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Ab Initio Theory of Collective Motion in Light Nuclei James P. Vary, Iowa State University
Nuclear Symmetries and Stewardship Science: the Research of Jolie Cizewski May 1-2, 2014
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FRIB
HIRFL
BRIF
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Fundamental questions of nuclear physics => discovery potential ! What controls nuclear saturation? ! How shell and collective properties emerge from the underlying theory? ! What are the properties of nuclei with extreme neutron/proton ratios?
! Can we predict useful cross sections that cannot be measured?
! Can nuclei provide precision tests of the fundamental laws of nature?
! Can we solve QCD to describe hadronic structures and interactions?
+ K-super. + Blue Waters + TianHe II + Tachyon-II
Edison
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The Nuclear Many-Body Problem
The many-body Schroedinger equation for bound states consists of 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 space Greens Function Monte Carlo (GFMC)
Hamiltonian matrix in basis function space No Core Configuration Interaction (NCSM/NCFC)
Cluster hierarchy in basis function space Coupled Cluster (CC)
Lattice Nuclear Chiral EFT, MB Greens Function, MB Perturbation Theory, . . . approaches
Comments All work to preserve and exploit symmetries
Extensions of each to scattering/reactions are well-underway They have different advantages and limitations
�
AZ
Meson Exchg interactions
Chiral EFT interactions
Featured results here
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• 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, α, β,… • 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 [α =(n,l,j,mj,τz)]
• 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
�
Φn = [aα+ • • • aς
+]n 0
�
n = 1,2,...,1010 or more!
No Core Shell Model A large sparse matrix eigenvalue problem
�
H = Trel +VNN +V3N + • • •H Ψi = Ei Ψi
Ψi = Ani
n= 0
∞
∑ Φn
Diagonalize Φm H Φn{ }
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P. Maris, J. P. Vary and P. Navratil, Phys. Rev. C87, 014327 (2013); arXiv 1205.5686
Note additional predicted states! Shown as dashed lines
CD= -0.2
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J. Phys. Conf. Ser. 454, 012063 (2013)
Renormalization scale invariance & agreement with experiment
8Be
λ=2.0 fm-1 λ=2.0 fm-1 λ=2.24 fm-1 λ=1.88 fm-1
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K=1/2 bands include Coriolis decoupling parameter:
Both natural and unnatural parity bands iden<fied Employed JISP16 interac<on; Nmax = 10 -‐ 7
K=1/2
K=1/2
K=3/2
K=3/2
K=1/2
K=1/2
Black line: Yrast band in collec<ve model fit Red line: excited band in collec<ve model fit
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M.A. Caprio, P. Maris and J.P. Vary, Phys. LeU. B 719, 179 (2013)
Note: Although Q, B(E2) are slowly converging, the ra<os within a rota<onal band appear remarkably stable
Next challenge: Investigate same phenomena with Chiral EFT interactions
Proton
Neutron
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9Be Translationally invariant gs density Full 3D densities = rotate around the vertical axis
Total density Proton-Neutron density
Shows that one neutron provides a “ring” cloud around two alpha clusters binding them together
C. Cockrell, J.P. Vary, P. Maris, Phys. Rev. C 86, 034325 (2012); arXiv:1201.0724; C. Cockrell, PhD, Iowa State University
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Pro
tons
Neu
trons
Monopole Quadrupole Hexadecapole 8Li gs
J=2
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How good is ab initio theory for predicting large scale collective motion?
Quantum rotator
EJ =J 2
2I=J(J +1)2
2IE4
E2
=206
= 3.33
Experiment = 3.17Theory(Nmax = 10) = 3.54
0+; 0
0+; 0
0
5
10
15
20
25
E (M
eV) 4+; 0
0+; 0
2+; 0
4+; 0
0+; 0
2+; 0
Exp Nmax
=10 Nmax
=6 Nmax
=4 Nmax
=0Nmax
=2Nmax
=8
3.173 3.535 3.333 3.129 2.9942.9273.470 E4+
/E2+
12C Ω = 20MeV
Dimension = 8x109
E4
E2
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0! 0
2! 0
0! 0
1! 0
4! 0
1! 12! 0
2! 1
0! 1
0! 0
6 8 6 8 Exp.Nmax
0
2
4
6
8
10
12
14
16
18
20
.
Ex
[MeV
]
chiral NN chiral NN+3N
3! 0
1! 0
2! 0
!2! 0"4! 0
5 7 5 7 Exp.Nmax
0
1
2
3
4
.
E−
E(3−
0)
[MeV
]
chiral NN chiral NN+3N
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 2 4 6 8 10
B(M
1) (1
+ ,1)
to (0
+ ,0)
g.s
.
Nmax
Experiment
20
24
20
16
InducedNNN only
!Ω12C
(MeV)
16
24
(µN2)
arXiv: 1405.1331
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M. A. Caprio, University of Notre Dame
No-core shell model dimension
0 2 4 6 8 10 12 14 16 18 20Excitation quanta
100
102
104
106
108
1010
1012
Dimension 8 Be12 C
16 O
20 Ne
24 Mg 12 C J=0
Valenceshell
Cluster structure expected torequire ⇠30–50~⌦ of oscillatorexcitation, e.g., for ↵+↵+↵Hoyle state in 12C.
r
RnHrL
a a
0+
0!W 2!W 4!W 6!W 8!W
0+
0+
0+
0+
Expt.
0+
Hoyle
0+
0
5
10
15
20
25
30
EHMeVL
Calculations from T. Ne↵ and H. Feldmeier,Eur. Phys. J. Special Topics 156, 69 (2008).
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(9 of 37)! International Conference on Nuclear Theory in the Superconducting Era, Iowa State, 12-17 May 2013 !
Unraveling Mysteries of the Strong Interaction !
Next Generation !
Symmetry Adapted NCSM (SA-NCSM) �(Dytrych ... ~2007-Present)�
*Stage I: SU(3)-adapted basis�– a multi-shell Elliott model�
– SA-NCSM� *Stage II: Sp(3,R)-adapted �
basis – NCSpM �
Ab initio evidence for symmetry patterns!
General Background!
*Realistic interaction (local/nonlocal; NN, NNN,…) !• In principle, exact solutions !• Successful description up through O-16 !
No-Core Shell Model (NCSM) �(Vary, Navratil, Barrett, … Maris … ~2000-Present)�
Shape����Driven�
T. Dytrych, et al., PRL 111, 252501 (2013)
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(19 of 37)! International Conference on Nuclear Theory in the Superconducting Era, Iowa State, 12-17 May 2013 !
Unraveling Mysteries of the Strong Interaction !
Dominant Structures!
0�� 2�� 4�� 6�� 8�� 10�� 12��
�1⇤2,1⇤2,0⇥�1⇤2,1⇤2,1⇥�1⇤2,3⇤2,1⇥�1⇤2,3⇤2,2⇥�3⇤2,1⇤2,1⇥�3⇤2,1⇤2,2⇥�3⇤2,3⇤2,0⇥�3⇤2,3⇤2,1⇥�3⇤2,3⇤2,2⇥�3⇤2,3⇤2,3⇥
Spins�S p,
S n,S⇥
�0,1⇥ �2,0⇥ �1,0⇥ �0,2⇥ �2,1⇥ �4,0⇥ �0,0⇥ �1,1⇥ �0,3⇥ �3,0⇥ �2,2⇥ �4,1⇥ �6,0⇥ �0,1⇥ �2,0⇥ �1,2⇥ �3,1⇥ �0,4⇥ �2,3⇥ �5,0⇥ �4,2⇥ �6,1⇥ �8,0⇥ �1,0⇥ �0,2⇥ �2,1⇥ �1,3⇥ �4,0⇥ �3,2⇥ �0,5⇥ �2,4⇥ �5,1⇥ �4,3⇥ �7,0⇥ �6,2⇥ �8,1⇥ �10,0⇥ �0,0⇥ �1,1⇥ �0,3⇥ �3,0⇥ �2,2⇥ �1,4⇥ �4,1⇥ �3,3⇥ �0,6⇥ �6,0⇥ �2,5⇥ �5,2⇥ �4,4⇥ �7,1⇥ �6,3⇥ �9,0⇥ �8,2⇥ �10,1⇥ �12,0⇥ �0,1⇥ �2,0⇥ �1,2⇥ �3,1⇥ �0,4⇥ �2,3⇥ �5,0⇥ �4,2⇥ �1,5⇥ �3,4⇥ �6,1⇥ �0,7⇥ �5,3⇥ �2,6⇥ �4,5⇥ �8,0⇥ �7,2⇥ �6,4⇥ �9,1⇥ �8,3⇥ �11,0⇥ �10,2⇥ �12,1⇥ �14,0⇥�⇥ ⇤⇥
Winnowing the model space: Nmax=12[6] (full up to 6�Ω; selected configurations in 8-12 �Ω)!
-0.1!
0.4!
0.9!
1.4!
1.9!
rms radius [fm]!
E2 moment [e fm2]!
M1 moment [mn]!
12[6]!12 (full)!
0!
5!
10!
15!
20!
25!
30!
BE [MeV]!
1%!100%!
Space dimension:!!!!
fm2! μN!
11� 0 0.000
31� 0 2.524
21� 0 5.135
12� 06.913
0.000
2.503
5.362
7.276
Full 12�6⇥ SU⇤3⌅
6Li�⇤⇥22.5 MeVNmax⇥12
0
1
2
3
4
5
6
7
8
Ex�MeV
⇥
Bare JISP16!
Efficacy of SA-NCSM: 6Li!
J.P. Draayer, et al
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E.D. Jurgenson, P. Maris, R.J. Furnstahl, P. Navratil, W.E. Ormand, J.P. Vary, Phys. Rev. C. 87, 054312 (2013); arXiv: 1302:5473
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ab initio predictions in close agreement with experiment
TAMU Cyclotron Institute
Experiment published: Aug. 3, 2010 Theory published PRC: Feb. 4, 2010
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Origin of the anomalously long life-time of 14C
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
GT
mat
rix e
lem
ent
no 3NF forceswith 3NF forces (cD= -0.2)with 3NF forces (cD= -2.0)
s p sd pf sdg pfh sdgi pfhj sdgik pfhjl
shell
-0.10
0.10.20.3
0.2924
near-completecancellationsbetweendominantcontributionswithin p-shell
very sensitiveto details
Maris, Vary, Navratil,
Ormand, Nam, Dean,
PRL106, 202502 (2011)
INT workshop on double beta decay, Aug. 2013, Seattle, WA – p. 32/35
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Many recent insights obtained from ab initio NCSM/NCFC: Collective modes in light nuclei accessible with ab initio approach 3NFs continue to play an important role in many observables Neutron drop results show (sub)shell closures IR and UV convergence in HO basis (Coon et al., Papenbrock et al.) Alternative basis spaces poised to relieve IR shortcomings of HO basis Alternative MB methods poised to access clustering, halo physics regions Computer Science and Applied Math collaborations invaluable Generous allocations of computer resources essential to progress
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Many outstanding nuclear physics puzzles and discovery opportunities
Clustering phenomena
Origin of the successful nuclear shell model Nuclear reactions and breakup
Astrophysical r/p processes & drip lines Predictive theory of fission
Existence/stability of superheavy nuclei Physics beyond the Standard Model
Possible lepton number violation Spin content of the proton
+ Many More!
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Recent Collaborators United States ISU: Pieter Maris, Alina Negoita, Chase Cockrell, Hugh Potter LLNL: Erich Ormand, Tom Luu, Eric Jurgenson, Michael Kruse ORNL/UT: David Dean, Hai Ah Nam, Markus Kortelainen, Witek Nazarewicz, Gaute Hagen,Thomas Papenbrock OSU: Dick Furnstahl, Kai Hebeler, students MSU: Scott Bogner, Heiko Hergert Notre Dame: Mark Caprio ANL: Harry Lee, Steve Pieper, Fritz Coester LANL: Joe Carlson, Stefano Gandolfi UA: Bruce Barrett, Sid A. Coon, Bira van Kolck, Matthew Avetian, Alexander Lisetskiy LSU: Jerry Draayer, Tomas Dytrych, Kristina Sviratcheva, Chairul Bahri UW: Martin Savage
International Canada: Petr Navratil Russia: Andrey Shirokov, Alexander Mazur, Eugene Mazur, Sergey Zaytsev, Vasily Kulikov Sweden: Christian Forssen, Jimmy Rotureau Japan: Takashi Abe, Takaharu Otsuka, Yutaka Utsuno, Noritaka Shimizu Germany: Achim Schwenk, Robert Roth, Javier Menendez, students South Korea: Youngman Kim, Ik Jae Shin Turkey: Erdal Dikman
ODU/Ames Lab: Masha Sosonkina, Dossay Oryspayev LBNL: Esmond Ng, Chao Yang, Hasan Metin Aktulga ANL: Stefan Wild, Rusty Lusk OSU: Umit Catalyurek, Eric Saule
Quantum Field
Theory
ISU: Xingbo Zhao, Pieter Maris, Germany: Hans-Juergen Pirner Paul Wiecki, Yang Li, Kirill Tuchin, Costa Rica: Guy de Teramond John Spence India: Avaroth Harindranath, Stanford: Stan Brodsky Usha Kulshreshtha, Daya Kulshreshtha, Penn State: Heli Honkanen Asmita Mukherjee, Dipankar Chakrabarti, Russia: Vladimir Karmanov Ravi Manohar
Computer Science/ Applied Math
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Best Wishes, Jolie, for Continued Success In All Your Endeavors
Including Dancing!