Part IV: Three-Nucleon Forces to Nuclei To understand the properties - - PowerPoint PPT Presentation

SLIDE 1

How will we approach this problem: QCD à à NN (3N) forces à à Renormalize à à “Solve” many-body problem à à Predictions

To understand the properties of complex nuclei from first principles Three-Nucleon Forces Basic ideas – why needed? 3N from chiral EFT Implementing in shell model Relation to monopoles Predictions/new discoveries Connections beyond structure

a b c

Part IV: Three-Nucleon Forces to Nuclei

SLIDE 2

Chiral Effective Field Theory: Nuclear Forces

Nucleons interact via pion exchanges and contact interactions Consistent treatment of NN, 3N,… NN couplings fit to scattering data

Weinberg, van Kolck, Kaplan, Savage, Wise

Δ(1232)

SLIDE 3

V3N

3 = gA 2

8F

4

• 1 · q

1 3 · q 3 q1

2 + M 2q3 2 + M 21 · 3− 4c1M 2

+ 2c3q 1 · q 3 + c41 3 · 2q 1 q 3 · 2 − gAD 8F

2

• 3 · q

3 q3

2 + M 2 1 · 3

1 · q 3 + 1 2E2 · 3,

Chiral EFT: N2LO 3N

First non-vanishing 3N contributions: Next-to-next-to-leading order ν = 3

SLIDE 4

Chiral EFT: N2LO 3N

First non-vanishing 3N contributions: Next-to-next-to-leading order ν = 3 Three undetermined πN couplings from NN fit

V3N

3 = gA 2

8F

4

• 1 · q

1 3 · q 3 q1

2 + M 2q3 2 + M 21 · 3− 4c1M 2

+ 2c3q 1 · q 3 + c41 3 · 2q 1 q 3 · 2 − gAD 8F

2

• 3 · q

3 q3

2 + M 2 1 · 3

1 · q 3 + 1 2E2 · 3,

SLIDE 5

Next-to-next-to-next-to-leading order

Chiral EFT: N3LO 3N

Good news: no new constants Bad news: well, there’s all this ν = 4

SLIDE 6

Aside: Effects of Adding Explicit Deltas

Reshuffles effects to different chiral orders

• π-π

π

• no effect up to N2LO (modulo reshuffling)

expect large contributions to the ring & 2π-1π-topologies saturating some of the N4,5,6LO graphs in the Δ-less theory What is more efficient: Δ-less N4LO (and beyond?) vs Δ-full N3LO ??

SLIDE 7

SRG Evolution in HO Basis

Most common to SRG evolve 3N in HO basis: 1) SRG-evolve both NN and 3N: NN+3N-full 2) NN Vlowk, refit 3N: NN+3N-fit

= 0.00 fm4

= ∞ fm1

EJT

• H Tint
• EJT

J = 1

2 +, T = 1 2 , Ω = 24 MeV

3B-Jacobi HO matrix elements

0 E 18 20 22 24 26 28 (E, ) 28 26 24 22 20 18

• E
• .

(E, )

2 1.16 0.64 0.32 0.12 [MeV]

NCSM ground state 3H

• 4

8 12 16 20 24 28 Nm

• 8.5
• 8
• 7.5
• 7
• 6.5

E [MeV]

SLIDE 8

SRG Evolution in HO Basis

Most common to SRG evolve 3N in HO basis: 1) SRG-evolve both NN and 3N: NN+3N-full 2) NN Vlowk, refit 3N: NN+3N-fit

= 0.02 fm4

= 2.66 fm1

EJT

• H Tint
• EJT

J = 1

2 +, T = 1 2 , Ω = 24 MeV

3B-Jacobi HO matrix elements

0 E 18 20 22 24 26 28 (E, ) 28 26 24 22 20 18

• E
• .

(E, )

2 1.16 0.64 0.32 0.12 [MeV]

NCSM ground state 3H

• 4

8 12 16 20 24 28 Nm

• 8.5
• 8
• 7.5
• 7
• 6.5

E [MeV]

SLIDE 9

SRG Evolution in HO Basis

Most common to SRG evolve 3N in HO basis: 1) SRG-evolve both NN and 3N: NN+3N-full 2) NN Vlowk, refit 3N: NN+3N-fit

= 1.28 fm4

= 0.94 fm1

EJT

• H Tint
• EJT

J = 1

2 +, T = 1 2 , Ω = 24 MeV

3B-Jacobi HO matrix elements

0 E 18 20 22 24 26 28 (E, ) 28 26 24 22 20 18

• E
• .

(E, )

2 1.16 0.64 0.32 0.12 [MeV]

NCSM ground state 3H

• 4

8 12 16 20 24 28 Nm

• 8.5
• 8
• 7.5
• 7
• 6.5

E [MeV]

SLIDE 10

Induced 3N Forces

Effect of including 3N-ind? Exactly initial up to neglected 4N-ind NN-only clear cutoff dependencs 3N-ind: dramatic reduction in cutoff dependence, no agreement with experiment

1 2 3 4 5 6 7 10 20

λ [fm

−1]

−8.6 −8.4 −8.2 −8.0 −7.8 −7.6 −7.4

Ground-State Energy [MeV]

NN-only NN + NNN-induced

3H

Expt.

N

3LO (500 MeV)

1 2 3 4 5 10 20

λ [fm

−1]

−29 −28 −27 −26 −25 −24

Ground-State Energy [MeV]

NN-only NN+NNN-induced

4He

N

3LO (500 MeV)

Expt.

VNN

SLIDE 11

Induced 3N Forces

Effect of including 3N-ind? Exactly initial up to neglected 4N-ind NN-only clear cutoff dependencs 3N-ind: dramatic reduction in cutoff dependence, no agreement with experiment NN+3N-full retains cutoff independence, reproduces experiment!

1 2 3 4 5 6 7 10 20

λ [fm

−1]

−8.6 −8.4 −8.2 −8.0 −7.8 −7.6 −7.4

Ground-State Energy [MeV]

NN-only NN + NNN-induced

3H

Expt.

N

3LO (500 MeV)

1 2 3 4 5 10 20

λ [fm

−1]

−29 −28 −27 −26 −25 −24

Ground-State Energy [MeV]

NN-only NN+NNN-induced

4He

N

3LO (500 MeV)

Expt.

VNN

1 2 3 4 5 6 7 10 20

λ [fm

−1]

−8.6 −8.4 −8.2 −8.0 −7.8 −7.6 −7.4

Ground-State Energy [MeV]

NN-only NN + NNN-induced NN + NNN

3H

Expt. 1 2 3 4 5 10 20

λ [fm

−1]

−29 −28 −27 −26 −25 −24

Ground-State Energy [MeV]

NN-only NN+NNN-induced +NNN-initial

4He

N

3LO (500 MeV)

Expt.

SLIDE 12

Benefits of Lower Cutoffs

Use cutoff dependence to assess missing physics: return to Tjon line Varying cutoff moves along line Still never reaches experiment Tool, not a parameter!

ing

SLIDE 13

Benefits of Lower Cutoffs

Use cutoff dependence to assess missing physics: return to Tjon line Varying cutoff moves along line Still never reaches experiment Tool, not a parameter! Including 3N reaches expt. Why not perfect fit?

ing

7.6 7.8 8 8.2 8.4 8.6 8.8

Eb(

3H) [MeV]

24 25 26 27 28 29 30

Eb(

4He) [MeV]

Tjon line for NN-only potentials SRG NN-only SRG NN+NNN (λ >1.7 fm

−1)

8.45 8.5 28.2 28.3 28.4

N

3LO

λ=3.0 λ=1.2 λ=2.5 λ=1.5 λ=2.0 λ=1.8 Expt. (500 MeV)

SLIDE 14

Cutoff Variation with 3N Forces

Use cutoff variation to assess missing physics in few body systems Radii of triton and alpha particle calculated from NN+3N forces Minimal cutoff variation

SLIDE 15

Chiral Three-Body Forces in Light Nuclei

Importance of chiral 3N forces established in light nuclei Converged NCSM (Navratil 2007) They work! What about nuclear matter?

SLIDE 16

Perturbative in Symmetric Nuclear Matter?

Significant improvement with low-momentum interactions!

Yes, but if I remember, saturation isn’t correct

H (Λ) = T + VNN (Λ) + V3N (Λ) + V4N (Λ) + · · ·

SLIDE 17

Perturbative in Symmetric Nuclear Matter?

Now NN+3N-fit remain perturbative and reproduce saturation! Minor but non-negligible cutoff variation

H (Λ) = T + VNN (Λ) + V3N (Λ) + V4N (Λ) + · · ·

empirical

SLIDE 18

Normal-ordered 3N: contribution to valence neutron interactions

3N Forces for Valence-Shell Theories

O core

16

O core

16

Effective two-body Effective one-body

Combine with microscopic NN: eliminate empirical adjustments

ab V3N,eff a'b' = αab

α =core

∑

V3N αa'b'

a V3N,eff a' = 1 2 αβa

αβ =core

∑

V3N αβa'

SLIDE 19

Normal-ordered 3N: microscopic contributions to inputs for CI Hamiltonian

3N Forces for Valence-Shell Theories

Effects of residual 3N between 3 valence nucleons?

Hagen, Papenbrock et al. (2007)

Coupled-Cluster theory with 3N: benchmark of 4He 0- 1- and 2-body of 3NF dominate Residual 3N can be neglected Work on 16O in progress Approximated residual 3N by summing over valence nucleon – Nucleus-dependent: effect small, not negligible by 24O Effects of residual 3N between 3 valence nucleons?

SLIDE 20

Dominant effect from

• ne-Δ – as expected

from cutoff variation Future: Improved treatment of high-lying orbits

Two-body 3N: Monopoles in sd-shell

3N forces produce clear repulsive shift in monopoles First calculations to show missing monopole strength due to neglected 3N

• 3.5
• 3
• 2.5
• 2
• 1.5
• 1
• 0.5

0.5 1

V(ab;T) [MeV]

Vlow k +3N (Δ) + 3N (N

2LO)

USDa USDb

d5d5 d5d3 d5s1 d3d3 d3s1 s1s1

T=1

SLIDE 21

?

F dripline

Oxygen Anomaly

d3/2 unbound at 24O with 3N forces First calculations using NN+3N

Otsuka, Suzuki, JDH, Schwenk, Akaishi, PRL (2010)

3N repulsion amplified with N: crucial for neutron-rich nuclei Probe limits of nuclear existence with 3N forces

Single-Particle Energy (MeV)

4

• 4
• 8

Neutron Number (N) 8 20 16 14

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

SLIDE 22

−60 −40 −20

8

Energy (MeV) Neutron Number (N)

8 16 20 14

(c) Energies calculated from V NN + 3N (∆,N LO) forces

low k

2

NN NN + 3N (N LO) NN + 3N (∆)

Exp.

2

?

F dripline

Oxygen Anomaly

d3/2 unbound at 24O with 3N forces First calculations using NN+3N

Isotopes unbound beyond 24O First microscopic explanation of oxygen anomaly

Otsuka, Suzuki, JDH, Schwenk, Akaishi, PRL (2010)

3N repulsion amplified with N: crucial for neutron-rich nuclei Probe limits of nuclear existence with 3N forces

Single-Particle Energy (MeV)

4

• 4
• 8

Neutron Number (N) 8 20 16 14

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

SLIDE 23

Large-space methods with same SRG-evolved NN+3N-ind forces Agreement between all methods with same input forces No reproduction of dripline in any case

Comparison with Large-Space Methods

16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130
• 120

Energy (MeV)

MR-IM-SRG IT-NCSM SCGF CC

• btained in large many-body spaces

AME 2012

NN+3N-ind

16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130

Energy (MeV)

Exp. NN+3N-ind

SLIDE 24

Normal-Ordered Hamiltonian

Now rewrite exactly the initial Hamiltonian in normal-ordered form

HN.O. = E0 + X

ij

fij n a†

iaj

• + 1

4 X

jkl

Γijkl n a†

ia† jalak

• + 1

36 X

ijklmn

Wijklmn n a†

ia† ja† kalaman

• E0 = + +

two-body formalism with f = + + Γ = + E0 = f = Γ = i j i j i j i j k l i j k l 1-body 2-body 3-body N.O. 0-body → N.O. 1-body → N.O. 2-body →

SLIDE 25

Normal-Ordered Hamiltonian

Now rewrite exactly the initial Hamiltonian in normal-ordered form Neglect residual 3N

HN.O. = E0 + X

ij

fij n a†

iaj

• + 1

4 X

jkl

Γijkl n a†

ia† jalak

• + 1

36 X

ijklmn

Wijklmn n a†

ia† ja† kalaman

• E0 = + +

two-body formalism with f = + + Γ = + E0 = f = Γ = i j i j i j i j k l i j k l 1-body 2-body 3-body N.O. 0-body → N.O. 1-body → N.O. 2-body →

SLIDE 26

Large-space methods with same SRG-evolved NN+3N-ind forces Agreement between all methods with same input forces No reproduction of dripline in any case

Comparison with Large-Space Methods

16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130
• 120

Energy (MeV)

MR-IM-SRG IT-NCSM SCGF CC

• btained in large many-body spaces

AME 2012

NN+3N-ind

16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130

Energy (MeV)

Exp. NN+3N-ind

SLIDE 27

Large-space methods with same SRG-evolved NN+3N-full forces Agreement between all methods with same input forces Clear improvement with NN+3N-full Validates valence-space results

Comparison with Large-Space Methods

16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130

Energy (MeV)

MR-IM-SRG IT-NCSM SCGF Lattice EFT CC

• btained in large many-body spaces

AME 2012

16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130

Energy (MeV)

Exp. NN+3N-ind NN+3N-full

NN+3N-full

SLIDE 28

Self-consistent Green’s Function with same SRG-evolved NN+3N forces Robust mechanism driving dripline behavior 3N repulsion raises d3/2, lessens decrease across shell Similar to first MBPT NN+3N calculations in oxygen

Oxygen Dripline Mechanism

2s1 2 1d5 2 1d3 2

8 6 4 2 2 4 6

i A 1 MeV

2N 3N full 2N 3N ind

60

14O 16O 22O 24O 28O

180

Cipollone, Barbieri, Navrátil, PRL (2013) 16 18 20 22 24 26 28

Mass Number A

• 12
• 8
• 4

4

Single-Particle Energy (MeV)

NN+3N-ind NN+3N-full

d5/2 d3/2 s1/2

SLIDE 29

Recent calculations at N2LO without 3N forces found a remarkable result Oxygen dripline reproduced with NN forces only! What does this mean about 3N?

Optimized Chiral Forces N2LO NN-Only

15 16 17 18 19 20 21 22 23 24 25 26 27 28

AO

−180 −170 −160 −150 −140 −130 −120 −110 −100 −90

E (MeV) Experiment NNLOopt N

3LO EM

16 18 20 22 24 26 28

• 70
• 60
• 50
• 40
• 30
• 20
• 10

E (MeV)

AO

Shell Model

Ekström et al (PRL 2013)

SLIDE 30

Recent calculations at N2LO without 3N forces found a remarkable result Oxygen dripline reproduced with NN forces only! Power counting dictates 3N forces be included

Optimized Chiral Forces N2LO NN-Only

15 16 17 18 19 20 21 22 23 24 25 26 27 28

AO

−180 −170 −160 −150 −140 −130 −120 −110 −100 −90

E (MeV) Experiment NNLOopt N

3LO EM

16 18 20 22 24 26 28

• 70
• 60
• 50
• 40
• 30
• 20
• 10

E (MeV)

AO

Shell Model

Ekström et al (PRL 2013)

SLIDE 31

Recent calculations at N2LO without 3N forces found a remarkable result Oxygen dripline reproduced with NN forces only Unnaturally large couplings when 3N fit in 3H(?) – results off the plot! Lesson: 3N forces unavoidable part of theory – must investigate importance

Optimized Chiral Forces N2LO NN-Only

Ekström et al (PRL 2013)

15 16 17 18 19 20 21 22 23 24 25 26 27 28

AO

−180 −170 −160 −150 −140 −130 −120 −110 −100 −90

E (MeV) Experiment NNLOopt N

3LO EM

16 18 20 22 24 26 28

• 70
• 60
• 50
• 40
• 30
• 20
• 10

E (MeV)

AO

Shell Model

SLIDE 32

Impact on Spectra: 23O

Neutron-rich oxygen spectra with NN+3N 5/2+, 3/2+ energies reflect 22,24O shell closures

sd-shell NN only

Wrong ground state 5/2+ too low 3/2+ bound NN+3N Clear improvement in extended valence space

NN sd NN sdf7/2p3/2 NN+3N sd NN+3N sdf7/2p3/2 Expt.

• 1

1 2 3 4 5

Energy (MeV)

23O

5/2

+

1/2

+

3/2

+

1/2

+

5/2

+

5/2

+

1/2

+

3/2

+

3/2

+

1/2

+

5/2

+

3/2

+

Sn

(5/2

+)

1/2

+

(3/2

+)

SLIDE 33

Oxygen spectra: Effective interactions from Coupled-Cluster theory MBPT in extended valence space IM-SRG/CCEI spectra agree within ~300 keV

Comparison with MBPT/CCEI Oxygen Spectra

MBPT CCEI IM-SRG Expt. 1 2 3 4 5 6 7 8 9

Energy (MeV)

+

2

+

2

+

2

+ + +

(2

+)

2

+

2

+

(0

+) + +

4

+

4

+

(4

+)

4

+

2

+ +

2

+ +

3

+

3

+

3

+

3

+ +

22O

MBPT CCEI IM-SRG Expt. 1 2 3 4 5 6

1/2

+

5/2

+

5/2

+

1/2

+

3/2

+

3/2

+

1/2

+

5/2

+

3/2

+

(5/2

+)

1/2

+

(3/2

+)

23O

MBPT CCEI IMSRG Expt. 1 2 3 4 5 6 7

+

2

+ +

2

+

1

+ +

1

+

1

+

2

+ +

2

+

1

+

24O

SLIDE 34

Physics beyond dripline highly sensitive to 3N and continuum effects Prediction of low-lying 2+ in 26O (recently measured at RIKEN)

Beyond the Oxygen Dripline

24O

–1 1 2 3

Energy (MeV)

MBPT IM-SRG CCEI CC MoNA/NSCL R3B/LAND 0+ MR-IM-SRG SCGF

25O (3/2+) 1 26O (0+) 1 26O (2+) 1

SLIDE 35

24F spectrum: IM-SRG (sd shell), full CC, USDB

New measurements from GANIL IM-SRG: comparable with phenomenology, good agreement with new data

Experimental Connection: 24F Spectrum

Ekström et al., PRL (2014) Cáceres et al., arXiv:1501.01166 Hebeler, JDH, Menéndez, Schwenk, ARNPS (2015)

CC IM-SRG Expt. USDB

0.5 1 1.5 2 2.5 3 3.5 4

Energy (MeV)

4

+ +

2

+

2

+ +

2

+

2

+

4

+

5

+

1

+

1

+

3

+

3

+

3

+

3

+

1

+

1

+

2

+

(4

+)

(3

+)

(4

+,2 +)

3

+

4

+

1

+

2

+

3

+

2

+

4

+

(2

+)

1

+

2

+

1

+

4

+

3

+

24F

SLIDE 36

Fluorine spectroscopy: MBPT and IM-SRG (sd shell) from NN+3N forces IM-SRG: competitive with phenomenology, good agreement with data Preliminary results already for scalar operators: charge radii, E0 transitions Upcoming: general operators M1, E2, GT, double-beta decay

Fully Open Shell: Neutron-Rich Fluorine Spectra

Bogner, Hergert, JDH, Schwenk, in prep.

MBPT IM-SRG Expt. USDB 1 2 3 4 5

5/2

+

5/2

+

1/2

+

5/2

+

7/2

+

7/2

+

3/2

+

1/2

+

1/2

+

9/2

+

5/2

+

9/2

+

3/2

+

1/2

+

5/2

+

(5/2

+)

5/2

+

9/2

+

1/2

+

3/2

+

3/2

+

3/2

+

(1/2

+)

(9/2

+)

(3/2

+)

(3/2

+)

(5/2

+)

25F

MBPT IM-SRG Expt. USDB 1 2 3 4

3

+

4

+

1

+

4

+

4

+

3

+

2

+

2

+

2

+

1

+

1

+

1

+

1

+

3

+

4

+

2

+

2

+

1

+

3

+

2

+

3

+

1

+

26F Stroberg et al.

MBPT IM-SRG Expt. USDB 1 2 3 4

Energy (MeV)

5/2

+

9/2

+

1/2

+

5/2

+

9/2

+

7/2

+

3/2

+

1/2

+

3/2

+

5/2

+

1/2

+

7/2

+

7/2

+

5/2

+

5/2

+

5/2

+

5/2

+

7/2

+

3/2

+

(3/2

+)

23F

SLIDE 37

42 44 46 48 50 52 54 56 58 1 2 3 4 5 6

2

+ Energy (MeV)

Experiment GXPF1 KB3G

42 44 46 48 50 52 54 56 58

G Vlow k G [SPE_KB3G] Vlow k [SPE_KB3G] Vlow k [fp+g9/2]

(a) Phenomenological Forces (b) NN-only Theory

1

Calcium Isotopes: Magic Numbers

Phenomenological Forces

Large gap at 48Ca

Discrepancy at N=34 Microscopic NN Theory Small gap at 48Ca N=28: first standard magic number not reproduced in microscopic NN theories

40 44 48 52 56 60

Mass Number A

• 15
• 10
• 5

Single-Particle Energy (MeV)

KB3G GXPF1

40 44 48 52 56 60

Mass Number A

G Vlow k f7/2 p3/2 p1/2 f5/2 f5/2 p1/2 p3/2 f7/2

(c) NN + 3N (b) NN-only Theory

(a) Phenomenological Forces

40Ca

GXPF1: Honma, Otsuka, Brown, Mizusaki (2004) KB3G: Poves, Sanchez-Solano, Caurier, Nowacki (2001)

? ?

8 28 20 50

0p3/2 0d5/2 1s1/2 0d3/2 0p1/2 0g9/2 0f5/2 1p3/2 1p1/2 0f7/2

SLIDE 38

Phenomenological vs. Microscopic

Compare monopoles from:

Microscopic low-momentum

interactions

Phenomenological KB3G, GXPF1

interactions Shifts in low-lying orbitals:

• T=1 repulsive shift

f7f7 f7p3 f7f5 f7p1 p3p3 f5p3 p3p1 f5f5 f5p1 p1p1

• 1
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4

V(ab;T) [MeV]

KB3G GXPF1 Vlow k

T=1

SLIDE 39

No clear dripline; flat behavior past 54Ca – Halos beyond 60Ca?

Calcium Ground State Energies and Dripline

Signatures of shell evolution from ground-state energies?

Holt, Otsuka, Schwenk, Suzuki, JPG (2012)

40 44 48 52 56 60 64 68

Mass Number A

• 150
• 120
• 90
• 60
• 30

Energy (MeV)

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

S2n = − BE(N,Z) − BE(N − 2,Z)

[ ] sharp decrease indicates shell closure

SLIDE 40

Experimental Connection: Mass of 54Ca

New precision mass measurement of 53,54Ca at ISOLTRAP: multi-reflection ToF TITAN Measurement Flat trend from 50-52Ca Mass 52Ca 1.74 MeV from AME ISOLTRAP Measurement Sharp decrease past 52Ca Unambiguous closed-shell 52Ca Test predictions of various models MBPT NN+3N Excellent agreement with new data Reproduces closed-shell 48,52Ca Weak closed sell signature past 54Ca

• Wienholtz et al., Nature (2013)

? ?

N=3 =34 m magic gic n num umbe ber in c r in calc lcium ium?

SLIDE 41

42 44 46 48 50 52 54 56 58 1 2 3 4 5 6

2

+ Energy (MeV)

Experiment GXPF1 KB3G

(a) Phenomenological Forces

1

Calcium Isotopes: Magic Numbers

Phenomenological Models

Large gap at 48Ca, discrepancy at N=34

Ab initio theories Reproduce all new magic numbers, consistent predictions

GXPF1: Honma, Otsuka, Brown, Mizusaki (2004) KB3G: Poves, Sanchez-Solano, Caurier, Nowacki (2001)

?

42 44 46 48 50 52 54 56

Mass number A

1 2 3 4 5

2+ Energy (MeV)

MBPT Experiment CC

SLIDE 42

42 44 46 48 50 52 54 56 58 1 2 3 4 5 6

2

+ Energy (MeV)

Experiment GXPF1 KB3G

(a) Phenomenological Forces

1

Calcium Isotopes: Magic Numbers

Phenomenological Models

Large gap at 48Ca, discrepancy at N=34

Ab initio theories Reproduce all new magic numbers, consistent predictions

GXPF1: Honma, Otsuka, Brown, Mizusaki (2004) KB3G: Poves, Sanchez-Solano, Caurier, Nowacki (2001)

?

42 44 46 48 50 52 54 56

Mass number A

1 2 3 4 5

2+ Energy (MeV)

MBPT Experiment CC

LETTER

doi:10.1038/nature12522

Evidence for a new nuclear ‘magic number’ from the level structure of 54Ca

• D. Steppenbeck1, S. Takeuchi2, N. Aoi3, P. Doornenbal2, M. Matsushita1, H. Wang2, H. Baba2, N. Fukuda2, S. Go1, M. Honma4,
• J. Lee2, K. Matsui5, S. Michimasa1, T. Motobayashi2, D. Nishimura6, T. Otsuka1,5, H. Sakurai2,5, Y. Shiga7, P.-A. So

¨derstro ¨m2,

• T. Sumikama8, H. Suzuki2, R. Taniuchi5, Y. Utsuno9, J. J. Valiente-Dobo

´n10 & K. Yoneda2

LETTER

doi:10.1038/nature12226

Masses of exotic calcium isotopes pin down nuclear forces

• F. Wienholtz1, D. Beck2, K. Blaum3, Ch. Borgmann3, M. Breitenfeldt4, R. B. Cakirli3,5, S. George1, F. Herfurth2, J. D. Holt6,7,
• M. Kowalska8, S. Kreim3,8, D. Lunney9, V. Manea9, J. Mene

´ndez6,7, D. Neidherr2, M. Rosenbusch1, L. Schweikhard1,

• A. Schwenk7,6, J. Simonis6,7, J. Stanja10, R. N. Wolf1 & K. Zuber10

SLIDE 43

The Challenge of Microscopic Nuclear Theory

How will we approach this problem: QCD à à NN (3N) forces à à Renormalize à à Solve many-body problem à à Predictions

To understand the properties of complex nuclei from elementary interactions

Low-momentum interactions

Three-Nucleon Forces Clear path from symmetries

• f QCD to shell model

Ideas of: Effective field theories Renormalization group Advances in many-body Advances in computing All essential for this progress Still much to do!!

SLIDE 44

protons

82 50 28 50 82 20 8 2 2 8 20 126

neutrons

28

Heavie vier se r semi-m i-magic gic c cha hains: MB ins: MBPT a PT as guide s guide Ab Ab initio v initio vale lenc nce-she

• shell H

ll Hamiltonia iltonians ns Towards full sd- and pf-shells Implement extended valence spaces Mo Moving be ving beyond sta

• nd stability

bility Include continuum effects Map sd- and pf-shell driplines?

New Directions and Outlook

SLIDE 45

protons

82 50 28 50 82 20 8 2 2 8 20 126

neutrons

28

sd pf

Heavie vier se r semi-m i-magic gic c cha hains: MB ins: MBPT a PT as guide s guide Ab Ab initio v initio vale lenc nce-she

• shell H

ll Hamiltonia iltonians ns Towards full sd- and pf-shells Implement extended valence spaces Mo Moving be ving beyond sta

• nd stability

bility Include continuum effects Map sd- and pf-shell driplines?

New Directions and Outlook

SLIDE 46

protons

82 50 28 50 82 20 8 2 2 8 20 126

neutrons

28

sd pf

Funda Fundamenta ntal sym l symmetrie tries s Effective electroweak operators ab initio calculation of 0νββ decay WIMP-nucleus scattering Heavie vier se r semi-m i-magic gic c cha hains: MB ins: MBPT a PT as guide s guide Ab Ab initio v initio vale lenc nce-she

• shell H

ll Hamiltonia iltonians ns Towards full sd- and pf-shells Implement extended valence spaces Mo Moving be ving beyond sta

• nd stability

bility Include continuum effects Map sd- and pf-shell driplines?

New Directions and Outlook

(T

1/2 0νββ )−1 = G0ν (Qββ,Z) M0ν 2 mββ 2

SLIDE 47

Final Thought

“Very soft (NN) potentials must be excluded because they do not give saturation; they give too much binding and too high density.”

• H. Bethe

How might you respond?

SLIDE 48

Final Thought

“Very soft (NN) potentials must be excluded because they do not give saturation; they give too much binding and too high density.”

• H. Bethe

How might you respond?

Thanks to (ie, results, plots, ideas, entire slides, jokes etc., used without citation from): Scott Bogner, Angelo Calci, Thomas Duguet, Dick Furnstahl, Alex Gezerlis, Gaute Hagen, Kai Hebeler, Heiko Hergert, Herman Krebs, Javier Menendez, Petr Navratil, Achim Schwenk, Johannes Simonis, Ragnar Stroberg

Further Reading Lepage, nucl-th/9706029 (1997) Epelbaum, Hammer, Meißner, Rev. Mod. Phys. (2009) Machleidt, Entem, Phys. Rep. (2011) Bogner, Furnstahl, Schwenk, Prog. Part. Nucl. Phys. (2010) Hebeler, Holt, Menendez, Schwenk, Ann. Rev. Nucl. Part. Sci. (2015)