Ab Initio Nuclear Structure Theory:

Progress and Prospects

James P. Vary, Iowa State University

Nuclei in the Laboratoryand in the Cosmos

Erice, Italy, September 20, 2014

FRIB

HIRFL

BRIF

RISP

Predic've  nuclear  theory  with    quan'fied  uncertain'es  for    

prac'cal  and  fundamental  physics  

Effec've  Field  Theory  (pionless,  pionful,  

deltaful,…)  

Ab-‐ini'o  many-‐body  theory:  structure  &  reac'ons  

Computa'onal  Science:  Fully  exploit  disrup've    

technologies  

Applied  Mathema'cs:  New/improved  algorithms  

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

∞

∑ ΦnDiagonalize Φm H Φn{ }

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  

Physics  Le]ers  B  719,  179  (2013)  

M.A.  Caprio,  P.  Maris  and  J.P.  Vary,  Physics  Le]ers  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:  Inves'gate  same  phenomena  with  Chiral  EFT  interac'ons  

Proton  

Neutron  

Collec've  model:    

Black  line:  Yrast  band  in  collec've  model  fit  Red  line:  excited  band  in  collec've  model  fit  

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

NN 3N 4N

long (2π) intermediate (π) short-range

c1, c3, c4 terms cD term cE term

1.5

large uncertainties in coupling constants at present:

Chiral EFT for nuclear forces, leading order 3N forces

lead to theoretical uncertainties inmany-body observables

use chiral interactions as input for RG evolution

NN 3N 4N

Adapted from Kai Hebeler, ECT* workshop May 2014

H

P

Q

P

Q

Nmax

•  n-body cluster approximation, 2≤n≤A •  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,…EdP ,…E∞

�

Heff : E1, E2, E3,…EdP

�

QXHX−1P = 0

�

Heff = PXHX−1P

X = − −+exp[ arctan ( )]h ω ωunitary

model space dimension

Effective Hamiltonian in the NCSM Okubo-Lee-Suzuki renormalization scheme

Adapted from Petr Navratil

Both OLS and SRG derivations of Heff will be used in applications here

Controlling the center-of-mass (cm) motion in order to preserve Galilean invariance

Add a Lagrange multiplier term acting on the cm alone so as not to interfere with the internal motion dynamics

H = Heff Nmax ,!!( )+"Hcm

Hcm =P2

2MA+ 1

2MA!

2R2

" "10 suffices

Low-lying “physical” spectrum

Approx. copy of low-lying spectrum

!!"Along with the Nmax truncation in the HO basis, the Lagrange multiplier term guarantees that all low-lying solutions have eigenfunctions that factorize into a 0s HO wavefunction for the cm times a translationaly invariant wavefunction.

Heff Nmax ,Ω( )≡ P[Trel +Va Nmax ,Ω( )]P

ab initio No Core

Shell Model “NCSM”

No Core Full Config

NCFC

NCSM- Reson’g Grp

Method & NCSM-

Contin’m

SU(3)-NCSM

Basis Light Front Quant’zn

J-matrix Scat’g phase

shifts

Structure

Reactions Effective Field

Theory - ext’l field

Monte Carlo

NCSM

Importance Truncated

NCSM

NCSM with Core

Extensions of the ab initio NCSM

Gamow- NCSM &

Density Matrix Renormaliz’n

Group

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)

SRG Renormalization scale invariance, convergence & agreement with experiment

8Be

λ=2.0 fm-1 λ=2.0 fm-1 λ=2.24 fm-1 λ=1.88 fm-1

0! 0

2! 0

0! 0

1! 0

4! 01! 12! 02! 1

0! 1

0! 0

2 4 6 8 Exp.Nmax

0

2

4

6

8

10

12

14

16

18

20

.

Ex

[MeV

]

0! 0

2! 0

0! 0

1! 0

4! 01! 12! 02! 1

0! 1

0! 0

2 4 6 8 Exp.Nmax

0

2

4

6

8

10

12

14

16

18

20

.

Ex

[MeV

]

NCSM  excita'on  spectra  for  12C  with  chiral  NN(N3LO)  +  3N(N2LO)  interac'on    

SRG  evolu'on  scale  (in  fm4)  dependence  

0.0625  0.08  

0.04  

HO  frequency  (in  MeV)    dependence  

P.  Maris,  J.P.  Vary,  A.  Calci,  J.  Langhammer,  S.  Binder  and  R.  Roth,  arXiv  1405.1331;to  appear  in  PRC    

20  

16  

0! 0

2! 0

0! 0

1! 0

4! 0

1! 12! 0

2! 1

0! 0

4 6 8 10 Exp.Nmax

0

2

4

6

8

10

12

14

16

.

Ex

[MeV

]

3! 0

1! 0

2! 0

!2! 0"4! 0

3 5 7 9 Exp.Nmax

0

1

2

3

4

.

E−

E(3−

0)

[MeV

]

P.  Maris,  J.P.  Vary,  A.  Calci,  J.  Langhammer,  S.  Binder  and  R.  Roth,  arXiv  1405.1331;to  appear  in  PRC    

Convergence  rates  of  excita'on  spectra  for  SRG  evolved  chiral  NN(N3LO)  +  3N(N2LO)    

α = 0.0625 fm4

λ = 2.0 fm−1

!Ω = 20 MeVIT-‐NCSM  

NCSM  

IT-‐NCSM  

NCSM  

Boxes  indicate  threshold-‐extrapola'on  uncertain'es  for  IT-‐NCSM  

JJJ

J

J

JJ

J

J

BBB

BB

B

B

B

B

HHH

HH

H

H

H

H

8

10

12

14

16

18

20

0 2 4 6 8

E ex(

3-) (

MeV

)

12C

Experiment

16

20

24

(MeV) !Ω

(0,1) (2,3) (4,5) (6,7) (8,9)(Nmax,Nmax+1)

α fm4( )0.080.06250.04

Convergence  rates  of  selected  observables  for  SRG  evolved  chiral  NN(N3LO)  +  3N(N2LO)    

P.  Maris,  J.P.  Vary,  A.  Calci,  J.  Langhammer,  S.  Binder  and  R.  Roth,  arXiv  1405.1331;to  appear  in  PRC    

JJ

JJ

JJJ

JJ

J

J

J

BB

BB

BBB

B

B

B

B

B

HHHH

HHHH

H

HH

H

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

!Ω 12C(MeV)

16

24

α fm4( )0.040.06250.08

(µN2)

JJJ

JJ

JJ

J

J

J

J

J

BBB

B

BB

BB

B

B

B

B

HHH

H

HH

HH H

HH

H

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10

B(E2

) (2+

,0) t

o (0

+ ,0)

g.s

. (e2

fm4 )

Nmax

Experiment

12C

16

20

24

!Ω (MeV)

α fm4( )0.080.06250.04

JJJJ

JJ

JJ J

J

J

J

BBBB

BB

BB

B

B

B

B

HHHH

HHH

H

H

H

H

H

1.9

2

2.1

2.2

2.3

2.4

0 2 4 6 8 10

Poin

t Pro

ton

RM

S R

adiu

s (fm

)

Nmax

Experiment

12C

α fm4( )0.080.06250.04

(MeV) !Ω

16

20

24

Next  Genera'on  Ab  Ini'o  Structure  Applica'ons  –  Aim  for  Precision    

Electroweak  processes  Beyond  the  Standard  Model  tests  (e.g.  CKM  unitarity  =>  vud  determina'on)  

Neutrinoful  and  neutrinoless  double  beta-‐decay  ?        

Each  puts  major  demands  on  theory,  algorithms  and  computa'onal  resources  Growing  demands  =>  larger  collabora'ng  teams,  growing  computa'onal  resources,  

Increase  in  the  mul'-‐disciplinary  character,  .  .  .    

Ground state magnetic moments with JISP16Maris, Vary, IJMPE, in press

µ =1

J + 1

(

⟨J · Lp⟩+ 5.586⟨J · Sp⟩ − 3.826⟨J · Sn⟩)

µ0

2 4 6 8 10 12 14 16A

-2

-1

0

1

2

3m

agne

tic m

omen

t (µ 0

)

exptJISP16

2H 6Li

8Li

8B

7Li

7Be9Be

9B9Li

9C

10B

11B

11C

11Be

15N

15O14N

13B

13O

13N

13C

?

?

12B

12N

3H

3He

Good agreement with data,given that we do not have any meson-exchange currents

SciDAC NUCLEI workshop, June 2013, Bloomington, IN – p. 13/37Pieter Maris

P. Maris and J.P. Vary, Int. J. Mod. Phys. E 22, 1330016 (2013)

M1, E2, F, GT transitionsNO EFFECTIVE CHARGES!

E2 = eP

k12

ˆ

r2kY2(r̂k)˜

(1 + τkz)

M1 = µNP

k[(Lk + gpSk)(1 + τkz)/2

+ gnSk (1 − τkz)/2]

F =P

kτk± ; GT =P

kσkτk±

Pervin, Pieper & Wiringa, PRC 76, 064319 (2007)

Marcucci, Pervin, et al., PRC 78, 065501 (2008)

Cohen-KurathNCSMGFMC(IA)GFMC(MEC)Experiment 0 1 2 3

Ratio to experiment

6He(2+;0→0+;0) B(E2)

6Li(3+;0→1+;0) B(E2)

6Li(0+;1→1+;0) B(M1)

7Li(1/2-→3/2-) B(E2)

7Li(1/2-→3/2-) B(M1)

7Li(7/2-→3/2-) B(E2)

7Be(1/2-→3/2-) B(M1)

6He(0+)→6Li(1+) B(GT)

7Be(3/2-)→7Li(3/2-) B(GT)

7Be(3/2-)→7Li(1/2-) B(GT)

7Be(3/2-) Branching ratio

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

Impact  Objec,ves    •  Predict  proper'es  of  neutron-‐rich  systems  which  relate  

to  exo'c  nuclei  and  nuclear  astrophysics  •  Determine  how  well  high-‐precision  phenomenological  

strong  interac'ons  compare  with  effec've  field  theory  based  on  QCD  

•  Produce  accurate  predic'ons  with  quan'fied  uncertain'es  

!  Improve  nuclear  energy  density  func'onals  used  in  extensive  applica'ons  such  as  fission  calcula'ons  

!  Demonstrate  the  predic've  power  of  ab  ini,o  nuclear  theory  for  exo'c  nuclei  with  quan'fied  uncertain'es  

!  Guide  future  experiments  at  DOE-‐sponsored  rare  isotope  produc'on  facili'es  

1. Demonstrates  predic've  power  of  ab  ini,o  nuclear  structure  theory.  

2.  Provides  results  for  next  genera'on  nuclear  energy  density  func'onals  

3.  Leads  to  improved  predic'ons  for  astrophysical  reac'ons  

4. Demonstrates  that  the  role  of  three-‐nucleon  (3N)  interac'ons  in  extreme  neutron  systems  is  significantly  weaker  than  predicted  from  high-‐precision  phenomemological  interac'ons  

Accomplishments  

Ab  ini&o  Extreme  Neutron  Ma2er  

Comparison  of  ground  state  energies  of  systems  with  N  neutrons  trapped  in  a  harmonic  oscillator  with  strength  10  MeV.    Solid  red  diamonds  and  blue  dots  signify  new  results  with  two-‐nucleon  (NN)  plus  three-‐nucleon  (3N)  interac,ons  derived  from  chiral  effec,ve  field  theory  related  to  QCD.  Inset  displays  the  ra,o  of  NN+3N  to  NN  alone  for  the  different  interac,ons.  Note  that  with  increasing  N,  the  chiral  predic,ons  lie  between  results  from  different  high-‐precision  phenomenological  interac,ons,  i.e.  between  AV8’+UIX  and  AV8’+IL7.  

References:  P.  Maris,  J.P.  Vary,  S.  Gandolfi,  J.  Carlson,  S.C.  Pieper,  Phys.  Rev.  C87,  054318  (2013);  H.  Po]er,  S.  Fischer,    P.  Maris,  J.P.  Vary,  S.  Binder,  A.  Calci,  J.  Langhammer  and  R.Roth,  arXiv:1406.1160;  Contact:    jvary@iastate.edu  

E tot

/(10

MeV⇥

N4/3)

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

N4 6 8 10 12 14 16 18 20 28 40 50

NN+3N-ind. ( NCSM)NN+3N-full ( NCSM)NN+3N-ind. (⇤CCSD(T))NN+3N-full (⇤CCSD(T))AV8’ (QMC)AV8’+UIX (QMC)AV8’+IL7 (QMC)

(NN

+3N

)/N

N

0.96

0.98

1.00

1.02

4 8 12 16

ChiralUIX

IL7

Summary:  Observables  in  light  nuclei  known  to  be  sensi've  to  3NFs    Binding  energies  (through  Oxygen)and  subshell  closures  (through  Calcium)  Spectral  proper'es  having  spin-‐orbit  sensi'vity  GS  quadrupole  moment  of  6Li  M1,  E2,  F,  GT  transi'ons  Ra'o  of  B(E2)’s  [GS  -‐>  11+  over  GS  -‐>  12+]  in  10B  10B  ground  state  spin  14C  anomalous  half-‐life      Other:  Elas'c  magne'c  form  factor  of  17O  (M5  region)        

Established  challenges  –  possible  roles  for  improved  3NFs    Gaps  between  natural  &  unnatural  parity  spectra  The  energy  of    J  =  1+,  T=0  state  in  12C    Two  low-‐lying  2+  states  in  10Be  with  radically  different  B(E2)’s  Level  crossing  of  J  =  5/2  and  J  =  1/2    states  in  9Be  Spectra  of  14N  Overbinding  of  Ca  isotopes  and  above  RMS  radii  too  small  in  ~all  nuclei  above  4He  Magne'c  FF  of  17O  –  in  the  M3  suppression  region  Extra  GT  transi'ons  (intruders,  clusters,  .  .  .)  in  p-‐shell  nuclei  (e.g.  A  =  14  PRL)  How  JISP16  and  NNLO_opt  do  a  ~reasonable  job  simula'ng    3NF  effects    

Future  Prospects    Extend  the  Precision  and  Reach  of  Ab  Ini'o  Applica'ons  by  Improved:  

 chiral  interac'ons,  EW  currents,  .  .    

basis  spaces  Renormaliza'on  theory  Extrapola'on  theory  

   

Op'mize  our  u'liza'on  of  available  algorithms  and  computa'onal  resources    =>  intense  theore'cal  developments  

=>  increase  in  mul'-‐disciplinary  collabora'ons  

Low Energy Nuclear Physics International Collaboration

E. Epelbaum, H. Krebs

A. Nogga

P. Maris, J. Vary

J. Golak, R. Skibinski, K. Tolponicki, H. Witala

S. Binder, A. Calci, K. Hebeler,J. Langhammer, R. Roth

R. Furnstahl

H. Kamada

Calculation of three-body forces at N3LO

Goal

Calculate matrix elements of 3NF in a partial-

wave decomposed form which is suitable for

different few- and many-body frameworks

Challenge

Due to the large number of matrix elements,

the calculation is extremely expensive.

Strategy

Develop an efficient code which allows to

treat arbitrary local 3N interactions.

(Krebs and Hebeler)

H

PHeffP  

PHeffQ  =  0  

QHeffP        =  0  

QHeffQ  

P Q

P

Q

Nmax

The “double Lee-Suzuki transform” for valence Heff

P’H’EFFP’ Nmax=0

Aim: Regain valence-core separation but retain full ab initio NCSM

=> “Double OLS” Approach

Now extend to s-d shell the successful p-shell applications

p-shell application:

A.  F. Lisetskiy, B. R. Barrett,

M. K. G. Kruse, P. Navratil,

I. Stetcu, J. P. Vary,

Phys. Rev. C. 78, 044302 (2008); arXiv:0808.2187

Preliminary Results

Excellent

Spectral

agreement!

Total Binding

Energies!

(26 of 37)! International Conference on Nuclear Theory in the Superconducting Era, Iowa State, 12-17 May 2013 !Unraveling Mysteries of

the Strong Interaction !

Choose Three Slices (ancient but current)!Hoyle State Example !

Main contribution to ground state rotational band (0g.s.+, 21+, 41+)

(0 4) Bandhead (Oblate)

0p-0h!

Main contribution to Hoyle state (02+)

4p-4h!

(12 0) Bandhead (More Prolate)

(6 2) Bandhead (Prolate)

Main contribution to the 03+

2p-2h!

‘Back to the Future’ !– déjà vu –!

Engeland & Ellis ‘67s

J.P. Draayer, et al

" Hardware  advances:  Moore’s  Law  " Theory/Algorithms/Sowware  advances:  Doubles  Moore’s  Law  

Discovery  poten'al  increases  geometrically  

B

B

B

B

B

J

J

J

J

J

HHHH

H

1.97

1.975

1.98

1.985

1.99

1.995

2

2.005

2.01

0 0.02 0.04 0.06 0.08 0.1

Mass/mf X

X

X

µ /mf

11S0

13S1

23P2

2nd degree polynomial fitsAll points are Nmax -> inf at largest K availableMax K = 65 for mu = 0.02, 0.04 & 45 for mu > 0.04

α = 0.3b= 0.4m f

Future Prospect: Fully Covariant Basis Light-Front Quantization (BLFQ) Example: Positronium in QED at strong coupling

P. Wiecki, Y. Li, X. Zhao, P. Maris and J.P. Vary, arXiv 1404.6234

X Pert. theory at α4

                                                                                       Conclusions/Outlook    #  Impressive  recent  progress  in  deriving  NN  and  NNN  interac'ons  from  QCD  

# Much  work  needs  to  be  done  to  improve  upon  these  interac'ons  and  the    many-‐body    approaches  that  employ  them  

# We  will  con'nue  to  apply  these  interac'ons  to  nuclei  as  they  are  developed    #  Collabora'ons  of  Chiral  EFT  theorists  and  ab-‐ini'o  many-‐body  theorists  underway  

 to  improve  the  proper'es  of  the  Chiral  EFT  interac'ons    

#  Collabora'ons  of  nuclear  theorists  with  computer  scien'sts      and  applied  mathema'cians  must  con'nue  

#  Increasing  computa'onal  resources  needed  (3NFs,  4NFs  are  major  challenges)  

#  Increased  manpower  needed  to  achieve  these  goals  in  larger  collabora'ng  teams  

Recent Collaborators United States ISU: Pieter Maris, George Papadimitriou, Chase Cockrell, Hugh Potter, Alina Negoita 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, 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, Kai Hebeler, 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