Computing Atomic NucleiWitold Nazarewicz (UTK/ORNL)

NUCL Symposium: Radiochemistry at FRIBFall 2010 ACS National Meeting, August 22, 2010

• IntroductionTerritory, Principles

• Frontiers• Challenges

Predictive capability and extrapolabilityHigh performance computing

• Perspectives

• IntroductionTerritory, Principles

• Frontiers• Challenges

Predictive capability and extrapolabilityHigh performance computing

• Perspectives

Modeling the Atomic Nucleus

Theoretical bag of tricks…

number of nuclei < number of processors!

Links to CMP/AMO science!!!

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� Coupled-Cluster Techniques 56Ni� Faddeev-Yakubovsky� Lattice EFT� Many-body perturbation theory� …

Input:• Excellent forces based on

the phase shift analysis and few-body data

• EFT based nonlocal chiral NN and NNN potentials

• SRG-softened potentials

NN+NNN

interactions

Renormalization

Ab initio input

Many body

method

Observables

• Direct comparison with experiment

• Pseudo-data to inform theory

Nuclear Coupled Cluster Theory Medium-mass nuclei from chiral nucleon-nucleon interactions

Radial density for 48Ca from the chiral nucleon-nucleonpotential at order N3LO calculated using microscopiccoupled-cluster theory with singles-and doubles excitations(CCSD). The calculations were performed on Cray XT5Kraken at the University of Tennessee and on Cray XT5Jaguar at ORNL.

Hagen et al., Phys. Rev. Lett. 101, 092502 (2008)

Hagen et al., Phys. Rev. Lett. 104, 182501 (2010)

The calculations reproduce the tiny separation energy of the halo and demonstrate that an appreciable contribution to its binding energy comes from the coupling to the particle continuum, a generic property of open systems.

Strongly paired fermions: Cold atoms and neutron matter

Gezerlis and Carlson, Phys. Rev. C 77, 032801(R) (2008)

an=-18.5 fm, re=2.7 fm

s-wave part of AV18

pairing gap

Configuration interaction techniques

• light and heavy nuclei• detailed spectroscopy• quantum correlations (lab-system description)

NN+NNN

interactionsRenormalization

Diagonalization

Truncation+diagonalization

Monte Carlo

Observables

• Direct comparison with experiment

• Pseudo-data to inform reaction theory and DFT

Matrix elements

fitted to experiment

Input: configuration space + forcesMethod

T. Otsuka et al. Phys. Rev. Lett. 104, 012501 (2010)

M. Hjorth-Jensen

M. Hjorth-Jensen et al., arXiv:1003.1452.

Many-body interactions and nuclear structure

NN+NNN

interactions

Density Matrix

Expansion

Input

Energy Density

Functional

Observables

• Direct comparison with

experiment

• Pseudo-data for reactions

and astrophysics

Density dependent

interactions

Fit-observables

• experiment

• pseudo data

Optimization

DFT variational principle

HF, HFB (self-consistency)

Symmetry breaking

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

A. Staszczak et al. B.Phys. Rev. C 80, 014309 (2009)

Multimodal fission in nuclear DFT

Two-dimensional total energy surface for 258Fm inthe plane of two collective coordinates: elongation,Q20, and reflection-asymmetry, Q30. Dashed linesshow the fission pathways. The symmetry-unrestricted DFT calculations were performed atORNL on a Cray XT3/XT4 Jaguar supercomputersystems. The novel features include theimplementation of the modified Broyden’s methodto solve self-consistent equations involving over7,000,000 variables and the use of the AugmentedLagrangian Method to solve the optimizationproblem with many constraints.

Shell structure: a moving target

Neutron star

crustAstronomical

observables

Nuclear

observablesMany-body

theory

Nuclear

interactions

Nuclear matter

equation of state

Microphysics

(transport,…)

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

N-1Z+1

NZ+1

N+1Z+1

N-1Z

NZ

N+1Z

N-2Z+1

N-2Z

N+2Z+1

N+2Z

N-1Z-1

NZ-1

N+1Z-1

N-2Z-1

N+2Z-1

N-1Z+1

NZ+1

N+1Z+1

N-1Z

NZ

N+1Z

N-2Z+1

N-2Z

N+2Z+1

N+2Z

N-1Z-1

NZ-1

N+1Z-1

N-2Z-1

N+2Z-1

interactionscorrelationsmany-body techniques

Nuclei: open quantum systems

Complex-energy Shell ModelGamow Shell Model Continuum coupling, thresholds &

clustering

Nuclear OQS: a major challenge for nuclear theory

• A unification of structure and reaction aspects of weakly-bound or unboun nuclei based on the open quantum system formalism

• Many phenomena (threshold effects, exceptional points, channel coupling…) are generic (atoms, molecules, nanotubes, quantum dots, microwave cavities,…)

Ab initio no-core shell model (NCSM) & resonating-group method (RGM)S.Quaglioni and P. Navrátil, PRL101, 092501 (2008); PRC79, 044606 (2009)

� NCSM/RGM – dynamic & static properties of light nuclei• Ab initio calculations for reactions

and clustering in nuclei• Unified description of bound,

resonant and continuum states• Understanding of reactions

for fusion-energy generation

Matrix diagonalization and eigenvector analysis Dimensions of ~ 109

Consider a model described by coupling constants

Any predicted expectation value of an observable is a function of these

parameters. Since the number of parameters is much smaller than the number of

observables, there must exist correlations between computed quantities.

Moreover, since the model space has been optimized to a limited set of

observables, there may also exist correlations between model parameters.

Statistical methods of linear-regression and error analysis P.G. Reinhard and WN, Phys. Rev. C 81, 051303 (R) (2010)

To what extent is a new observable independent of existing ones and what new

information does it bring in? Without any preconceived knowledge, all different

observables are independent of each other and can usefully inform theory. On the

other extreme, new data would be redundant if our theoretical model were

perfect. Reality lies in between.

fit-observables

(may include pseudo-data)

Objective

function

Assessing importance of new observables

An example…

A 10% experimental uncertainty due to statistical and photon-beam calibration errors makes it impossible to use the current best value of αD as an independent check on neutron skin.

A.Veyssiere et al., Nucl. Phys. A 159, 561 (1970)

E. Lipparini and S. Stringari, Phys. Rep. 175, 103 (1989)

To estimate the impact of precise experimental determination of neutron skin, we generated

a new functional SV-min-Rn by adding the value of neutron radius in 208Pb, rn=5.61 fm, with

an adopted error 0.02 fm, to the set of fit observables. With this new functional, calculated

uncertainties on isovector indicators shrink by about a factor of two.

Computational Strategy

1Teraflop=1012 flops1peta=1015 flops (today)1exa=1018 flops (next 10 years)

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

Towards Exascale

Universal Nuclear Energy Density Functional

http://unedf.org/

•Funded (on a competitive basis) by

•Office of Science•ASCR•NNSA

•16 institutions• ~50 researchers

•physics•computer science•applied mathematics

• foreign collaboratorsFunded for 5 years

…unprecedentedtheoretical effort !

The ADLB version of GFMC was used tomake calculations of 12C with a completeHamiltonian (two- and three-nucleonpotentials -- AV18+IL7) on 32,000processors of the Argonne BGP. Theseare believed to be the best converged abinitio calculations of 12C ever made. Thecomputed binding energy is 93.5(6) MeVcompared to the experimental value of92.16 MeV and the point rms radius is2.35 fm vs 2.33 from experiment. Thefigure compares the computed 12Cdensity with that extracted from electron-scattering experiments.

Recent examples from UNEDF

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

• We need to improve predictive capability by developing methods to quantify uncertainties

• New-generation computers will continue to provide unprecedented opportunities• Large coherent theory effort is needed to make 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 YouThank You

Summary

Backup

Low-lying Hadron SpectrumDürr, Fodor, Lippert et al., BMW Collaboration

Science 322, 1224 November 2008More than 99% of the mass of the visible universe is made up of protons and neutrons. Both particles are much heavier than their quark and gluon constituents, and the Standard Model of particle physics should explain this difference. We present a full ab initio calculation of the masses of protons, neutrons, and other light hadrons, using lattice quantum chromodynamics. Pion masses down to 190 mega–electron volts are used to extrapolate to the physical point, with lattice sizes of approximately four times the inverse pion mass. Three lattice spacings are used for a continuum extrapolation. Our results completely agree with experimental observations and represent a quantitative confirmation of this aspect of the Standard Model with fully controlled uncertainties

Nuclear forceNuclear forceNuclear forceNuclear force

Realistic nuclear force

N. Ishii, S. Aoki, T. Hatsuda, Phys. Rev. Lett. 99, 022001 (2007)

• Nucleon r.m.s. radius ~0.86 fm• Comparable with interaction range• Half-density overlap at max. attarction• VNN not fundamental (more like inter-

molecular van der Waals interaction)• Since nucleons are composite objects,

three-and higher-body forces are expected.

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

nucleon-nucleon interactions

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

Vlow-k unifies NN interactions at low energyVlow-k unifies NN interactions at low energy

Effective-field theory potentials Renormalization group (RG) evolved

nuclear potentials

GFMC: S. Pieper, ANL

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

Consider a model described by coupling constants

The optimum

parameter set

Uncertainty in variable A:

Correlation between variables A and B:

The reasonable domain is defined as that multitude of parameters

around minimum that fall inside the covariance ellipsoid :

ALSDA, P=0.37J. Pei et al. 2010

pairing with nonzero momentum: Flude-Ferrell-Larkin-Ovchinnikov phase (FFLO)

244Pu243Am

+ 48Ca

248Cm

2004

…also: 286,28711448Ca+242Pu from LBNL

From Y. Oganessian

Limits of Mass and Charge: SuperheaviesLimits of Mass and Charge: Superheavies

hot fusion245Cm249Cf

237Np

226Ra238U

242Pu

2008

2 events/year

Y. Oganessian et al.,submitted

• The nucleon-based description works to <0.5 fm • Effective Field Theory/Renormalization Group provides missing links

Short-range repulsion: a red herring!• Accurate ab-initio methods allow for interaction tests• Worldwide attack on the nuclear energy density functional• Quantitative microscopic nuclear structure• Integrating nuclear structure and reactions • High-performance computing continues to revolutionize microscopic nuclear many-body problem: impossible becomes possible

• Some of the most interesting physics outcomes will be at the interfaces:

• QCD to forces to structure• Fruitful interactions with quantum chemistry• Structure and reactions with nuclear astrophysics

• many new ideas leading to new understanding• new theoretical frameworks• exciting developments• high-quality calculations

Recent years: very successful period for theory of nuclei

The computational cost of nuclear 3-body forces can be greatly reduced by decoupling low-energy parts from high-energy parts, which can then be discarded.

Three-body forces between protons and neutrons are analogous to tidal forces: the gravitational force on the Earth is not just the sum of Earth-Moon and Earth-Sun forces.

Recently the first consistent Similarity Renormalization Group softening of three-body forces was achieved, with rapid convergence in helium. With this faster convergence, calculations of larger nuclei are possible!

three-nucleon interactions

Jurgenson, Navratil, and FurnstahlPhys. Rev. Lett. 80, 082501 (2009)

Mass table

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

δm=0.581 MeV

Cwiok, Heenen, WN, Nature, 433, 705 (2005)

BE differences

Nuclear Density Functional Theory: applications

Traditional (limited) functionals provide quantitative description