Three-nucleon forces and exotic nuclei Javier Menndez Institut fr - - PowerPoint PPT Presentation

SLIDE 1

Three-nucleon forces and exotic nuclei

Javier Menéndez

Institut für Kernphysik (TU Darmstadt) and ExtreMe Matter Institute (EMMI) with Jason D. Holt (TU Darmstadt/EMMI), Achim Schwenk (EMMI/TU Darmstadt) and Johannes Simonis (TU Darmstadt/EMMI) NUSTAR Annual Meeting, GSI, 28 February 2013

SLIDE 2

Outline Theoretical Approach: NN+3N forces in Shell Model

The nuclear interaction: need of 3N forces Shell Model interactions with microscopic chiral NN+3N forces

Results for exotic nuclei

Neutron rich O isotopes Neutron rich Ca isotopes Proton rich N=8 and N=20 isotopes

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SLIDE 3

Outline Theoretical Approach: NN+3N forces in Shell Model

The nuclear interaction: need of 3N forces Shell Model interactions with microscopic chiral NN+3N forces

Results for exotic nuclei

Neutron rich O isotopes Neutron rich Ca isotopes Proton rich N=8 and N=20 isotopes

SLIDE 4

The Nuclear interaction

Ideally, QCD interaction (Latice QCD) ⇒ Hard problem: QCD non-perturbative at low energy Alternatively, bare NN potential (spirit of Shell Model) ⇒ Drawback: manipulate the interaction to solve the many-body nuclear problem Finally, use selected nuclei (Energy Density Functionals) ⇒ Drawback: loss of predictive power

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SLIDE 5

The Nuclear interaction

Ideally, QCD interaction (Latice QCD) ⇒ Hard problem: QCD non-perturbative at low energy Alternatively, bare NN potential (spirit of Shell Model) ⇒ Drawback: manipulate the interaction to solve the many-body nuclear problem Finally, use selected nuclei (Energy Density Functionals) ⇒ Drawback: loss of predictive power

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SLIDE 6

Limitation of NN potentials

Ab initio calculations (No Core Shell Model) with perfect NN potentials (AV18) fail to reproduce light nuclei spectra

Navratil et al. PRL99 042501(2007)

⇒ Confirms experience of Shell Model (monopole adjustments)

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SLIDE 7

Need of 3N forces

Need 3N forces!

Zuker PRL90 042502 (2003)

3N forces originate in the elimination of degrees of freedom (N-body forces appear in any effective theory)

Bogner, Schwenk, Furnstahl PPNP65 94 (2010)

But few NNN scattering data available! ⇒ Need a framework that, in a natural manner, describes 3N forces consistent with NN forces

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SLIDE 8

Chiral EFT

• Chiral EFT is a low energy approach to QCD

valid for nuclear structure energies

• Exploits approximate chiral symmetry of QCD:

pions are special particles (pseudo-Goldstone bosons)

• Nucleons interact via pion exchanges and contact interactions

(physics non-resolved at nuclear structure energies)

• Enables a systematic basis for strong interactions,

expansion in powers of Q/Λb Q ∼ mπ, typical momentum scale Λb ∼ 500 MeV, breakdown scale

• Systematic expansion naturally includes NN, 3N, 4N... forces

(at different orders)

• Short-range couplings are fitted to experiment once

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SLIDE 9

Chiral EFT NN+3N forces

Systematic expansion: state-of-the-art chiral EFT forces

• NN forces included up to N3LO
• 3N forces included up to N2LO

NN fitted to:

• NN scattering data

3N fitted to:

• 3H Binding Energy
• 4He radius

Weinberg, van Kolck, Kaplan, Savage, Wise, Epelbaum, Kaiser, Meißner...

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SLIDE 10

Many Body Perturbation Theory

Better convergence through Vlowk transformation Many-body Perturbation Theory up to third order to build an effective Shell Model interaction in a valence space

Single Particle Energies (SPEs) Two-Body Matrix Elements (TBMEs)

Full diagonalizations using codes ANTOINE and NATHAN

Caurier et al. RMP77 427(2005) and compare to experiment

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SLIDE 11

3N Forces

Treatment of 3N forces: normal-ordered 2B: 2 valence, 1 core particle ⇒ (effective) Two-body Matrix Elements (TBME) normal-ordered 1B: 1 valence, 2 core particles ⇒ (effective) Single particle energies (SPE) residual 3B: ⇒ Estimated to be suppressed by Nvalence/Ncore

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SLIDE 12

Outline Theoretical Approach: NN+3N forces in Shell Model

The nuclear interaction: need of 3N forces Shell Model interactions with microscopic chiral NN+3N forces

Results for exotic nuclei

Neutron rich O isotopes Neutron rich Ca isotopes Proton rich N=8 and N=20 isotopes

SLIDE 13

O isotopes: dripline anomaly

O isotopes: ’anomaly’ in the dripline at 24O, doubly magic nucleus

2 8 20 28 Z N 2 8

stability line

O 1970 F 1999 N 1985 C 1986 B 1984 Be 1973 Li 1966 H 1934 He 1961 Ne 2002 Na 2002 Mg2007 Al 2007 Si 2007

unstable oxygen isotopes unstable fluorine isotopes stable isotopes unstable isotopes neutron halo nuclei

Theoretical calculations predict the dripline at 26O or 28O: a fit to this property is needed to correctly reproduce experiment (e.g. USD interactions, EDFs)

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SLIDE 14

O isotopes: effective SPE’s

8 20 16 14 Neutron Number (N) Neutron Number (N) 8 20 16 14

s 1/2

(c) G-matrix NN + 3N (∆) forces

d3/2 d5/2

NN NN + 3N (∆)

d3/2 d5/2 s 1/2

NN + 3N (N LO) NN NN + 3N (∆)

low k

(d) V NN + 3N (∆,N LO) forces

2 2

Single-Particle Energy (MeV)

4

• 4
• 8

Single-Particle Energy (MeV) 8 20 16 14

d3/2 d5/2 s 1/2

(a) Forces derived from NN theory V G-matrix (b) Phenomenological forces

d3/2 s 1/2 d5/2

USD-B SDPF-M 8 20 16 14

Neutron Number (N) Neutron Number (N)

low k

4

• 4
• 8

Evolution of d3/2 orbit (and to a less extent s1/2 and d5/2 orbits) incorrectly predicted by NN forces Phenomenological interactions include further repulsive contributions The effect of 3N forces is similar to phenomenological ’cures’

Otsuka et al. PRL105 032501 (2010)

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SLIDE 15

O isotopes: masses and spectra

Chiral NN+3N forces give the correct picture for masses and spectra

16 18 20 22 24 26 28 Mass Number A

• 80
• 70
• 60
• 50
• 40
• 30
• 20
• 10

Energy (MeV)

sd-shell (2nd) sd-shell (3rd) sdf7/2p3/2-shell 16 18 20 22 24 26 28

Mass Number A

USDb sd-shell sdf7/2p3/2-shell (c) NN + 3N (b) NN

Otsuka et al. PRL105 032501 (2010) Holt, JM, Schwenk EPJA in press (2013)

3N forces provide repulsion missing in NN-only forces 3N forces crucial also for reliable description of spectra

NN NN+3N Exp 1 2 3 4 5 6 7 8 9 Energy (MeV) 24O

4

+

2

+ +

2

+ +

1

+

3

+ +

2

+

1

+ +

2

+

3

+

4

+ +

2

+

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SLIDE 16

Residual 3N Forces

In the most neutron-rich oxygen isotopes, 3N forces between 3 valence neutrons (remember, suppressed by Nvalence/Ncore) can give a relevant contribution

d3/2 s 1/2 d5/2

(a) G-matrix NN + 3N ( forces

d3/2 s 1/2 d5/2

4

• 4
• 8

Single-Particle Energy (MeV) Neutron Number (N) 8 20 16 14 Neutron Number (N) 8 20 16 14

NN + 3N (N LO) NN NN + 3N ( NN NN + 3N (

low k

(b) V NN + 3N ( ,N LO forces

2 2

(d) 3-body interactions with one more neutron added to (c) (c) 3-body interaction O core

16

0.5 1 1.5

Energy (MeV)

26O 2

+

25O NN+3N NN+3N + residual 3N 3/2

+ +

24O

+

MoNA/NSCL (2008, 2012) R3B-LAND (this work) + residual 3N

Residual 3N contributions are repulsive They are small compared to normal-ordered 3N force, but increase with N Very good agreement with resonances in 25O and 26O

Caesar, Simonis et al, arXiv:1209.0156

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SLIDE 17

Ca isotopes: 2n separation energies

Compare S2n theoretical calculations with experimental results S2n = −[B(N, Z) − B(N − 2, Z)]

28 29 30 31 32 33 34 35 4 6 8 10 12 14 16 18

S2n (MeV)

TITAN AME2003 NN+3N (emp) NN+3N (MBPT)

Gallant et al. PRL109 032506 (2012)

New precision measurements change previous slope from AME 2003 ∼ 2 MeV change in 52Ca! Very good agreement between calculation and experimental trend (Similar level as phenomenological interactions) Two sets of spe’s, empirical and calculated, in pfg9/2 valence space

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SLIDE 18

Nuclear Pairing Gaps

Compare also to experimental three-point mass differences: ∆(3)

n

= (−1)N 2 [B(N + 1, Z) + B(N − 1, Z) − 2B(N, Z)]

28 29 30 31 32 33 34 35

Neutron Number N

1 2 3

∆n

(3) (MeV)

TITAN+ AME2003

Gallant et al. PRL109 032506 (2012)

The experimental trend is very well reproduced by theory Theoretical results systematically 0.5 MeV higher than experiment Prediction of sub-shell closure candidates N = 32 (moderate closure) and N = 34 (no apparent closure)

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SLIDE 19

Shell closures in Ca isotopes

2+

1 energies

characterize shell closures

• f Ca isotopes

Closure at N = 28 with 3N forces in (pfg9/2)

Holt et al. JPG39 085111(2012) Holt, JM, Schwenk, to be submitted 42 44 46 48 50 52 54 56 58 60 62 64 66 68

Mass Number A

1 2 3 4 5 6 7

2

+ Energy (MeV)

NN NN+3N [emp] NN+3N [MBPT]

1

3N forces enhance closure at N = 32 (more moderate than N = 28) 3N forces reduce strong closure at N = 34 (no apparent closure) Predicted shell closure at N = 60, unaffected by 3N forces (but continuum missing in our calculations!)

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SLIDE 20

Proton dripline at N = 8

16 17 18 19 20 21 22 23 24 Mass Number A

• 12
• 10
• 8
• 6
• 4
• 2

Ground-State Energy (MeV)

NN NN+3N NN+3N (sdf7/2p3/2) AME2011 IMME

N=8

Holt, JM, Schwenk PRL110 022502 (2013)

Theory complements/improves mass extrapolations and isomeric mass-multiplet formula (IMME) E(A, T, Tz) = E(A, T, −Tz) + 2b(A, T)Tz NN forces oberbind 3N forces essential to describe masses and the predict the proton dripline Proton dripline not certain predicted either in 20Mg or 22Si: S2p= -0.12 (Theory) / +0.01 (IMME) Measurement needed! Calculations in standard and extended spaces

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SLIDE 21

Spectra of N = 8 isotones

Exp Exp Exp

1 2 3 4 5 6

Excitation Energy (MeV)

18Ne

4

+ +

2

+

3/2

+

5/2

+

2

+ +

4

+

1/2

+

(5/2

+)

(1/2

+)

(3/2

+)

2

+ +

2

+

19Na 20Mg

+

2

+

4

+

(4

+)

21Al 22Si

+

2

+

2

+ +

1/2

+

5/2

+

3/2

+

3/2

+

5/2

+

1/2

+

7/2

+

Including NN+3N forces good agreement with known spectra Prediction of 2+,4+ doublet close to previously unpublished 4+ state in 20Mg (I. Mukha) Prediction of 21Al and 22Si spectra

Holt, JM, Schwenk PRL110 022502 (2013)

In 22Si calculations point to a sub-shell closure (analogous to 22O) More experimental information greatly appreciated!

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SLIDE 22

Masses and spectra of N = 20 isotones

40 41 42 43 44 45 46 47 48 Mass Number A

• 12
• 10
• 8
• 6
• 4
• 2

Ground-State Energy (MeV)

NN NN+3N NN+3N (pfg9/2) Exp and AME2011 extrapolation IMME

N=20

Exp

1 2 3 4 5

Excitation Energy (MeV)

42Ti

6

+ +

2

+

7/2

+ + +

6

+ +

7/2

+ +

4

+

(2

+)

2

+

4

+

5/2

+

3/2

+

3/2

+

11/2

+

9/2

+

2

+

4

+

2

+

4

+

2

+

43V 44Cr 45Mn 46Fe 47Co 48Ni

2

+

3/2

+

1/2

+

5/2

+

3/2

+

5/2

+

2

+

5/2

+ +

4

+

4

+

3/2

+

7/2

+

1/2

+

3/2

+

7/2

+ + + +

4

+

2

+

2

+

Holt, JM, Schwenk PRL110 022502 (2013)

Dripline robustly predicted at 46Fe Good description of 48Ni: S2p= -1.02 (Th) vs -1.28(6) (Exp) Pomorski (2012)

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SLIDE 23

Summary and Outlook

Shell Model calculation based on chiral EFT (NN+3N forces) and MBPT gives good agreement with experimental masses, two-neutron separation energies, pairing gaps and excitation spectra for oxygen, calcium isotopes and proton-rich N=8,20 isotones:

• Neutron rich O masses and spectra reproduced with NN+3N forces
• Residual 3N forces needed for very neutron-rich 25,26O
• Predicted neutron rich Ca S2n’s agree with recent measurements
• Ca pairing gaps and spectra (shell closures) including NN+3N forces
• Dripline and spectra of proton-rich N = 8, 20 isotones predicted

Outlook: Explore heavier isotope and isotone chains: include T=0 TBME Explore uncertainties in the theoretical calculation

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