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
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