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Computing Atomic NucleiTowards the microscopic nuclear energy density functional

Witold Nazarewicz (UTK/ORNL/UWS)IOP Annual Nuclear Physics Group Conference, Liverpool, April 1-3, 2008

• Introduction• Theory: progress report• The UNEDF project• Computational strategy• Perspectives

• Introduction• Theory: progress report• The UNEDF project• Computational strategy• Perspectives

Introduction

Nuclear Structure

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

First Law: “The conservation of Information” (You will get nowhere by churning equations)

Second Law: “Do not trust arguments based on the lowest order of perturbation theory”

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!”

number of nuclei < number of processors!

Links to CMP/AMO science!!! Links to CMP/AMO science!!!

Nuclear Structure TheoryProgress Report

Bogner, Kuo, Schwenk, Phys. Rep. 386, 1 (2003)

Nuclear Structure: the interactionNuclear Structure: the interaction

N3LO: Entem et al., PRC68, 041001 (2003)Epelbaum, Meissner, et al.

Vlow-k: can it describe low-energy observables?Vlow-k: can it describe low-energy observables?

• Quality two- and three-nucleon interactions exist

• Not uniquely defined (local, nonlocal)

• Soft and hard-core

• Quality two- and three-nucleon interactions exist

• Not uniquely defined (local, nonlocal)

• Soft and hard-core

Effective-field theory (χPT) potentials

Effective-field theory (χPT) potentials

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

GFMC: S. Pieper, ANL

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

Quantum Monte Carlo (GFMC) 12C

No-Core Shell Model 13C

Coupled-Cluster Techniques 40Ca

Faddeev-Yakubovsky Bloch-Horowitz …

Quantum Monte Carlo (GFMC) 12C

No-Core Shell Model 13C

Coupled-Cluster Techniques 40Ca

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

Coupled ClusterTheory

David J. Dean, "Beyond the nuclear shell model”, Physics Today 60, 48 (2007).

Converged results for 40Ca and 56Ni using N3LO evolved down using RGM

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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

• Constrained by microscopic theory: ab-initio functionals • Not all terms are equally important. Usually ~12 terms considered• Some terms probe specific experimental data• Pairing functional poorly determined. Usually 1-2 terms active.• Becomes very simple in limiting cases (e.g., unitary limit)

Construction of the functionalPerlinska et al., Phys. Rev. C 69, 014316 (2004)

Most general second order expansion in densities and their derivatives

p-h density p-p density (pairing functional)

isoscalar (T=0) density

€

ρ0 = ρ n + ρ p( )

isovector (T=1) density

€

ρ1 = ρ n − ρ p( )

+isoscalar and isovector densities:spin, current, spin-current tensor, kinetic, and kinetic-spin

+ pairing densities

S. Cwiok, P.H. Heenen, W. NazarewiczNature, 433, 705 (2005)

Nuclear DFT: works well for BE differences

• Global DFT mass calculations: HFB mass formula: m~700keV

Stoitsov et al., 2008

Nature 449, 1022 (2007)

Can dynamics be incorporated directly into the functional?Example: Local Density Functional Theory for Superfluid Fermionic Systems: The

Unitary Gas, Aurel Bulgac, Phys. Rev. A 76, 040502 (2007)

See also:

Density-functional theory for fermions in the unitary regimeT. PapenbrockPhys. Rev. A72, 041603 (2005)

Density functional theory for fermionsclose to the unitary regime A. Bhattacharyya and T. PapenbrockPhys. Rev. A 74, 041602(R) (2006)

UNEDF Project

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SciDAC 2 Project: Building a Universal Nuclear Energy Density Functional

• Understand nuclear properties “for element formation, for properties of stars, and for present and future energy and defense applications”

• Scope is all nuclei, with particular interest in reliable calculations of unstable nuclei and in reactions

• Order of magnitude improvement over present capabilities Precision calculations

• Connected to the best microscopic physics• Maximum predictive power with well-quantified uncertainties

[See http://www.scidacreview.org/0704/html/unedf.html

by Bertsch, Dean, and Nazarewicz]

Scientific Discovery Through Advanced Computing

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SciDAC 2 Project: Building a Universal Nuclear Energy Density Functional

• Understand nuclear properties “for element formation, for properties of stars, and for present and future energy and defense applications”

• Scope is all nuclei, with particular interest in reliable calculations of unstable nuclei and in reactions

• Order of magnitude improvement over present capabilities Precision calculations

• Connected to the best microscopic physics• Maximum predictive power with well-quantified

uncertainties

[See http://www.scidacreview.org/0704/html/unedf.html

by Bertsch, Dean, and Nazarewicz]

Universal Nuclear Energy Density Functional

http://unedf.org/

•Funded (on a competitive basis) by

•Office of Science•ASCR•NNSA

•15 institutions• ~50 researchers

•physics•computer science•applied mathematics

• foreign collaborators• annual budget $3M• 5 years

…unprecedentedtheoretical effort !

Other SciDAC Science at the Petascale Projects

• Physics (Astro): Computational Astrophysics Consortium: Supernovae, Gamma Ray Bursts, and Nucleosynthesis, Stan Woosley (UC/Santa Cruz) [$1.9 Million per year for five years]

• Physics (QCD): National Computational Infrastructure for Lattice Gauge Theory, Robert Sugar (UC/Santa Barbara) [$2.2 Million per year for five years]

• Physics (Turbulence): Simulations of Turbulent Flows with Strong Shocks and Density Variations, Sanjiva Lele (Stanford) [$0.8 million per year for five years]

• Physics (Petabytes): Sustaining and Extending the Open Science Grid: Science Innovation on a PetaScale Nationwide Facility, Miron Livny (U. Wisconsin) [$6.1 Million per year for five years]

Computational Strategy

1Teraflop=1012 flops1peta=1015 flops (next 2-3 years)1exa=1018 flops (next 10 years)

Connections to computational science

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Example:Example: Large Scale Mass Table Calculations Large Scale Mass Table CalculationsScience scales with processors

The SkM* mass table contains 2525 even-even nucleiThe SkM* mass table contains 2525 even-even nuclei A single processor calculates each nucleus 3 times (prolate, oblate, spherical) A single processor calculates each nucleus 3 times (prolate, oblate, spherical)

and records all nuclear characteristics and candidates for blocked calculations and records all nuclear characteristics and candidates for blocked calculations in the neighborsin the neighbors

Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration)Using 2,525 processors - about 4 CPU hours (1 CPU hour/configuration)

9,210 nuclei9,210 nuclei 599,265 configurations599,265 configurations Using 3,000 processors - about 25 CPU hoursUsing 3,000 processors - about 25 CPU hours

Even-Even NucleiEven-Even Nuclei

All NucleiAll Nuclei

M. Stoitsov

HFB+LN mass table, HFBTHO

Jaguar Cray XT4 at ORNL

INCITE awardDean et al. 17.5M hours

INCITE awardDean et al. 17.5M hours

Bimodal fission in nuclear DFT

Global calculations of ground-state spins and parities for odd-mass nuclei

L. Bonneau, P. Quentin, and P. Möller, Phys. Rev. C 76, 024320 (2007)

Density Matrix Expansion for RG-Evolved InteractionsS.K. Bogner, R.J. Furnstahl et al.

see also:EFT for DFTR.J. Furnstahlnucl-th/070204

From Ian Thompson

Perspectives

• Young talent• Focused effort• Large collaborations

• Data from terra incognitaRNB facilities provide strongmotivation!

• High-performance computing

What is needed/essential?

UNEDF

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RIBF

Radioactive Ion Beam Facilities Timeline

20002000 20052005 20102010 20152015 20202020

CARIBU@ATLAS

NSCL

HRIBF

FRIB

ISOLDE

ISAC-II

SPIRAL2

SIS FAIR

RARF

ISAC-I

In FlightISOLFission+Gas Stopping

Beam on target

SPIRAL

HIE-ISOLDE

• Solid microscopic foundation link to ab-initio approaches limits obeyed (e.g., unitary regime)

• Unique opportunities provided by coupling to CS/AM• Comprehensive phenomenology probing crucial parts of the

functional different observables probing different physics

• Stringent optimization protocol providing not only the coupling constants but also their uncertainties (theoretical errors)

• Unprecedented international effort• Unique experimental data available (in particular: far from

stability; link to FRIB science)

Conclusion: we can deliver a well theoretically founded EDF, of spectroscopic quality, for structure and reactions, based on as much as possible ab initio input at this point in time

Why us? Why now?There is a zoo of nuclear functionals on the market. What makes us believe we can make a breakthrough?

Conclusions

• Exciting science; old paradigms revisited • Interdisciplinary (quantum many-body problem, cosmos,…)• Relevant to society (energy, medicine, national security, …)

• Theory gives the mathematical formulation of our understanding and predictive ability

• New-generation computers provide unprecedented opportunities

• Large coherent international theory effort is needed to make a progress

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

Thank You

Role of theory…Role of theory…

http://www.uws.ac.uk/schoolsdepts/es/nuclearstructure/

Nuclear Structure at the ExtremesUniversity of the West of Scotland (Paisley Campus)

Thursday 8th – Saturday 10th May 2008

Nuclear.Structure@uws.ac.uk

Akito Arima  (Tokyo)

Juha Äystö (Jyväskylä)

Cyrus Baktash (ORNL)

Jim Beene (ORNL)

Peter Butler (Liverpool)

Larry Cardman (J-Lab)

Bob Chapman (UWS)

David Dean (ORNL)

Jacek Dobaczewski (Warsaw/Jyväskylä)

Jerzy Dudek (Strasbourg)

Thomas Duguet (Saclay)

Piet Van Duppen (Leuven)

Paul Fallon (Berkeley)

Martin Freer (Birmingham)

Sean Freeman (Manchester)

Bill Gelletly (Surrey)

Morten Hjorth-Jensen (Oslo)

Jan Jolie (Cologne)

Silvia Lenzi (Legnaro)

Kim Lister (Argonne)

Craig McNeile (Glasgow)

Nigel Orr (LPC Caen)

Takaharu Otsuka (Tokyo)

Thomas Papenbrock (Tennessee)

Marek Pfutzner (Warsaw)

Marek Ploszajczak (GANIL)

Achim Richter (Darmstadt)

Guenther Rosner (Glasgow)

Dirk Rudolph (Lund/GSI)

Hendrik Schatz (MSU)

Nicolas Schunck (Tennessee)

Achim Schwenk* (TRIUMF)

Dan Watts (Edinburgh)

* To be confirmed