ab initio no core shell modelstatus and prospects

James P. VaryIowa State University

Computational Forefront in Nuclear Theory:Preparing for FRIB

Argonne National LaboratoryMarch 26, 2010

Ab initio nuclear physics - fundamental questions

What controls nuclear saturation?

How does the nuclear shell model emerge from the underlying theory?

What are the properties of nuclei with extreme neutron/proton ratios?

Can nuclei provide precision tests of the fundamental laws of nature?

Jaguar Franklin Blue Gene/p Atlas

Nuclear Structure

QCD

Applications in astrophysics, defense, energy, and medicine

Bridging the nuclear physics scales

- D. Dean, JUSTIPEN Meeting, February 2009

List of Priority Research Directions• Physics of extreme neutron-rich nuclei and matter• Microscopic description of nuclear fission• Nuclei as neutrino physics laboratories• Reactions that made us - triple process and 12C()16O

2(12C 12C(16O

DOE Workshop on Forefront Questions in Nuclear Science and the Role of High Performance Computing,

Gaithersburg, MD, January 26-28, 2009Nuclear Structure and Nuclear Reactions

http://extremecomputing.labworks.org/nuclearphysics/report.stm

ab initio nuclear theory - building bridges

Standard Model (QCD + Electroweak)

NN + NNN interactions & effective EW operators

quantum many-body theory

describe/predict experimental data

UPDATE

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Thus, even the Standard Model, incorporating QCD,is an effective theory valid below the Planck scale

< 1019 GeV/c

The “bare” NN interaction, usually with derived quantities,is thus an effective interaction valid up to some scale, typicallythe scale of the known NN phase shifts and Deuteron gs properties ~ 600 MeV/c (3.0 fm-1)

Effective NN interactions can be further renormalized to lower scalesand this can enhance convergence of the many-body applications ~ 300 MeV/c (1.5 fm-1)

“Consistent” NNN and higher-body forces are those valid to the same scale as their corresponding NN partner, and obtained in the same renormalization scheme.

All interactions are “effective” until the ultimate theory unifying all forces in nature is attained.

Realistic NN & NNN interactionsHigh quality fits to 2- & 3- body data

Meson-exchange NN: AV18, CD-Bonn, Nijmegen, . . . NNN: Tucson-Melbourne, UIX, IL7, . . .

Chiral EFT (Idaho) NN: N3LO NNN: N2LO 4N: predicted & needed for consistent N3LO

Inverse Scattering NN: JISP16

NeedImproved NNN

NeedFully derived/coded

N3LO

NeedJISP40

Consistent NNN

NeedConsistent

EW operators

Effective Nucleon Interaction

(Chiral Perturbation Theory)

R. Machleidt, D. R. Entem, nucl-th/0503025

Chiral perturbation theory (PT) allows for controlled power series expansion

Expansion parameter: Q

, Q momentum transfer,

1 GeV , - symmetry breaking scale

Within PT 2-NNN Low Energy Constants (LEC) are related to the NN-interaction

LECs {ci}.

Terms suggested within theChiral Perturbation Theory

Regularization is essential, which is obvious within the Harmonic Oscillator wave function basis.

CD CE

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The Nuclear Many-Body Problem

The many-body Schroedinger equation for bound states consistsof 2( ) coupled second-order differential equations in 3A coordinates

using strong (NN & NNN) and electromagnetic interactions.

Successful ab initio quantum many-body approaches (A > 6)

Stochastic approach in coordinate spaceGreens Function Monte Carlo (GFMC)

Hamiltonian matrix in basis function spaceNo Core Shell Model (NCSM)

No Core Full Configuration (NCFC)

Cluster hierarchy in basis function spaceCoupled Cluster (CC)

CommentsAll work to preserve and exploit symmetries

Extensions of each to scattering/reactions are well-underwayThey have different advantages and limitations

A

Z

NCSM

NCFC

RGM

SpNCSMQFT

BLFQ

J-matrix

NCSM with Core

Structure

Reactions

• Adopt realistic NN (and NNN) interaction(s) & renormalize as needed - retain induced many-body interactions: Chiral EFT interactions and JISP16

• Adopt the 3-D Harmonic Oscillator (HO) for the single-nucleon basis states, , ,…• Evaluate the nuclear Hamiltonian, H, in basis space of HO (Slater) determinants

(manages the bookkeepping of anti-symmetrization)• Diagonalize this sparse many-body H in its “m-scheme” basis where [ =(n,l,j,mj,z)]

• Evaluate observables and compare with experiment

Comments• Straightforward but computationally demanding => new algorithms/computers• Requires convergence assessments and extrapolation tools• Achievable for nuclei up to A=16 (40) today with largest computers available

n [a a

]n 0

n 1,2,...,1010 or more!

No Core Shell Model

A large sparse matrix eigenvalue problem

H Trel VNN V3N

H i E i i

i Ani

n0

n

Diagonalize m H n

HA Trel V [(p i

p j )

2

2mAVij

i j

A

]VNNN

P. Navratil, J.P. Vary and B.R. Barrett, Phys. Rev. Lett. 84, 5728(2000); Phys. Rev. C62, 054311(2000)C. Viazminsky and J.P. Vary, J. Math. Phys. 42, 2055 (2001);K. Suzuki and S.Y. Lee, Progr. Theor. Phys. 64, 2091(1980);

K. Suzuki, ibid, 68, 246(1982); K. Suzuki and R. Okamoto, ibid, 70, 439(1983)

Preserves the symmetries of the full Hamiltonian:Rotational, translational, parity, etc., invariance

ab initio NCSMEffective Hamiltonian for A-Particles

Lee-Suzuki-Okamoto Method plus Cluster Decomposition

Select a finite oscillator basis space (P-space) and evaluate an - body cluster effective Hamiltonian:

Guaranteed to provide exact answers as or as .

a

a A

P 1

Heff P Trel V a (Nmax ,) P

H

P

Q

P

Q

Nmax

• n-body cluster approximation, 2nA

• H(n)eff n-body operator

• Two ways of convergence:– For P 1 H(n)

eff H

– For n A and fixed P: H(n)eff Heff

Heff 0

0 QXHX-1Q

H : E1, E2, E3,Ed P,E

Heff : E1, E2, E3,EdP

QXHX 1P 0

Heff PXHX 1PX exp [ arc tan ( )]h unitary

model space dimension

Effective Hamiltonian in the NCSMLee-Suzuki-Okamoto renormalization scheme

H (a) (Pa T) 1/ 2(Pa Pa

TQa )Ha(QaPa Pa )(Pa

T) 1/ 2

Ha k Ek k

Q P Q kkK ˆ k P

where : ˆ k P Inverse{ k P }

Pa PPP P

Qa QQQ Q

Pa Qa 1a

Key equations to solve at the a-body cluster level

Solve a cluster eigenvalue problem in a very large but finite basisand retain all the symmetries of the bare Hamiltonian

A. Negoita, et al, to be published

JISP16 results with HH methodLee-Suzuki-Okamoto Veff

6He

6Li

NCSM with Chiral NN (N3LO) + NNN (N2LO, CD=-0.2)

P. Maris, P. Navratil, J. P. Vary, to be published

P. Maris, P. Navratil, J. P. Vary, to be published

(CD= -0.2)

P. Maris, P. Navratil, J. P. Vary, to be published

Note additional predicted states!Shown as dashed lines

(CD= -0.2)

ab initio NCSM with EFT Interactions• Only method capable to apply the EFT NN+NNN interactions to all p-shell nuclei • Importance of NNN interactions for describing nuclear structure and transition rates

• Better determination of the NNN force itself, feedback to EFT (LLNL, OSU, MSU, TRIUMF)• Implement Vlowk & SRG renormalizations (Bogner, Furnstahl, Maris, Perry, Schwenk & Vary, NPA 801,

21(2008); ArXiv 0708.3754)• Response to external fields - bridges to DFT/DME/EDF (SciDAC/UNEDF) - Axially symmetric quadratic external fields - in progress - Triaxial and spin-dependent external fields - planning process• Cold trapped atoms (Stetcu, Barrett, van Kolck & Vary, PRA 76, 063613(2007); ArXiv 0706.4123) and

applications to other fields of physics (e.g. quantum field theory)• Effective interactions with a core (Lisetsky, Barrett, Navratil, Stetcu, Vary)• Nuclear reactions & scattering (Forssen, Navratil, Quaglioni, Shirokov, Mazur, Vary)

Extensions and work in progress

P. Navratil, V.G. Gueorguiev, J. P. Vary, W. E. Ormand and A. Nogga, PRL 99, 042501(2007);ArXiV: nucl-th 0701038.

12C B(M1;0+0->1+1)

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6

Nma

B(M

1;0

+0

->1

+1

)

15

Expt.

15 N3LO

16 N3LO

Nmax

-12C cross section and the 0+ -> 1+ Gamow-Teller transitionA.C.Hayes, P. Navratil, J.P. Vary, PRL 91, 012502 (2003); nucl-th/0305072

First successful description of the GT data requires 3NF

N3LO + 3NF(TM’)

N3LO only

Exp

JISP16

Non-local NN interaction from inverse scattering also successful

Will be updated withNmax = 8 results

Inelastic - 12C scattering

86%

Isospin weighting:(1-T)B(E2)

96%

J. P. Vary, et al, to be published

Good spread of T=0 E2 EWSR but still ~8 MeV too high at Nmax=8

Collaboration: T. S. H. Lee, S. Nakamura, C. Cockrell, P. Maris, J. P. Vary

Long-baseline neutrino mixing experiments:Need A(, ’)A* cross sections since

A* -> A + gamma&

gamma -> e production=> background for the CC signal

Plan: Evaluate NCSM static and transition1-body density matrices and electroweak

amplitudes from the SM and, together,evaluate the cross section

Expanding the range of applications“Tests of fundamental symmetries”

Preliminary

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Ground statenon-local 1-body density matrices

7Li

12C

(r, 0, 0,r ', ' 0, ' 0)

r x2 z2

x x

x x xz

x

z z

z z z

r ' 0

r ' 0

r ' 1 fm

r ' 1 fm

r ' 2 fm

r ' 2 fm

Chase Cockrell, et al,to be published

Note: These peaksbecome delta functionsin the limit of a local approximation

Preliminary

Innovations underway to improve the NCSMAim: improve treatment of clusters/intruders

Initially, all follow the NCFC approch = extrapolations

“Realistic” single-particle basis - Woods-Saxon exampleControl the spurious CM motion with Lagrange multiplier term

A. Negoita, ISU PhD thesis project

Symplectic No Core Shell ModelAdd symmetry-adapted many-body basis states

Preserve exactly the CM factorizationLSU - OSU - ISU collaboration

No Core Monte Carlo Shell ModelInvokes single particle basis truncation

Separate spurious CM motion in same way as CC approach Scales well to larger nuclei

U. Tokyo - ISU collaboration

A. Negoita, ISU Ph D thesis

A. Negoita, ISU Ph D thesis

12C

Now underway: Halo nuclei - 6He, . . .

How good is ab initio theory for predicting large scale collective motion?

Quantum rotator

EJ J 2

2I

J(J 1)2

2IE4

E2

20

63.33

Experiment 3.17

Theory(Nmax 10) 3.54

Dimension = 8x109

Theory(Nmax = 4) = 3.27TheoryWS(Nmax = 4) = 3.36

12CħΩ= 25 MeV

E2

E4

Novel approach Sp-CI: exploiting symmetries of

nuclear dynamics Innovative workload balancing

techniques & representations of multiple levels of parallelism for ultra-large realistic problems

Impact Applications for nuclear science

and astrophysics

Goals Ab initio calculations of nuclei with

unprecedented accuracy using basis-space expansions

Current calculations limited to nuclei with A ≤16 (up to 20 billion basis states with 2-body forces)

Progress Scalable CI code for nuclei Sp(3,R)/SU(3)-symmetry vital

Challenges/Promises Constructing hybrid Sp-CI code Publicly available peta-scale

software for nuclear science

Taming the scale explosion in nuclear calculationsTaming the scale explosion in nuclear calculationsNSF PetaApps - Louisiana State, Iowa State, Ohio State collaborationNSF PetaApps - Louisiana State, Iowa State, Ohio State collaboration

Proton-Dripping Fluorine-14

First principles quantum solution for yet-to-be-measured unstable nucleus 14F

Apply ab initio microscopic nuclear theory’s predictive power to major test case Robust predictions important for improved energy sources Providing important guidance for DOE-supported experiments Comparison with new experiment will improve theory of strong interactions Dimension of matrix solved for 14 lowest states ~ 2x109 Solution takes ~ 2.5 hours on 30,000 cores (Cray XT4 Jaguar at ORNL)

Predictions:

Binding energy: 72 ± 4 MeV indicatingthat Fluorine-14 will emit (drip) oneproton to produce more stable Oxygen-13.

Predicted spectrum (Extrapolation B)for Fluorine-14 which is nearly identical with predicted spectrum of its “mirror” nucleus Boron-14. Experimental data exist only for Boron-14 (far right column).

Ab initio Nuclear Structure

Ab initio Nuclear Reactions

J-matrix formalism:scattering in the oscillator basis

GNN E N 2

E E0

N

Hnn 'I

n '0

N

n' E n , n N

S CNl

( ) q GNN E TN ,N 1I CN 1,l

( ) q CNl

() q GNN E TN ,N 1I CN 1,l

() q

Forward scattering J-matrix1. Calculate and with NCSM2. Solve for S-matrix and obtain phase shifts

Inverse scattering J-matrix1. Obtain phase shifts from scattering data2. Solve for n(p)+nucleus potential, resonance params

E

N A.M. Shirokov, A.I. Mazur, J.P. Vary, and E.A. Mazur, Phys. Rev. C. 79, 014610 (2009), arXiv:0806.4018; and references therein

n(p)+nucleus applications

n scattering

A. M. Shirokov, A. I. Mazur, J. P. Vary and E. A. Mazur, Phys. Rev. C. 79, 014610 (2009), arXiv 0806.4018

Basis Light-Front Quantized (BLFQ) Field Theory

J. P. Vary, H. Honkanen, Jun Li, P. Maris, S. J. Brodsky, A. Harindranath, G. F. de Teramond, P. Sternberg, E. G. Ng, C. Yang, “Hamiltonian light-front field theory in a basis function approach”, Phys. Rev. C 81, 035205 (2010); arXiv nucl-th 0905.1411

H. Honkanen, P. Maris, J. P. Vary and S. Brodsky, to be published

First non-perturbative field theory application:

Preliminary

Observation

Ab initio nuclear physics maximizes predictive power& represents a theoretical and computational physics challenge

Key issue

How to achieve the full physics potential of ab initio theory

Conclusions

We have entered an era of first principles, high precision,nuclear structure and nuclear reaction theory

Linking nuclear physics and the cosmosthrough the Standard Model is well underway