theories

Models

The Nuclear Landscape

• QCD transition (color singlets formed): 10 ms after Big Bang (13.8 billion years ago)

• D, ^3,4 He, ⁷ Be/ ⁷ Li formed 3-50 min after Big Bang

• Other nuclei born later in heavy stars and supernovae

The Nuclear Landscape and the Big Questions (NAS report)

• How did visible matter come into being and how does it evolve? (origin of nuclei and atoms)

• How does subatomic matter organize itself and what phenomena emerge? (self-organization)

• Are the fundamental interactions that are basic to the structure of matter fully understood?

• How can the knowledge and technological progress

provided by nuclear physics best be used to benefit society?

wh ere th e a cti on is …

p ro to n s

neutrons

The Grand Nuclear Landscape

(finite nuclei + extended nucleonic matter)

82

50 28

28

50 82

20 2 8

2 8

20

stable nuclei stable nuclei known nuclei

known nuclei

126 terra incognita terra incognita

neutron stars

neut ron drip line

probably known only up to oxygen

pro ton dr ip line

known up to Z=91

superheavy nuclei

Z=118, A=294

Nuclear structure Nuclear reactions New standard model

Hot and dense quark-gluon matter Hadron structure

Applications of nuclear science Hadron-Nuclear interface

R es ol ut io n E ffe ct iv e F ie ld T h e or y

DFT

collective models

CI

ab initio LQCD

quark models

scale separation

To explain, predict, use…

To explain, predict, use…

How are nuclei made?

Origin of elements, isotopes

The challenge and the prospect: NN force

Beane et al. PRL 97, 012001 (2006)

and Phys. Rev. C 88, 024003 (2013)

Ishii et al. PRL 99, 022001 (2007)

The Nuclear Many-Body Problem

coupled integro-differential

equations in 3A dimensions

dim ens ion of th e pr oble m

How to explain the nuclear landscape from the bottom up? Theory roadmap

11 Li

100 Sn

240 Pu

298 U

Theory 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 ab initio schemes 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

• unified picture of structure and reactions

Illustrative physics examples

GFMC: S. Pieper, ANL

1-2% calculations of A = 6 – 12 nuclear energies are possible excited states with the same quantum numbers computed

Ab initio: Examples

0 1 2 3 4 q ( f m ^{- 1} )

1 0

1 0

1 0

1 0

1 0

|F (q )|

e x p r

r

0 2 4

r ( f m ) 0 . 0 0

0 . 0 4 0 . 0 8 r

( r)

Results - Longitudinal form factor

• Experimental data are well reproduced by theory over the whole range of

momentum transfers;

• Two-body terms become appreciable only for q > 3 fm

, where they interfere destructively with the one- body contributions bringing theory into closer

agreement with experiment.

Monday, June 24, 13

12 C Electron Scattering

Ground-state and Hoyle-state form factor

Epelbaum et al., Phys. Rev.

Lett. 109, 252501 (2012).

Lattice EFT Pieper et al., QMC

The ADLB (Asynchronous Dynamic Load- Balancing) version of GFMC was used to make calculations of ¹² C 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 ¹² C 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.

Wiringa et al. Phys. Rev. C 89,

024305 (2014); A. Lovato et al.,

arXiv: 1305.6959

The frontier: neutron-rich calcium isotopes

probing nuclear forces and shell structure in a neutron-rich medium

2 4 6 8 1 0 1 2 1 4 1 6 1 8

E x p e r i m e n t I S O L T R A P N N + 3 N ( M B P T ) C C ( H a g e n e t a l .) K B 3 G

G X P F 1 A

2 8 2 9 3 0 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 S 2n (M eV )

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

ISOLTRAP@CERN

Wienholtz et al, Nature (2013)

TITAN@TRIUMF

Gallant et al, PRL 109, 032506 (2012)

CC theory

Hagen et al., PRL109, 032502 (2012)

52 Ca mass

54 Ca mass

54 Ca 2 ⁺

54 Ca: 20 protons, 34 neutrons

RIBF@RIKEN

Steppenbeck et al

Nature (2013)

Ab Initio Path to Heavy Nuclei

Binder et al., arXiv:1312.5685

• The first accurate ab initio cupled cluster calculations for heavy nuclei using SRG-evolved chiral interactions. A number of technical hurdles eliminated

• Many-body calculations up to ¹³² Sn are now possible with controlled uncertainties on the order of 2%

• A first direct validation of chiral Hamiltonians in the regime of heavy nuclei using ab initio techniques.

• Future studies will have to involve consistent chiral Hamiltonians at N ³ LO considering initial

and SRG-induced 4N interactions and provide an exploration of other observables.

Microscopic valence-space Shell Model Hamiltonian

G.R. Jansen et al., arXiv:1402.2563

S.K. Bogner et al., arXiv:1402.1407 Coupled Cluster Effective Interaction

(valence cluster expansion)

In-medium SRG Effective Interaction

MBPT IM-SRG

NN+3N-ind IM-SRG

NN+3N-full Expt.

0 1 2 3 4 5 6 7 8

E ne rg y (M eV )

0

2

2

2

0

0

(2

) 2

2

(0

) 0

0

4

4

(4

)

4

2

0

2

0

3

3

3

3

0

22 O

Anomalous Long Lifetime of ¹⁴ C

Dimension of matrix solved for 8 lowest states ~ 10 ⁹ Solution took ~ 6 hours on 215,000 cores on Cray XT5 Jaguar at ORNL

Determine the microscopic origin of the suppressed b-decay rate: 3N force

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

G T m at ri x el em en t

N3LO NN only

N3LO + 3NF (c _D = -0.2)

N3LO + 3NF (c _D = -2.0)

s p sd pf sdg pfh sdgi pfhj sdgik pfhjl

configuration space

-0.1 0 0.1 0.2 0.3

0.29

Maris et al., PRL 106, 202502 (2011)

Fusion of Light Nuclei

Ab initio theory reduces uncertainty due

to conflicting data ^{ The n- 3} H elastic cross section for 14 MeV neutrons, important for NIF, was not known precisely enough.

 Delivered evaluated data with required 5%

uncertainty and successfully compared to

measurements using an Inertial Confinement Facility

 ``First measurements of the differential cross sections for the elastic n- ² H and n- ³ H 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

NIF

Computational nuclear physics enables us to reach into regimes where experiments and analytic theory are not possible, such as the cores of fission reactors or hot and dense

evolving environments such as those found in

inertial confinement fusion environment.

Mean-Field Theory Density Functional Theory ⇒

• 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.

Nuclear DFT

• two fermi liquids

• self-bound

• superfluid

Degrees of freedom: nucleonic densities

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

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

HFB+LN mass table, HFBTHO

0 40 80 120 160 200 240 280

neutron number

0 40 80 120

p ro to n n um b er ^{tw o - p r o}

to n d r i p lin e

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

p ro to n n u m be r

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

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

Skyrme-DFT: 6,900±500 _syst Skyrme-DFT: 6,900±500 _syst Literature: 5,000-12,000

288

~3,000

Erler et al.

Nature 486, 509 (2012)

Asymptotic freedom ?

from B. Sherrill

DFT FRIB

current

Quantified Nuclear Landscape

8 9 10 11 12 13 14 15 R (km)

0 1 2

M ( M so la r )

2r ⁰ 4r ⁰

1.4 1.97(4)

NN

3r ⁰ 5r ⁰

0 . 3 0 f m 0 . 1 5 f m

r 0 N N

+N NN

Gandolfi et al. PRC85, 032801 (2012)

The covariance ellipsoid for the neutron skin R _skin in ²⁰⁸ Pb and the radius of a 1.4M _⊙ neutron star.

The mean values are: R(1.4M _⊙ )

=12 km and R _skin = 0.17 fm.

J. Erler et al., PRC 87, 044320 (2013)

From nuclei to neutron stars (a multiscale problem)

Major uncertainty: density

dependence of the symmetry

energy. Depends on T=3/2

three-nucleon forces

supernova neutron star merger

velocity entropy

mass number

m as s fr ac tio n _r-process solar system oldest

stars Big

Bang

0 50 100 150 200

0 50 100 150 200

0 50 100

0 50

10 ^-12 10 ^-9 10 ^-6 10 ^-3

S. Bruenn et al., ApJ 767, L6 (2012) S. Rosswog et al., MNRAS 430, 2585 (2013)

The radioactive galaxy demonstrates the continuing formation of new

radioactive isotopes

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)

Experimental context: governing principles

• Beam time is expensive. New facilities/detectors are expensive.

Theory should be involved in assessing the impact of planned runs and projects.

• Helping planning future experiments and experimental programs

• Assessing the uniqueness and usefulness of an observable, i.e., its information content with respect to current theoretical models

• Are estimated errors of measured observables meaningful?

• Theory should be more aggressive at the planning stage of future experiments

• What experimental data are crucial for better constraining current nuclear models?

• How to validate and verify model-based extrapolations?

• Nuclear theory should team with computer science/applied mathematics to make uncertainty quantifications

• Early interaction with theory can be helpful in preventing unpleasant surprises

• We need to increase community awareness regarding experimental data

assessment

Quality control

Uncertainty quantification

“Remember that all models are wrong;

the practical question is how wrong do they have to be to not be useful”

(E.P. Box)

-1 0 1 2 3 4 5 6

s 2 (1 0 -3 fm 2 )

200 204 208 212 216 220 224

A

remaining

left bars: UNEDF0 right bars: SV-min

a _sym L

C ^rDr

r sk in

1

Information content of future measurements

M. Kortelainen et al., Phys. Rev. C 88, 031305 (2013)

Nuclear theory is developing tools to deliver uncertainty quantification and error analysis for the assessment of new experimental data. Theoretical tools can also be used to assess the

information content of an observable with respect to current theoretical models, and evaluate the degree of correlation between different observables.

see “Error Estimates of Theoretical Models: a Guide” (arXiv:1402.4657)

1teraflop=10 ¹² flops

1peta=10 ¹⁵ flops (today)

1exa=10 ¹⁸ flops (next 10 years)

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

Tremendous opportunities

for nuclear theory!

Future: large multi-institutional efforts involving strong coupling between

physics, computer science, and applied math

“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.”

• 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

Recent Past: Universal Nuclear Energy Density Functional

(other, smaller, collaborations exist: NuN, TORUS, PetaApps,…)

• 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

• Recent summary (to be published in CPC)

• “Computational Nuclear Quantum Many-Body Problem: The UNEDF Project arxiv.org:1304.3713

Focus on:

• Predictive power

• Robust extrapolations

• Validation

• Guidance

Focus on:

• Predictive power

• Robust extrapolations

• Validation

• Guidance

Nuclear SciDAC-2

UNEDF in 2007

UNEDF in 2011

• 9 universities and 7 national labs

• Junior scientists: 11 students, 19 postdocs/year

• ~50 researchers in PHY/CS/AM

• International partners

Validated Nuclear Interactions Validated Nuclear

Interactions

Structure and Reactions:

Light and Medium Nuclei Structure and Reactions:

Light and Medium Nuclei

Structure and Reactions:

Heavy Nuclei Structure and Reactions:

Heavy Nuclei

Chiral EFT Ab-initio

Optimization Model validation

Uncertainty Quantification

Neutron Stars

Neutron Stars Fission Fission

Neutrinos and Fundamental Symmetries

Neutrinos and Fundamental Symmetries

Ab-initio RGM CI

Load balancing Eigensolvers Nonlinear solvers Model validation

Uncertainty Quantification

DFT TDDFT

Load balancing Optimization Model validation

Uncertainty Quantification Eigensolvers

Nonlinear solvers Multiresolution analysis

Stellar burning Stellar burning

fusion fusion

Neutron drops EOS Correlations

TJNAF FRIB

LANL LLNL NIF

Majorana

LENP facilities

SNS

EXO