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ab initio no core shell model
status and prospects
James P. Vary
Iowa State University
Computational Forefront in Nuclear Theory:
Preparing for FRIB
Argonne National Laboratory
March 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
Bridging the nuclear physics scales
QCD
Nuclear
Structure
Applications in astrophysics,
defense, energy, and medicine
- D. Dean, JUSTIPEN Meeting, February 2009
DOE Workshop on Forefront Questions in Nuclear Science
and the Role of High Performance Computing,
Gaithersburg, MD, January 26-28, 2009
Nuclear Structure and Nuclear Reactions
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
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
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
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U
P
D
A
T
E
All interactions are “effective” until the ultimate theory
unifying all forces in nature is attained.
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, typically
the 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 scales
and 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.
Realistic NN & NNN interactions
High quality fits to 2- & 3- body data
Meson-exchange
NN: AV18, CD-Bonn, Nijmegen, . . .
NNN: Tucson-Melbourne, UIX, IL7, . . .
Need
Consistent
EW operators
Need
Improved NNN
Need
Chiral EFT (Idaho)
Fully derived/coded
NN: N3LO
N3LO
NNN: N2LO
4N: predicted & needed for consistent N3LO
Inverse Scattering
NN: JISP16
Need
JISP40
Consistent NNN
Effective Nucleon Interaction
(Chiral Perturbation Theory)
Chiral perturbation theory (PT) allows for controlled power series expansion

 Q 
Expansion parameter : 
 
 , Q  momentum transfer,
  
   1 GeV,  - symmetry breaking scale
Within PT 2-NNN Low Energy Constants (LEC)

are related to the NN-interaction LECs {ci}.
CD
CE
Terms suggested within the
Chiral Perturbation Theory
R. Machleidt, D. R. Entem, nucl-th/0503025
Regularization is essential, which
is obvious within the Harmonic
Oscillator wave function basis.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
The Nuclear Many-Body Problem
The many-body Schroedinger equation for bound states consists
A
of 2( Z ) 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 space
Greens Function Monte Carlo (GFMC)
Hamiltonian matrix in basis function space
No Core Shell Model (NCSM)
No Core Full Configuration (NCFC)
Cluster hierarchy in basis function space
Coupled Cluster (CC)
Comments
All work to preserve and exploit symmetries
Extensions of each to scattering/reactions are well-underway
They have different advantages and limitations
Structure
NCSM
NCFC
J-matrix
NCSM
with Core
SpNCS
M
RGM
QFT
BLFQ
Reactions
No Core Shell Model
A large sparse matrix eigenvalue problem
H  Trel  VNN  V3N  
H i  E i i

i   Ani n
n 0
Diagonalize
•
•
•
•
 m H n 
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, , ,…
nuclear Hamiltonian, H, in basis space of HO (Slater) determinants
Evaluate the
(manages the bookkeepping of anti-symmetrization)
Diagonalize this sparse many-body H in its “m-scheme” basis where [ =(n,l,j,mj,z)]
n  [a  a ]n 0
n 1,2,...,1010 or more!
•
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
ab initio NCSM
Effective Hamiltonian for A-Particles
Lee-Suzuki-Okamoto Method plus Cluster Decomposition
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
( pi  p j )2
HA  Trel V  [
 Vij ]  VNNN
2mA
i j
A
Select a finite oscillator basis space (P-space) and evaluate an
a- body cluster effective Hamiltonian:
Heff  PTrel  V a (Nmax , )P
Guaranteed to provide exact answers as a  A or as P  1 .
Effective Hamiltonian in the NCSM
Lee-Suzuki-Okamoto renormalization scheme
Heff
H : E1, E 2 , E 3 ,
0
H eff : E1, E 2 , E 3,
1
0
-1
QXHX
 Q

QXHX P  0
H eff  PXHX 1P
unitary
• n-body cluster approximation, 2nA
• H(n)eff n-body operator
• Two ways of convergence:


EdP ,
– For P  1 H(n)eff  H
– For n  A and fixed P: H(n)eff  Heff
E
EdP
model space
dimension
Key equations to solve at the a-body cluster level
Solve a cluster eigenvalue problem in a very large but finite basis
and retain all the symmetries of the bare Hamiltonian
Pa    P  P
P P
Qa    Q  Q
Q Q
Pa  Qa  1a
H
a k  Ek k
Q   P 

k K
 Q k kˆ  P
where : kˆ  P  Inverse{ k  P }
H (a)  (Pa  T ) 1/ 2(Pa  PaT Qa )Ha(QaPa  Pa )(Pa  T) 1/ 2
A. Negoita, et al, to be published
JISP16 results with HH method
Lee-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
(CD= -0.2)
P. Maris, P. Navratil, J. P. Vary, to be published
(CD= -0.2)
Note additional predicted states!
Shown as dashed lines
P. Maris, P. Navratil, J. P. Vary, to be published
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
P. Navratil, V.G. Gueorguiev,
J. P. Vary, W. E. Ormand
and A. Nogga,
PRL 99, 042501(2007);
ArXiV: nucl-th 0701038.
Extensions and work in progress
•
•
•
•
•
•
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)
12C B(M1;0+0->1+1)
A.C.Hayes, P. Navratil, J.P. Vary,
PRL 91, 012502 (2003);
nucl-th/0305072
 First successful description
of the GT data requires 3NF
Will be updated with
Nmax = 8 results
 Non-local NN interaction
from inverse scattering
also successful
4
3.5
3
B(M1;0+0->1+1)
-12C cross section
and the 0+ -> 1+
Gamow-Teller transition
Exp
2.5
N3LO +
3NF(TM’)
2
1.5
1
N3LO only
0.5
0
0
2
4
6
N
N
max
ma
JISP16
15
Expt.
15 N3LO
16 N3LO
Good spread of T=0 E2 EWSR
but still ~8 MeV too high at Nmax=8
96%
Isospin weighting:
(1-T)B(E2)
86%
Inelastic  - 12C scattering
J. P. Vary, et al, to be published
Expanding the range of applications
“Tests of fundamental symmetries”
Long-baseline neutrino mixing experiments:
Need A(, ’)A* cross sections since
A* -> A + gamma
&
gamma -> e production
=> background for the CC signal
Preliminary
Plan: Evaluate NCSM static and transition
1-body density matrices and electroweak
amplitudes from the SM and, together,
evaluate the cross section
Collaboration: T. S. H. Lee, S. Nakamura, C. Cockrell, P. Maris, J. P. Vary
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
r '  1 fm
r'  0
7Li
Ground state
non-local 1-body density matrices
r '  2 fm
x
z
x
z
r '  1 fm
r'  0
12C
x
z
r '  2 fm
x
z
x
(r,   0,   0, r ',  '  0,  '  0)
r  x2  z2
Preliminary
z
x
z
Note: These peaks
become delta functions
in the limit of a local
approximation
Chase Cockrell, et al,to be published
Innovations underway to improve the NCSM
Aim: improve treatment of clusters/intruders
Initially, all follow the NCFC approch = extrapolations
“Realistic” single-particle basis - Woods-Saxon example
Control the spurious CM motion with Lagrange multiplier term
A. Negoita, ISU PhD thesis project
Symplectic No Core Shell Model
Add symmetry-adapted many-body basis states
Preserve exactly the CM factorization
LSU - OSU - ISU collaboration
No Core Monte Carlo Shell Model
Invokes 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
12C
Now underway: Halo nuclei - 6He, . . .
A. Negoita, ISU Ph D thesis
How good is ab initio theory
for predicting large scale collective motion?
Quantum rotator
Ĵ 2 J(J  1)
EJ 

2I
2I
E4 20

 3.33
E2
6
12C
ħΩ= 25 MeV
2
Experiment  3.17
Theory(N max  10)  3.54
E4
E2
Theory(Nmax = 4) = 3.27
TheoryWS(Nmax = 4) = 3.36
Dimension = 8x109
Taming the scale explosion in nuclear calculations
NSF PetaApps - Louisiana State, Iowa State, Ohio State collaboration

Goals



Novel approach



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)
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

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
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 indicating
that Fluorine-14 will emit (drip) one
proton 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
N
H
I
nn'
n'   E  n  ,
nN
n' 0

n(p)+nucleus applications
2
N 
GNN E   
 0 E   E
N

()
I
()
CNl
q  GNN E TN,N

1CN 1,l q
S  ()
I
()
CNl q  GNN E TN,N
C
1 N 1,l q
Forward scattering J-matrix
1. Calculate E  and N  with NCSM
2. Solve for S-matrix and obtain phase
 shifts
Inverse scattering J-matrix
1. Obtain
phase
shifts from scattering data


2. Solve for n(p)+nucleus potential, resonance params
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 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
First non-perturbative field theory application:
Preliminary
H. Honkanen, P. Maris, J. P. Vary and S. Brodsky, to be published
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 cosmos
through the Standard Model is well underway