Ab Initio Valence-Space Hamiltonians for Exotic Nuclei Jason D son - - PowerPoint PPT Presentation

SLIDE 1

Jason D son D. H . Holt

• lt

Ab Initio Valence-Space Hamiltonians for Exotic Nuclei

• A. Schwenk J. Menendez
• S. Bogner H. Hergert
• R. Stroberg

SLIDE 2

protons

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

neutrons

Frontiers and Impact of Nuclear Science

28

Aim of ab initio nuclear theory: Develop unified first-principles picture of structure and reactions

• Nuclear forces (QCD/strong interaction at low energies)
• Electroweak physics
• Nuclear many-body problem

SLIDE 3

protons

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

neutrons

Medium- and Heavy-Mass Exotic Nuclei

28

π π π

What are the properties of proton/neutron-rich matter? What are the limits of existence of matter? How do magic numbers form and evolve? Worldwide joint experimental/theoretical effort!

3N f for

• rces e

s esse ssentia ntial l for e

• r exotic
• tic n

nuc ucle lei i Advanc nces in m s in many-body m ny-body methods thods Treatm tment of nt of n nuc ucle lear f r for

• rces

s

SLIDE 4

The Nuclear Many-Body Problem

Nucleus strongly interacting many-body system – A-body problem impossible Quasi-exact solutions in light nuclei (GFMC, (IT)NCSM, …) Large space: controlled approximations to full Schrödinger Equation

Coupled Cluster In-Medium SRG Green’s Function Limited range: Closed shell ±1 Even-even Limited properties: Ground states only Some excited state

Hψn = Enψn

Large-space approach

SLIDE 5

The Nuclear Many-Body Problem

Nucleus strongly interacting many-body system – A-body problem impossible Quasi-exact solutions in light nuclei (GFMC, (IT)NCSM, …) Large space: controlled approximations to full Schrödinger Equation Valence space: diagonalize exactly with reduced number of degrees of freedom

Coupled Cluster In-Medium SRG Green’s Function Limited range: Closed shell ±1 Even-even Limited properties: Ground states only Some excited state

Hψn = Enψn

Valence-space approach Coupled Cluster In-Medium SRG Perturbation Theory All nuclei near closed-shell cores All properties: Ground states Excited states EW transitions Large-space approach

SLIDE 6

Continuous unitary trans (basis change) decouples “off-diagonal” physics Interaction in new basis is simple

In-Medium Similarity Renormalization Group

Tsukiyama, Bogner, Schwenk, PRL (2011)

H(s) = U(s)HU †(s) ≡ Hd(s) + Hod(s) → Hd(∞)

SLIDE 7

Continuous unitary trans (basis change) decouples “off-diagonal” physics Interaction in new basis is simple Can always write , for some generator For incline plane:

In-Medium SRG

Tsukiyama, Bogner, Schwenk, PRL (2011)

H(s) = U(s)HU †(s) ≡ Hd(s) + Hod(s) → Hd(∞) U = eη η η = ✓ θ −θ ◆

SLIDE 8

Life Is Difficult: Particle/Hole Excitations

Consider basis states as excitations from uncorrelated reference state Hamiltonian schematically in terms of ph excitations Ground-state coupled to excitations is difficult

Unoccupied (Particles) Occupied (Holes)

εF

hi|H|ji

• Ref. Slater Determinant

1p-1h excitation 2p-2h excitation

16O

Hod = hp|H|hi + hpp|H|hhi + · · · + h.c.

|Φ0i =

N

Y

i=1

a†

i |0i

|Φa

i i = a† aai |Φ0i

• Φab

ij

↵ = a†

aaia† baj |Φ0i

SLIDE 9

For nuclear Hamiltonian, take with Perform multiple rotations until Fully correlated ground state: one matrix element Also flow equation approach

In-Medium SRG for Nuclei

hi|H|ji U = eη η = Hod ∆ + h.c. UN = eηN · · · eη2eη1 ηN = 0 dH(s) ds = [η(s), H(s)] hΦ0| ˜ H|Φ0i hnpnh| ˜ H|Φ0i = 0

SLIDE 10

Separate p states into valence states (v) and those above valence space (q) Redefine Hod to decouple valence space from excitations outside v

IM-SRG for Valence-Space Hamiltonians

8 28 20 50

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

h p v q H(s = 0) → H(∞)

Hod = hp|H|hi + hpp|H|hhi + hv|H|qi + hpq|H|vvi + hpp|H|hvi + h.c.

Tsukiyama, Bogner, Schwenk, PRC (2012)

• 16O

Heff Core Energy Single-particle energies Two-body valence particle interaction matrix elements

SLIDE 11

Large/valence-space methods with same SRG-evolved NN+3N-full forces Agreement between all methods with same input forces Clear improvement with NN+3N-full Still significant discrepancy between valence/large-space results

Ground-State Energies in Oxygen Isotopes

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

NN+3N-full

Hebeler, JDH, Menéndez, Schwenk, ARNPS (2015) Bogner et al, PRL (2014) 16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130

Energy (MeV)

AME 2012 NN+3N-ind NN+3N-full

SLIDE 12

Normal-ordered 3N: contribution from core with valence particles Neglect 3N forces between valence particles – significant as

How Do We Handle 3N Forces?

O core

N.O. 2-body

O core

N.O. 1-body

• +
• +

O core

16

N.O. 0-body

• +

Nv ∼ Nc

SLIDE 13

Normal-ordered 3N: contribution from core with valence particles Neglect 3N forces between valence particles – significant as Capture these effects with new Targeted N.O.

Targeted Normal Ordering

O core

N.O. 2-body

O core

N.O. 1-body

• +
• +

O core

16

• re

16O

O core

16

N.O. 0-body

• +

Nv ∼ Nc

SLIDE 14

Normal-ordered 3N: contribution from core with valence particles Neglect 3N forces between valence particles – significant as Capture these effects with new Targeted N.O. Initial N.O. wrt nearest closed shell Still decouple standard sd valence space

Targeted Normal Ordering

O core

N.O. 2-body

O core

16

N.O. 0-body

O core

N.O. 1-body

• +
• +
• +

O core

16

• re

16O →22 O

Nv ∼ Nc

SLIDE 15

Large/valence-space methods with same SRG-evolved NN+3N-full forces Agreement between all methods with same input forces Clear improvement with NN+3N-full Still significant discrepancy between valence/large-space results

Ground-State Energies in Oxygen Isotopes

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

NN+3N-full

Hebeler, JDH, Menéndez, Schwenk, ARNPS (2015) Bogner et al, PRL (2014) 16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130

Energy (MeV)

AME 2012 NN+3N-ind NN+3N-full

SLIDE 16

Large/valence-space methods with same SRG-evolved NN+3N-full forces Improved method to capture neglected 3N forces in valence space “Targeted” IMSRG results agree well with data and large-scale methods

Targeted N.O. in Oxygen Isotopes

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

NN+3N-full

Hebeler, JDH, Menéndez, Schwenk, ARNPS (2015) 16 18 20 22 24 26 28

Mass Number A

• 180
• 170
• 160
• 150
• 140
• 130

Energy (MeV)

AME 2012 Targeted NO NN+3N-ind NN+3N-full

Bogner et al., PRL (2015)

SLIDE 17

IM-SRG valence-space results for fully open F/Ne isotopes NN+3N-full improves agreement with experiment; overbound past N=14

Beyond Semi-Magic: Ground States of F/Ne

16 18 20 22 24 26 28 30

Mass Number A

• 220
• 200
• 180
• 160
• 140
• 120

Energy (MeV)

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

18 20 22 24 26 28 30

Mass Number A

• 240
• 220
• 200
• 180
• 160
• 140

Energy (MeV)

AME 2012

Ne F

Stroberg et al., arXiv:1511.03802

SLIDE 18

IM-SRG valence-space results for fully open F/Ne isotopes NN+3N-full improves agreement with experiment; overbound past N=14 Targeted N.O. results further improved – similar to phenomenology

Beyond Semi-Magic: Ground-States of F/Ne

18 20 22 24 26 28 30

Mass Number A

• 240
• 220
• 200
• 180
• 160
• 140

Energy (MeV)

AME 2012 Targeted N.O.

Ne

Stroberg et al., arXiv:1511.03802

16 18 20 22 24 26 28 30

Mass Number A

• 220
• 200
• 180
• 160
• 140
• 120

Energy (MeV)

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

F

SLIDE 19

Beyond Semi-Magic: Ground-States of F/Ne

16 18 20 22 24 26 28 30

Mass Number A

• 220
• 200
• 180
• 160
• 140
• 120

Energy (MeV)

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

18 20 22 24 26 28 30

Mass Number A

• 240
• 220
• 200
• 180
• 160
• 140

Energy (MeV)

AME 2012 Targeted NO MR-IM-SRG

Ne F

Stroberg et al., arXiv:1511.03802

IM-SRG valence-space results for fully open F/Ne isotopes NN+3N-full improves agreement with experiment; overbound past N=14 Targeted N.O. results further improved – similar to phenomenology Good agreement with large-space MR-IM-SRG!

SLIDE 20

3N force effects significant as becomes large Targeted N.O. valence-space results agrees with large-space in all cases!

28Si not good closed shell (single ref. incorrect)

Discrepancy with experiment from initial nuclear interactions

Ground States from Oxygen to Calcium

Stroberg et al., in prep

Nv

SLIDE 21

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

Hebeler, JDH, Menéndez, Schwenk, ARNPS (2015)

SLIDE 22

Fluorine spectroscopy: MBPT and IM-SRG (sd shell) from NN+3N forces IM-SRG: competitive with phenomenology, good agreement with data

Doubly Open Shell: Neutron-Rich F Spectra

3N-ind 3N-full Expt. USDB 1 2 3 4 5

5/2

+

5/2

+

1/2

+

3/2

+

7/2

+

7/2

+

3/2

+

1/2

+

1/2

+

9/2

+

1/2

+

9/2

+

3/2

+

5/2

+

5/2

+

(5/2

+)

5/2

+

1/2

+

5/2

+

9/2

+

3/2

+

3/2

+

(1/2

+)

(9/2

+)

(3/2

+)

(3/2

+)

(5/2

+)

25F

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

3N-ind 3N-full Expt. USDB 1 2 3 4

3

+

4

+

3

+

4

+

4

+

3

+

2

+

2

+

2

+

1

+

1

+

1

+

1

+ +

4

+

2

+

2

+

1

+

3

+

2

+

3

+

1

+

2

+

3

+

26F Stroberg et al., arXiv:1511.03802

SLIDE 23

Ground-state rotational band for well-known deformed nuclei IM-SRG: competitive with phenomenology, good agreement with data Further observables (quadrupole moments, E2 transitions) needed

Deformed Systems: 20Ne and 24Mg

3N-ind 3N-full Expt. USDB 2 4 6 8 10 12 14

Energy (MeV)

6

+

6

+

4

+

2

+

2

+

2

+ + + + +

8

+

2

+

6

+

4

+

8

+

8

+

4

+

8

+

4

+

6

+

20Ne

3N-ind 3N-full Expt. USDB 2 4 6 8 10 12 14 16 18

Energy (MeV)

8

+

8

+

4

+

2

+

2

+

6

+

2

+ + + + +

2

+

6

+

4

+

4

+

6

+

6

+

4

+

8

+

24Mg Stroberg et al., arXiv:1511.03802

SLIDE 24

Ground states in light neon isotopes – clear discrepancies in 20,22Ne MR-IM-SRG built on spherical reference state Not expected to produce deformed ground states – not a problem for SM

Deformation with Large-Space MR-IM-SRG?

18 20 22 24 26 28 30

Mass Number A

• 240
• 220
• 200
• 180
• 160
• 140

Energy (MeV)

AME 2012 Targeted NO MR-IM-SRG

Ne

18 20 22 24

Mass Number A

• 200
• 180
• 160
• 140

Energy (MeV)

Targeted NO MR-IM-SRG

Ne

SLIDE 25

Deformed Systems: 20Ne and 24Mg

18 20 22 24 26 28 30

Mass Number A

• 240
• 220
• 200
• 180
• 160
• 140

Energy (MeV)

AME 2012 Targeted NO MR-IM-SRG

Ne

18 20 22 24

Mass Number A

• 200
• 180
• 160
• 140

Energy (MeV)

Targeted NO MR-IM-SRG

Ne

+

2

Ground states in light neon isotopes – clear discrepancies in 20,22Ne MR-IM-SRG built on spherical reference state Not expected to produce deformed ground states – not a problem for SM First (likely spherical) excited 0+ SM state agrees remarkably with MR-IM-SRG Indicates SM captures physics of deformed ground state

SLIDE 26

Previous SM radii calculations rely on empirical input or as relative to core Radii for stable sd-shell nuclei calculated in shell model NN+3N Next: general tensor operators M1, E2, GT, double-beta decay

RMS Charge Radii in sd Shell Model

Stroberg et al., in prep

SLIDE 27

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 28

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 29

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 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 30

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 3N couplings fit to 3/4-body systems Consistent EW/WIMP interactions

Weinberg, van Kolck, Kaplan, Savage, Wise…

SLIDE 31

Normal-Ordered Hamiltonian

Now rewrite exactly the initial Hamiltonian in normal-ordered form Normal-ordered Hamiltonian w.r.t. reference state Loop = sum over occupied states Include dominant 1-,2-,3-body physics in NO

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 32

Define U(s) implicitly from particular choice of generator: chosen for desired decoupling behavior – e.g., Solve flow equation for Hamiltonian (coupled DEs for 0,1,2-body parts) Hamiltonian and generator truncated at 2-body level: IM-SRG(2) 0-body flow drives uncorrelated ref. state to fully correlated ground state Ab initio method for energies of closed-shell systems

IM-SRG: Flow Equation Formulation

η(s) ≡ (dU(s)/ds) U †(s) dH(s) ds = [η(s), H(s)] ηI(s) = ⇥ Hd(s), Hod(s) ⇤

Wegner (1994)

E0(∞) → Core Energy

H(s) = E0(s) + f(s) + Γ(s) + · · ·

SLIDE 33

Magnus expansion: explicitly construct unitary transformation With flow equation: Leads to commutator expression for evolved Hamiltonian Nested commutator series – in practice truncate numerically All calculations truncated at normal-ordered two-body level

New Approach: Magnus Expansion

Morris, Parzuchowski, Bogner, PRC (2015)

H(s) = eΩ(s)He−Ω(s) = H + 1 2 [Ω(s), H] + 1 12 [Ω(s), [Ω(s), H]] + · · · dΩ(s) ds = η(s) + 1 2 [Ω(s), η(s)] + 1 12 [Ω(s), [Ω(s), η(s)]] + . . . U(s) = exp Ω(s)

SLIDE 34

Keep unitary transformation from evolution of Hamiltonian Can generalize to arbitrary operators Must work out normal-ordered operators in J-coupled basis First apply to scalar operators

Effective Operators

OΛ(s) = eΩ(s)OΛe−Ω(s) = OΛ + 1 2 ⇥ Ω(s), OΛ⇤ + 1 12 ⇥ Ω(s), ⇥ Ω(s), OΛ⇤⇤ + · · ·

H(s) = eΩ(s)He−Ω(s) = H + 1 2 [Ω(s), H] + 1 12 [Ω(s), [Ω(s), H]] + · · ·

SLIDE 35

Seldom calculated in nuclear shell model In single HO shell: Must resort to phenomenological gymnastics IM-SRG: straightforward to calculate effective valence-space operator: Commutators induce important higher-order and two-body parts Quantify importance of induced higher-body contributions!

E0 Transitions and Radii

where |hf|ρE0|ii|2 / δij ρE0 = 1 e2R X

i

eir2

i

ρE0(s) = eΩ(s)ρE0e−Ω(s) = ρE0 + 1 2 [Ω(s), ρE0] + · · ·

SLIDE 36

Previous SM radii calculations rely on empirical input or as relative to core Absolute radii for entire sd shell calculated in shell model NN+3N Benchmarked against NCSM in various SM codes ~10% too small – deficiencies expected to come from initial Hamiltonian Two-body part important 15-20%

RMS Charge Radii in sd Shell Model

Stroberg, Bogner, Hergert, JDH, Schwenk , in prep

SLIDE 37

Preliminary results in sd shell: Promising but need additional benchmarks

E0 Transitions in sd Shell Model

SLIDE 38

Variation of step size Evident error accumulation in flow-equation for small step sizes Magnus: rapid convergence, independent of step size

Magnus vs Flow-Equation

SLIDE 39

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 Bogner et al., PRL (2014)

SLIDE 40

Perturbative Approach

1) Effective Hamiltonian: sum excitations outside valence space to MBPT(3) 2) Self-consistent single-particle energies 3) Harmonic-oscillator basis of 13-15 major shells: converged 4) NN and 3N forces from chiral EFT a

c b d ˆ Q = a c b d + a c b d a b d c + a c b d + V + + . . .

Veff

b d = a c b d Vlow-k + a c + . . . b d

k

εeff

a a a a a a

x

V

SLIDE 41

−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 42

Physics beyond dripline highly sensitive to 3N forces 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

Hebeler, JDH, Menéndez, Schwenk, ARNPS (2015)

SLIDE 43

Physics beyond dripline highly sensitive to 3N forces 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

Hebeler, JDH, Menéndez, Schwenk, ARNPS (2015) Kondo et al, preliminary

SLIDE 44

Neon spectra: extended-space MBPT and IM-SRG (sd shell) NN+3N-ind: clear deficiencies NN+3N-full: competitive with phenomenology, good agreement with data

Doubly Open Shell: Neutron-Rich Ne Spectra

Bogner, Hergert, JDH, Schwenk, Stroberg in prep.

3N-ind 3N-full Expt. USDB 1 2 3 4 5

Energy (MeV)

+

3

+

2

+

4

+ +

2

+

2

+

2

+

2

+ + + + +

4

+

2

+

2

+

4

+ +

3

+ +

4

+

2

+

3

+

2

+

24Ne

3N-ind 3N-full Expt. USDB 1 2 3 4

5/2

+

9/2

+

5/2

+

5/2

+

9/2

+

7/2

+

5/2

+

5/2

+

3/2

+

5/2

+

3/2

+

3/2

+

3/2

+

1/2

+

1/2

+

1/2

+

(1/2

+)

7/2

+

3/2

+

7/2

+

1/2

+

3/2

+

(5/2

+)

(3/2

+)

25Ne

3N-ind 3N-full Expt. USDB 1 2 3 4 5

+ +

2

+

4

+ +

2

+

2

+

2

+

2

+ + + + +

4

+

2

+

2

+

4

+

2

+

26Ne

SLIDE 45

Where is the nuclear dripline? Limits defined as last isotope with positive neutron separation energy

• Nucleons “drip” out of nucleus

Neutron dripline experimentally established to Z=8 (Oxygen) Regular dripline trend… except anomalous oxygen Adding one proton binds 6 additional neutrons

Limits of Nuclear Existence: Oxygen Anomaly

SLIDE 46

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

Ground-State Energies in Oxygen Isotopes

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)

AME 2012 NN+3N-ind