New Horizons in Ab Initio Nuclear Structure Theorycrunch.ikp.physik.tu-darmstadt.de/tnp/pres/2013_inpc.pdf · 2020-03-31 · New Era of Nuclear Structure Theory Robert Roth – TU

New Horizons in

Ab Initio Nuclear Structure Theory

Robert Roth

1

New Era of Nuclear Structure Theory

Robert Roth – TU Darmstadt – 06/2013

QCD at low energies

improved understanding through effec-tive field theories & lattice simulations

quantum many-body methods

advances in ab initio treatment of thenuclear many-body problem

computing & algorithms

increase of computational resources &improved algorithms

experimental facilities

amazing perspectives for the study ofnuclei far-off stability

2

Ab Initio Nuclear Structure


Nuclear Structure Observables

Low-Energy Quantum Chromodynamics

LatticeQCD

quarks&gluononalattice

LatticeEFT

nucleons&pionsonalattice

Energ

y-D

ensityFunct.

guidedbychiralEFT

Chiral EFT Hamiltoniansconsistent NN,3N,... interactions & current operators

Chiral Effective Field Theorybased on relevant degrees of freedom & symmetries of QCD

Exact Solutionssolve nuclear many-

body problem with

converged truncations

Controlled Approx.treat many-body prob-

lem with controlled & im-

provable approximations

Similarity Transformationsphysics-conserving unitary transformation to

adapt Hamiltonian to limited model space

3





LatticeQCD


LatticeEFT


Energ

y-D

ensityFunct.

guidedbychiralEFT




body problem with con-

verged truncations

Controlled Approx.treat many-body problem

with controlled & improv-

able approximations



Machleid

t

Bacca,

Forssén

,

Leidemann Hag

en

Meißner

Davies,

Detmold

Khan

4





LatticeQCD


LatticeEFT


Energ

y-D

ensityFunct.

guidedbychiralEFT





verged truncations



able approximations



PREDICTIO

NVALID

ATIO

N

5





LatticeQCD


LatticeEFT


Energ

y-D

ensityFunct.

guidedbychiralEFT





verged truncations



able approximations



6

Nuclear Interactions from Chiral EFT


Weinberg, van Kolck, Machleidt, Entem, Meißner, Epelbaum, Krebs, Bernard,...

talks by Machleidt & Meißner

low-energy effective field theory forrelevant degrees of freedom (π,N) basedon symmetries of QCD

long-range pion dynamics explicitly,short-range physics absorbed in contactterms fitted to data (NN, πN,...)

hierarchy of consistent NN, 3N,...interactions plus currents

standard Hamiltonian:

NN at N3LO:Entem & Machleidt, 500 MeV cutoff

3N at N2LO:Navrátil, A=3 fit, 500 MeV cutoff

NN 3N 4N

LO

NLO

N2LO

N3LO

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7





LatticeQCD


LatticeEFT


Energ

y-D

ensityFunct.

guidedbychiralEFT





verged truncations



able approximations



8

Similarity Renormalization Group


Wegner, Glazek, Wilson, Perry, Bogner, Furnstahl, Hergert, Roth, Jurgenson, Navratil,...

continuous transformation drivingHamiltonian to band-diagonal formwith respect to a uncorrelated basis

unitary transformation of Hamiltonian and other observables

Hα = Uα†HUα Oα = Uα

†OUα

evolution equations for Hα and Uα depending on generator ηαd

dαHα = [ηα,Hα]

d

dαUα = −Uαηα

dynamic generator: commutator with the operator in whoseeigenbasis Hα shall be diagonalized

ηα = (2μ)2[Tint,Hα]

simplicity and flexibilityare great advantages of

the SRG approach

solve SRG evolutionequations using two-,

three- & four-body matrixrepresentation

9

SRG Evolution in Three-Body Space


chiral NN+3NN3LO + N2LO, triton-fit, 500 MeV

α = 0.000 fm4

Λ = ∞ fm−1

Jπ = 12

+

, T = 12, hΩ = 28MeV

3B-Jacobi HO matrix elements

0 → E → 18 20 22 24 26 28(E, )

28

26

24

22

20

18

↓E′

↓

0

.

(E′,′)

NCSM ground state 3H

0 2 4 6 8 101214161820Nmx

-8

-6

-4

-2

0

2

.

E[M

eV]

10

SRG Evolution in Three-Body Space


α = 0.320 fm4

Λ = 1.33 fm−1

Jπ = 12

+

, T = 12, hΩ = 28MeV

3B-Jacobi HO matrix elements

0 → E → 18 20 22 24 26 28(E, )

28

26

24

22

20

18

↓E′

↓

0

.

(E′,′)

NCSM ground state 3H

0 2 4 6 8 101214161820Nmx

-8

-6

-4

-2

0

2

.

E[M

eV]

suppression ofoff-diagonal coupling =pre-diagonalization

significantimprovementof convergence

behavior

11

Hamiltonian in A-Body Space


evolution induces n-body contributions H[n]α to Hamiltonian

Hα = H[1]α +H

[2]α +H

[3]α +H

[4]α +H

[5]α + . . .

truncation of cluster series formally destroys unitarity and in-variance of energy eigenvalues (independence of α)

flow-parameter α provides diagnostic tool to assess neglectedhigher-order contributions

SRG-Evolved Hamiltonians

NNonly use initial NN, keep evolved NN

NN +3Nind use initial NN, keep evolved NN+3N

NN +3Nfull use initial NN+3N, keep evolved NN+3N

NN +3Nfull +4Nind use initial NN+3N, keep evolved NN+3N+4N

12





LatticeQCD


LatticeEFT


Energ

y-D

ensityFunct.

guidedbychiralEFT




body problem with




able approximations



13

No-Core Shell Model


Barrett, Vary, Navratil, Maris, Nogga, Forssen, Roth,...

NCSM is one of the most powerful anduniversal exact ab-initio methods

construct matrix representation of Hamiltonian using a basis of HOSlater determinants truncated w.r.t. HO excitation energy NmxhΩ

solve large-scale eigenvalue problem for a few extremal eigenvalues,all relevant observables can be computed from the eigenstates

range of applicability limited by factorial growth of basis with Nmx & A

Roth, PRC 79, 064324 (2009); PRL 99, 092501 (2007)

adaptive importance truncation extends the range of NCSM by reduc-ing the model space to physically relevant states

Otsuka, Abe, Draayer, Dytrych,...

Monte-Carlo NCSM and symmetry-adapted NCSM employ analogousstrategies to reduce model-space dimension

14

4He: Ground-State Energies


Roth, et al; PRL 107, 072501 (2011)

NNonly

2 4 6 8 10 12 14 16 ∞Nmx

-29

-28

-27

-26

-25

-24

-23

.

E[M

eV]

NN+3Nind

2 4 6 8 10 12 14 ∞Nmx

Exp.

NN+3Nfull

2 4 6 8 10 12 14 ∞Nmx

∎

α = 0.04 fm4 α = 0.05 fm4 α = 0.0625 fm4 α = 0.08 fm4 α = 0.16 fm4

Λ = 2.24 fm−1 Λ = 2.11 fm−1 Λ = 2.00 fm−1 Λ = 1.88 fm−1 Λ = 1.58 fm−1

hΩ = 20MeV

15

16O: Ground-State Energies


Roth, et al; PRL 107, 072501 (2011)

NNonly

2 4 6 8 10 12 14 ∞Nmx

-180

-160

-140

-120

-100

-80

.

E[M

eV]

NN+3Nind

2 4 6 8 10 12 ∞Nmx

Exp.

NN+3Nfull

2 4 6 8 10 12 ∞Nmx

∎



hΩ = 20MeV

in progress:

explicit inclusion of

induced 4N clear signature ofinduced 4N originating

from initial 3N

16

16O: Ground-State Energies


Roth, et al; PRL 107, 072501 (2011); PRL 109, 052501 (2012)

NNonly

2 4 6 8 10 12 14 ∞Nmx

-180

-160

-140

-120

-100

-80

.

E[M

eV]

NN+3Nind

2 4 6 8 10 12 ∞Nmx

Exp.

NN+3Nfull

2 4 6 8 10 12 ∞Nmx

∎



hΩ = 20MeV

simple fix:3N interaction with

400 MeV cutoff, cE refittedto 4He ground state

17

Ground States of Oxygen Isotopes


oxygen isotopic chain has received significant attention anddocuments the rapid progress over the past years

Otsuka, Suzuki, Holt, Schwenk, Akaishi, PRL 105, 032501 (2010)

2010: shell-model calculations with 3N effects highlighting therole of 3N interaction for drip line physics

Hagen, Hjorth-Jensen, Jansen, Machleidt, Papenbrock, PRL 108, 242501 (2012)

2012: coupled-cluster calculations with phenomenologicaltwo-body correction simulating chiral 3N forces

Hergert, Binder, Calci, Langhammer, Roth, PRL 110, in print (2013)

2013: ab initio IT-NCSM with explicit chiral 3N interactions...

18



Hergert et al., PRL (2013); arXiv:1302.7294

NN+3Nind(chiral NN)

2 4 6 8 10 12 14 16 18Nmx

-160

-140

-120

-100

-80

-60

-40

.

E[M

eV]

12O

14O

16O18O20O22O24O26O

NN+3Nfull(chiral NN+3N)

2 4 6 8 10 12 14 16 18Nmx

12O

14O

16O18O20O22O26O24O

Λ3N = 400 MeV, α = 0.08 fm4, E3mx = 14, optimal hΩ

19




NN+3Nind(chiral NN)

12 14 16 18 20 22 24 26

A

-180

-160

-140

-120

-100

-80

-60

-40

.

E[M

eV]


12 14 16 18 20 22 24 26

A

AO

experiment

IT-NCSM


parameter-freeab initio calculations with

full 3N interactionshighlights predictive power

of chiral NN+3N Hamiltonians

20

Spectroscopy of Carbon Isotopes


Forssen et al., JPG 40, 055105 (2013); Roth et al., in prep.

0+ 1

2+ 1

2+ 1

2 4 6 8 Exp.0

2

4

6

8

.

E[M

eV]

10C

0+ 0

0+ 0

0+ 0

1+ 0

1+ 1

2+ 0

2+ 02+ 1

4+ 0

2 4 6 8 Exp.

0

2

4

6

8

10

12

14

16

12C

0+ 1

0+ 1

0+ 1

1+ 1

2+ 1

2+ 1

2+ 14+ 1

2 4 6 8 Exp.0

2

4

6

8

10

14C

0+ 2

0+ 2

2+ 2

2+ 23? 24+ 2

2 4 6 Exp.Nmx

0

1

2

3

4

.

E[M

eV]

16C

0+ 3

2+ 3

2+ 3

2 4 6 Exp.

Nmx

0

1

2

3

4

18C

0+ 4

2+ 4

2 4 6 Exp.Nmx

0

1

2

3

4

20C

NN+3Nfull

Λ3N = 400MeV

α = 0.08 fm4

hΩ = 16MeV

21

Spectroscopy of Carbon Isotopes


INPR

OGRES

S2 4 6 8

0

1

2

3

4

5

6

7

8

.

B(E2,2+→0+)[e

2fm

4] 10C

2 4 6 80

1

2

3

4

5

6

7

8

12C

2 4 6 80

1

2

3

4

5

6

7

8

14C

2 4 6Nmx

0

0.5

1

1.5

2

2.5

3

.

B(E2,2+→0+)[e

2fm

4] 16C

2 4 6Nmx

0

0.5

1

1.5

2

2.5

3

18C

2 4 6Nmx

0

1

2

3

4

5

20C

NN+3Nfull

Λ3N = 400MeV

α = 0.08 fm4

hΩ = 16MeV

B(E2,2+1 → 0+gs)

B(E2,2+2 → 0+gs)

NEW

EXPE

RIME

NT

ANL,Mc

Cutch

anetal.

NEW

EXPE

RIME

NT

NSCL, Petrietal.

NEW

EXPE

RIME

NT

NSCL, Voss e

t al.

NEW

EXPE

RIME

NT

NSCL, Petrietal.

22





LatticeQCD


LatticeEFT


Energ

y-D

ensityFunct.

guidedbychiralEFT




body problem with







23

Frontier: Medium-Mass Nuclei


advent of novel ab initio many-body approachesapplicable in the medium-mass regime

Hagen, Papenbrock, Dean, Piecuch, Binder,...

coupled-cluster theory: ground-state parametrized by exponentialwave operator applied to single-determinant reference state

truncation at doubles level (CCSD) plus triples corrections (Λ-CCSD(T))

equations of motion for excited states and near-closed-shell nuclei

Bogner, Tsukiyama, Schwenk, Hergert,...

in-medium SRG: complete decoupling of particle-hole excitations frommany-body reference state through SRG evolution

normal-ordered evolving A-body Hamiltonian truncated at two-body level

both closed- and open-shell ground states; excitations via EOM or SM

Barbieri, Soma, Duguet,...

self-consistent Green’s function approaches and others...

control

lingand

quantif

ying th

e

uncerta

inties d

ueto v

arious t

runcat

ions is

major ch

allenge

24

CCSD with Explicit 3N Interactions


Roth, et al., PRL 109, 052501 (2012); Binder et al., PRC 87, 021303(R) (2013)

NN+3Nfull

-130

-120

-110

-100

.

E[M

eV]

16OhΩ = 20 MeV

-170

-160

-150

-140

-130

-120

-11024OhΩ = 20 MeV

4 6 8 10 12emx

-380

-360

-340

-320

-300

-280

-260

.

E[M

eV]

40CahΩ = 24 MeV

4 6 8 10 12emx

-500

-450

-400

-350

-300

-25048CahΩ = 28 MeV

CCSD-3B

( )

CCSD-NO2B

( )

α = 0.02 fm4

α = 0.04 fm4

α = 0.08 fm4

HF basis

E3mx = 12

Λ3N = 400 MeVnormal-ordering

approximation reproducesexplicit-3N results to

better than 1%

25




NN+3Nind(chiral NN)

12 14 16 18 20 22 24 26

A

-180

-160

-140

-120

-100

-80

-60

-40

.

E[M

eV]


12 14 16 18 20 22 24 26

A

AO

experiment

IT-NCSM


26




NN+3Nind(chiral NN)

12 14 16 18 20 22 24 26

A

-180

-160

-140

-120

-100

-80

-60

-40

.

E[M

eV]


12 14 16 18 20 22 24 26

A

AO

experiment

IT-NCSM

MR-IM-SRG


27




NN+3Nind(chiral NN)

12 14 16 18 20 22 24 26

A

-180

-160

-140

-120

-100

-80

-60

-40

.

E[M

eV]


12 14 16 18 20 22 24 26

A

AO

experiment

IT-NCSM

MR-IM-SRG

CCSD Λ-CCSD(T)


different many-bodyapproaches using sameNN+3N Hamiltonian give

consistent results minor differences are consis-

tent with uncertainty analysis

28

Next Step: Calcium & Nickel Isotopes


INPR

OGRES

S

NN+3Nind NN+3Nfull

-10

-9

-8

-7

-6

.

E/A[M

eV]

α-dependence α-dependence

36Ca 40Ca 48Ca 52Ca 54Ca-10

-9

-8

-7

-6

.

E/A[M

eV]

CCSD vs. IM-SRG

36Ca 40Ca 48Ca 52Ca 54Ca

CCSD vs. IM-SRG

α = 0.02 fm4

α = 0.04 fm4

α = 0.08 fm4

CCSD

E3mx = 14

Λ3N = 400 MeV

CCSD

IM-SRG

α = 0.08 fm4

E3mx = 14

Λ3N = 400 MeV

29

Next Step: Calcium & Nickel Isotopes


INPR

OGRES

S

NN+3Nind NN+3Nfull

-10

-9

-8

-7

-6

.

E/A[M

eV]

α-dependence α-dependence

48Ni 56Ni 60Ni 62Ni 68Ni-10

-9

-8

-7

-6

.

E/A[M

eV]

CCSD vs. IM-SRG

48Ni 56Ni 60Ni 62Ni 68Ni

CCSD vs. IM-SRG

α = 0.02 fm4

α = 0.04 fm4

α = 0.08 fm4

CCSD

E3mx = 14

Λ3N = 400 MeV

CCSD

IM-SRG

α = 0.08 fm4

E3mx = 14

Λ3N = 400 MeV

30





LatticeQCD


LatticeEFT


Energ

y-D

ensityFunct.

guidedbychiralEFT




body problem with







31

Ab Initio Hyper-Nuclear Structure


Hyper-Nuclear Structure Observables


LatticeQCD


LatticeEFT


Energ

y-D

ensityFunct.

guidedbychiralEFT

Chiral EFT Hamiltoniansconsistent NN,3N,YN,YY,... interactions & current operators



body problem with







32

Motivation: Hyper-Nuclear Structure


precision data on ground statesand spectroscopy of hyper-nuclei: talk by Nakamura

ab initio few-body (A ≲ 4) andphenomenological shell modelor cluster calculations so far

Haidenbauer et al.

chiral YN & YY interactions atLO and NLO are available

constrain YN & YY interactionby ab initio hyper-nuclear struc-ture calculations

33

Application: Λ7Li


INPR

OGRES

S1+

3+

-45

-40

-35

-30

-25

.

E[M

eV]

1+

3+

2 4 6 8 10 Exp.Nmx

0

1

2

3

.

E[M

eV]

12+32+

52+72+

12+

32+

52+

72+

2 4 6 8 10 Exp.Nmx

6Li 7ΛLi

Jülich’04

NN @ N3LOEntem&MachleidtΛNN = 500 MeV

3N @ N2LONavratil

Λ3N = 500 MeVtriton fit

Jülich’04Haidenbauer et al.scatt. & hypertriton

α = 0.08 fm4

hΩ = 20 MeV

34

Application: Λ7Li


INPR

OGRES

S1+

3+

-45

-40

-35

-30

-25

.

E[M

eV]

1+

3+

2 4 6 8 10 Exp.Nmx

0

1

2

3

.

E[M

eV]

12+32+

52+72+

12+

32+

52+

72+

2 4 6 8 10 Exp.Nmx

6Li 7ΛLi

chiral YN @ LOΛYN = 700 MeV

NN @ N3LOEntem&MachleidtΛNN = 500 MeV

3N @ N2LONavratil

Λ3N = 500 MeVtriton fit

YN @ LOHaidenbauer et al.ΛYN = 700 MeV

scatt. & hypertriton

α = 0.08 fm4

hΩ = 20 MeV

hyper-nuclear structuresets tight constraints on

YN interaction

start investigating

sensitivity of spectra

on YN input

35

New Horizons...


nuclear structure theory connected to QCD via chiral EFT

chiral EFT as universal, controlled and improvable starting point

consistent and optimized interactions at N2LO, N3LO,...

consistent similarity transformation of Hamiltonian and observables

innovations in ab initio many-body theory

consistent inclusion of 3N (and 4N) interactions

precision structure and spectroscopy in p- and sd-shell (IT-NCSM,...)

access to the medium-mass regime (CC, IM-SRG,...)

extension to ab initio hyper-nuclear structure

bridge to reaction theory (NCSM/RGM, NCSMC)

uncertainty quantification, error propagation, feedback cycle

many exciting applications ahead...

36

Epilogue


thanks to my group & my collaborators

S. Binder, A. Calci, S. Fischer, E. Gebrerufael,H. Krutsch, J. Langhammer, S. Reinhardt, S. Schulz,C. Stumpf, A. Tichai, R. Trippel, R. WirthInstitut für Kernphysik, TU Darmstadt

P. NavrátilTRIUMF Vancouver, Canada

J. Vary, P. MarisIowa State University, USA

S. Quaglioni, G. HupinLLNL Livermore, USA

P. PiecuchMichigan State University, USA

H. Hergert, K. HebelerOhio State University, USA

P. PapakonstantinouIPN Orsay, F

C. ForssénChalmers University, Sweden

H. Feldmeier, T. NeffGSI Helmholtzzentrum

JUROPA LOEWE-CSC HOPPER

COMPUTING TIME

37

Documents

New Horizons in Ab Initio Nuclear Structure Theorycrunch.ikp.physik.tu-darmstadt.de/tnp/pres/2013_inpc.pdf · 2020-03-31 · New Era of Nuclear Structure Theory Robert Roth – TU