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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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

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

•  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{ }

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

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

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  

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

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

Pro

tons

Neu

trons

Monopole Quadrupole Hexadecapole 8Li gs

J=2

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

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−

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[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

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1) (1

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to (0

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.

Nmax

Experiment

20

24

20

16

InducedNNN only

!Ω12C

(MeV)

16

24

(µN2)

arXiv: 1405.1331

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+

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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).

(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)

(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��

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S n,S⇥

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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

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

ab initio predictions in close agreement with experiment

TAMU Cyclotron Institute

Experiment published: Aug. 3, 2010 Theory published PRC: Feb. 4, 2010

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

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

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!

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

Best Wishes, Jolie, for Continued Success In All Your Endeavors

Including Dancing!