recent developments in nuclear structure theory

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Recent Developments in Nuclear Structure Theory

Sonia Bacca | Scientist Jan. 26th 2017

Bormio55th International Winter Meeting on Nuclear Physics

Wednesday, 25 January, 17

Title TextNuclear Structure

2

The nucleus

quarks and gluons

N

Z

neutron

proton

quarks and gluons

stable nuclei

unstable nuclei

Terra Incognita



2

The nucleus

quarks and gluons

N

Z

neutron

proton

quarks and gluons

stable nuclei

unstable nuclei

Terra Incognita

• How is the nuclear force related to QCD?



2

The nucleus

quarks and gluons

N

Z

• What are the limits of nuclear existence?

neutron

proton

quarks and gluons

stable nuclei

unstable nuclei

Terra Incognita




2

The nucleus

quarks and gluons

N

Z

• What is the nature of neutron stars?


neutron

proton

quarks and gluons

stable nuclei

unstable nuclei

Terra Incognita




2

The nucleus

quarks and gluons

N

Z

• What is the nature of neutron stars?


• How can we use the nucleus to test physics beyond the standard model?

neutron

proton

quarks and gluons

stable nuclei

unstable nuclei

Terra Incognita



Recent development in nuclear structure theoryJan 26th 2017 3

“Ab initio” theory

• Start from neutrons and protons as building blocks (centre of mass coordinates, spins, isospins)





H|�i� = Ei|�i�

H = T + VNN (⇤) + V3N (⇤) + . . .

• Solve the non-relativistic quantum mechanical problem of A-interacting nucleons





• Find numerical solutions with no approximations or controllable approximations

H|�i� = Ei|�i�

H = T + VNN (⇤) + V3N (⇤) + . . .






• Find numerical solutions with no approximations or controllable approximations

• Calibrate the force and then calculate A-body nuclei to compare with experiment or to provide predictions for observables which are hard or impossible to measure

H|�i� = Ei|�i�

H = T + VNN (⇤) + V3N (⇤) + . . .




Chiral Effective Field Theory

π(q/Λ)0

(q/Λ)3

(q/Λ)4

(q/Λ)2

LO

NLO

N2LO

N3LO

⌫ = 0

⌫ = 2

⌫ = 3

⌫ = 4

Systematic expansion L =X

⌫

c⌫

✓Q

⇤b

◆⌫

Weinberg, van Kolck, Epelbaum, Meissner, Machleidt, Phillips, ... Talk on Tue by Epelbaum




π(q/Λ)0

(q/Λ)3

(q/Λ)4

(q/Λ)2

LO

NLO

N2LO

N3LO

⌫ = 0

⌫ = 2

⌫ = 3

⌫ = 4


⌫

c⌫

✓Q

⇤b

◆⌫

Epelbaum et al. (2009)

Details of short distance physics not resolved, but captured in low energy constants (LEC)

Future: lattice QCD?Now fit to experiment

LEC fit to experiment - NN sector -

0 50 100 150 200 250Lab. Energy [MeV]

N3LO

NLON2LO

LEC fit to NN experimental data - 3N sector using A=3 data

Weinberg, van Kolck, Epelbaum, Meissner, Machleidt, Phillips, ... Talk on Tue by Epelbaum




π(q/Λ)0

(q/Λ)3

(q/Λ)4

(q/Λ)2

LO

NLO

N2LO

N3LO

⌫ = 0

⌫ = 2

⌫ = 3

⌫ = 4


⌫

c⌫

✓Q

⇤b

◆⌫

Epelbaum et al. (2009)

Details of short distance physics not resolved, but captured in low energy constants (LEC)

Future: lattice QCD?Now fit to experiment

LEC fit to experiment - NN sector -

0 50 100 150 200 250Lab. Energy [MeV]

N3LO

NLON2LO

LEC fit to NN experimental data - 3N sector using A=3 data

Weinberg, van Kolck, Epelbaum, Meissner, Machleidt, Phillips, ...

Goal: Calibrate Hamiltonian and then predict other observables

Talk on Tue by Epelbaum



Goal: develop a theory of nuclei with predictive power

Nuclear Structure Theory

http://unedf.org


http://unedf.org

http://unedf.org


Goal: develop a theory of nuclei with predictive power

Nuclear Structure Theory

http://unedf.org

16 18 20 22 24 26 28

Mass Number A

-180

-170

-160

-150

-140

-130

Ener

gy (

MeV

)MR-IM-SRG

IT-NCSMSCGFLattice EFTCC

obtained in large many-body spaces

AME 2012

Ann. Rev. Part. Nucl. Sci. 65 (2015) 457


http://unedf.org

http://unedf.org

Recent development in nuclear structure theoryJan 26th 2017

Electroweak probes

6

• How does the nucleus respond to external electroweak excitations?

0 5 10 15 20 25 30 35 40 ω [MeV]

0

100

200

300

400Counts

R(!, q) =X

f

Z|h f |O(q)| 0i|2�(! � Ef + E0)

Res

pons

e Fu

nctio

n

giant resonances

narrow resonances


Recent development in nuclear structure theoryJan 26th 2017

Electroweak probes

6

• Provide important informations in other fields of physics, where nuclear physics plays a crucial role:

- Astrophysics: - Atomic physics - Particle physics

• How does the nucleus respond to external electroweak excitations?

0 5 10 15 20 25 30 35 40 ω [MeV]

0

100

200

300

400Counts

R(!, q) =X

f

Z|h f |O(q)| 0i|2�(! � Ef + E0)

Res

pons

e Fu

nctio

n

giant resonances

narrow resonances



The Continuum Problem

Excitation Energyground state

“

“

bound excited state

continuum

2-body break-up 3-body break-up ... A-body break-up

� � |⇥�f |Jµ|�0⇤|2

Exact knowledge limited inenergy and mass number

R(!, q)



The Continuum Problem

Excitation Energyground state

“

“

bound excited state

continuum

2-body break-up 3-body break-up ... A-body break-up

� � |⇥�f |Jµ|�0⇤|2

Exact knowledge limited inenergy and mass number

R(!, q)

Lorentz Integral Transform Reduce the continuum problem to a bound-state-like equationEfros, et al., JPG.: Nucl.Part.Phys. 34 (2007) R459

Similar to Laplace Transform discussed on Wed by S.Gandolfi

(H � z)| i = Jµ| 0i


8

Selected Highlights

Interfacing with precision atomic physics to search for beyond standard model physics



e-

The proton-radius puzzle

The proton charge radius is measured from: electron-proton interactions: 0.8770 ± 0.0045 fm

eH spectroscopy e-p scattering

fm

Pohl et al., Nature (2010)Antognini et al., Science (2013)

µ- muonic -proton interactions: 0.8409 ± 0.0004 fm 𝜇H Lamb-shift

Merkel Talk on Tue & Vanderhaeghen Talk on Fri.



e-

The proton-radius puzzle

Is lepton universality violated?

The proton charge radius is measured from: electron-proton interactions: 0.8770 ± 0.0045 fm

eH spectroscopy e-p scattering

fm

Pohl et al., Nature (2010)Antognini et al., Science (2013)

µ- muonic -proton interactions: 0.8409 ± 0.0004 fm 𝜇H Lamb-shift

Merkel Talk on Tue & Vanderhaeghen Talk on Fri.



Understanding the proton-radius puzzle

µ-

Strong experimental program at PSI (Switzerland) from the CREMA collaboration to unravel the mystery by studying other muonic atoms:

𝜇D 𝜇4He+

𝜇3He+

𝜇3H

𝜇6Li2+, 𝜇7Li2+




µ-


𝜇D 𝜇4He+

𝜇3He+

𝜇3H


�E2S�2P = �QED +AOPEhr2c i+ �TPE




µ-


𝜇D 𝜇4He+

𝜇3He+

𝜇3H



well known




µ-


𝜇D 𝜇4He+

𝜇3He+

𝜇3H



well known '

m4r(Z↵4)

12

4




µ-


𝜇D 𝜇4He+

𝜇3He+

𝜇3H



well known '

m4r(Z↵4)

12

4

unknown

�TPE !Z

d! R(!, q) g(!)




µ-


𝜇D (results just released) 𝜇4He+ (analyzing data) 𝜇3He+ (analyzing data) 𝜇3H (impossible/possible?) 𝜇6Li2+, 𝜇7Li2+ (future)


well known '

m4r(Z↵4)

12

4

unknown

�TPE !Z

d! R(!, q) g(!)






-9.58(38) meV ⇒ PRL 111, 143402 (2013) -1.727(20) meV ⇒ PLB 736, 334 (2014)

-15.46(39) meV ⇒ PLB 755, 380 (2016) -0.767(25) meV ⇒ PLB 755, 380 (2016)







-9.58(38) meV ⇒ PRL 111, 143402 (2013) -1.727(20) meV ⇒ PLB 736, 334 (2014)

-15.46(39) meV ⇒ PLB 755, 380 (2016) -0.767(25) meV ⇒ PLB 755, 380 (2016)

1%

3%

6%







-9.58(38) meV ⇒ PRL 111, 143402 (2013) -1.727(20) meV ⇒ PLB 736, 334 (2014)

-15.46(39) meV ⇒ PLB 755, 380 (2016) -0.767(25) meV ⇒ PLB 755, 380 (2016)

1%

3%

6%

Theory provides crucial information for precision experiments





𝜇D (results just released) -1.727(20) meV ⇒ PLB 736, 334 (2014)



�TPE work led by J. Hernandez⇒R.Pohl et al., Science 2016

1%

7.5 deviations from 𝜇D and CODATA�

�A TPE

with Epelbaum chiral potentials




𝜇D (results just released) -1.727(20) meV ⇒ PLB 736, 334 (2014)



�TPE work led by J. Hernandez⇒R.Pohl et al., Science 2016

1%

7.5 deviations from 𝜇D and CODATA�

with Ekstroem potentials [PRX6 (2016)011019], propagating LEC error bars into observables

Preliminary

�A TPE

with Epelbaum chiral potentials


14

Pushing the limits in mass number to challenge our understanding of neutron-rich nuclei

Selected Highlights



5 10 15 20 25ω [MeV]

0

5

10

15

20

25

σγ(ω) [

mb]

Leistenschneider et al.

22O

Data from GSI

core

Pigmy Dipole Resonance (PDR)

Photoexcitation of neutron-rich nuclei

PDR

core



5 10 15 20 25ω [MeV]

0

5

10

15

20

25

σγ(ω) [

mb]


22O

Data from GSI

core



PDR

5 10 15 20 25ω [MeV]

0

5

10

15

20

25

σγ(ω) [

mb]


22O

CCSDNN(N3LO)

Sexp

n

S.B. et al., PRC 90, 064619 (2014)

Well described by ab initio theory

core



5 10 15 20 25ω [MeV]

0

5

10

15

20

25

σγ(ω) [

mb]


22O

Data from GSI

core



PDR

5 10 15 20 25ω [MeV]

0

5

10

15

20

25

σγ(ω) [

mb]


22O

CCSDNN(N3LO)

Sexp

n

S.B. et al., PRC 90, 064619 (2014)

Well described by ab initio theory

Theory provides a deeper understanding: microscopic interpretation of collective phenomena

Theory motivates new experiments: e.g. 8He will be measured in RIKEN by T. Aumann

core



48Ca from first principles

Ab initio with three nucleon forces from chiral EFT

Nature Physics 12, 186 (2016)

Rskin

0.15 0.18 0.21

Rskin [fm]

3.1

3.2

3.3

3.4

3.5

3.6

Rp

[fm]

3.3 3.4 3.5 3.6

Rn [fm]2.0 2.4 2.8

↵D [fm3]

International collaboration (USA/Canada/Europe/Israel) using coupled-cluster theory

Hagen et al., Nature Physics 12, 186 (2016)

Rskin





Strong correlations with Rp allow to put narrow constraints to Rskin and ↵D

Ab-initio predictions: 0.12 Rskin 0.15 fm

2.19 ↵D 2.60 fm3


Rskin

0.15 0.18 0.21

Rskin [fm]

3.1

3.2

3.3

3.4

3.5

3.6

Rp

[fm]

3.3 3.4 3.5 3.6

Rn [fm]2.0 2.4 2.8

↵D [fm3]



Rskin







2.19 ↵D 2.60 fm3

Theory provides predictions for modern experiments


Rskin

0.15 0.18 0.21

Rskin [fm]

3.1

3.2

3.3

3.4

3.5

3.6

Rp

[fm]

3.3 3.4 3.5 3.6

Rn [fm]2.0 2.4 2.8

↵D [fm3]



Rskin







2.19 ↵D 2.60 fm3

Theory provides predictions for modern experiments


Rskin

0.15 0.18 0.21

Rskin [fm]

3.1

3.2

3.3

3.4

3.5

3.6

Rp

[fm]

3.3 3.4 3.5 3.6

Rn [fm]2.0 2.4 2.8

↵D [fm3]



Rskin

Rskin will be measured with Parity violation electron scattering CREX

measured at Osaka with (p,p’) ↵D

J.Birkhan, et al., arXiv:1611.07072



Future Developments

Adding triple corrections to coupled cluster theory

M.Miorelli. et al., (2017)

0 50 100 150 200 250 300 350 400 450 500

! [MeV]

0.4

0.6

0.8

1.0

m0

[fm2 ]

CCSD

CCSD + T corrections

EIHH

4HeExact

Preliminary


18

Frontiers at higher energies

How nuclear theory can help particle physics searches of fundamental neutrino properties



Neutrino scattering ⬄ electron scattering

Neutrino-Nucleus Cross Section Neutrino long baseline experiments require understanding of interactions of neutrinos with the detector material (12C, 16O, 40Ar, ...). So far very simple models are used.

How well do we understand neutrino nucleus cross sections?

Lovato et al., PRL 117, 082501 (2016)

q = 570 MeV/c

12C

QE

(!, q)

AX

e0, ⌫0 or `e, ⌫

�, Z0,W±

Monte Carlo Calculations - Talk by S.Gandolfi



Neutrino scattering ⬄ electron scattering

Neutrino-Nucleus Cross Section Neutrino long baseline experiments require understanding of interactions of neutrinos with the detector material (12C, 16O, 40Ar, ...). So far very simple models are used.

How well do we understand neutrino nucleus cross sections?

Lovato et al., PRL 117, 082501 (2016)

q = 570 MeV/c

12C

QE

(!, q)

AX

e0, ⌫0 or `e, ⌫

�, Z0,W±

Monte Carlo Calculations - Talk by S.Gandolfi

0 100 200 300 400 500q [MeV/c]

0.0

0.2

0.4

0.6

0.8

1.0

S L(q

)

4He

LIT-CCSDBuki et. al, w tailWorld Data, w tail

Prelim

inary

T.Xu et al., EPJ Web of Conferences 113, 04016 (2016)

Coupled-Cluster Calculations of the Coulomb Sum Rule


• Remarkable progress has been done in ab initio calculations of nuclear structure

20

• Electroweak probes are very reach tools to investigate nuclear dynamics which allow an interplay with atomic, particle and astrophysics

Outlook

IMSRG Exp. IMSRG Exp.

0

1

2

3

4

5

E (

0+)

(MeV

)

-666.61 -662.07-668.38-661.60

76Ge

76Se

Fig from J.D. Holt

★ Neutrinoless double beta decay

Future long term goals:


• Remarkable progress has been done in ab initio calculations of nuclear structure

21

• Electroweak probes are very reach tools to investigate nuclear dynamics which allow an interplay with atomic, particle and astrophysics

Outlook

Thank you!Merci!

Thanks to my collaborators:

N.Barnea, B.Carlsson, C. Drischler, A. Ekstrom, C.Forssen, G. Hagen, O.H. Hernandez, J.D.Holt, K.Hebeler, M. Hjorth-Jensen, G.R. Jansen, C.Ji, M.Miorelli, W. Nazarewicz, N.Nevo Dinur, G.Orlandini, T.Papenbrock, J. Simonis, A.Schwenk, S.R. Stroberg, K.Wendt, T. Xu


22

Backup Slides



Calculating TPE with HH

Drop Times (Seconds)

OBJECT A OBJECT B

-6.48 -6.63

0.23 0.24

-0.10 -0.11

1.00 1.02

0.08 0.05

-8.54 -8.71

8.10 8.33

0.63 0.65

1.02 1.04

-0.84 -0.86

-1.29 -1.31

2.26 2.29

-0.18 -0.19

-4.11 -4.20

-10.36 -10.62

-14.47 -14.82

-15.0 -12.0 -9.0 -6.0 -3.0 0 3.0 6.0 9.0

meV

Table 6

OBJECT C OBJECT D

-0.77 -0.78

0.03 0.03

-0.01 -0.01

0.07 0.07

0.01 0.01

0.00 0.00

0.18 0.18

0.02 0.02

0.03 0.04

-0.08 -0.08

0.03 0.03

0.05 0.05

-0.03 -0.03

-0.47 -0.48

-0.22 -0.23

-0.69 -0.71

�(0)T

�(0)C

�(0)M

�(1)R3

�(1)Z3

�(2)R2

�(2)Q

�(2)D1D3

�(1)R1

�(1)Z1

�(2)NS

�Apol

�AZem�ATPE

�(0)D1

�(0)L

AV18/UIX�EFT

3He 3H

-0.8 -0.6 -0.4 -0.2 0 0.2meV

N.Nevo-Dinur et al., PLB 755, 380 (2016)

Total error budget: numerical error, atomic physics error, nuclear physics error (in quadrature)



Pushing the mass limits...With M. Miorelli

3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2

Rch [fm]

2.0

2.5

3.0

3.5

4.0

4.5

5.0

↵D

[fm3 ]

68Ni

Very preliminary

GSI dataRossi et al.(2013)

64Ni Rch = 3.8572 fm

3.8 3.9 4.0 4.1 4.2 4.3 4.4

Rch [fm]

2.0

3.0

4.0

5.0

6.0

7.0

8.0

↵D

[fm3 ]

90Zr

Consistent with DFT calculations, Roca-Maza (2015)

↵D ⇡ 5.65 fm3

Very preliminary



Lorentz Integral Transform Method Equation can be solved with any bound-state method

L(�,�) =�

d⇥R(⇥)

(⇥ � �)2 + �2 =��|�

⇥< 1

Reduces the continuum problem to a bound-state problem

�

�(H � E0 � � + i�)|⇥⇥ = O|⇥0⇥Jµ

We solved this equation with HH, NCSM and Coupled-cluster Theory

Efros, et al., JPG.: Nucl.Part.Phys. 34 (2007) R459

⇥




L(�,�) =�

d⇥R(⇥)

(⇥ � �)2 + �2 =��|�

⇥< 1


�

�

inversionR(!)h | i

(H � E0 � � + i�)|⇥⇥ = O|⇥0⇥Jµ



⇥




L(�,�) =�

d⇥R(⇥)

(⇥ � �)2 + �2 =��|�

⇥< 1


�

�

inversionR(!)h | i

(H � E0 � � + i�)|⇥⇥ = O|⇥0⇥Jµ



0 30 60 90 120 150

Nucl.Phys. A707 365 (2002) Phys.Rev.C 69 (2004)

Benchmarks with methods that calculate the final states

⇥



Following Lovato et al. PRL 111 092501 (2013), we starting from the Coulomb sum rule

RL(⇤,q) =⌅⇤

f

|⇥�f | ⇥(q) |�0⇤|2 �

�Ef � E0 � ⇤ +

q2

2M

⇥

SL(q) =1

Z

Z 1

!th

d!RL(!, q)

GpE2(Q2)

Total inelastic strength

Coulomb Sum Rule With Tianrui Xu, undergrad at UBC




RL(⇤,q) =⌅⇤

f

|⇥�f | ⇥(q) |�0⇤|2 �

�Ef � E0 � ⇤ +

q2

2M

⇥

SL(q) =1

Z

Z 1

!th

d!RL(!, q)

GpE2(Q2)


0 100 200 300 400 500q [MeV/c]

0.0

0.2

0.4

0.6

0.8

1.0

S L(q

)

4He


Prelim

inaryT.Xu et al., EPJ Web of Conferences 113, 04016 (2016)





RL(⇤,q) =⌅⇤

f

|⇥�f | ⇥(q) |�0⇤|2 �

�Ef � E0 � ⇤ +

q2

2M

⇥

SL(q) =1

Z

Z 1

!th

d!RL(!, q)

GpE2(Q2)


16O

Prelim

inary

0 100 200 300 400 500q [MeV/c]

0.0

0.2

0.4

0.6

0.8

1.0

S L(q

)

4He


Prelim






RL(⇤,q) =⌅⇤

f

|⇥�f | ⇥(q) |�0⇤|2 �

�Ef � E0 � ⇤ +

q2

2M

⇥

SL(q) =1

Z

Z 1

!th

d!RL(!, q)

GpE2(Q2)


16O

Prelim

inary

0 100 200 300 400 500q [MeV/c]

0.0

0.2

0.4

0.6

0.8

1.0

S L(q

)

4He


Prelim


Future:Addressing transverse and weak

response in 16O with two-body currents







-9.58(38) meV ⇒ PRL 111, 143402 (2013) -1.727(20) meV ⇒ PLB 736, 334 (2014)

-15.46(39) meV ⇒ PLB 755, 380 (2016) -0.767(25) meV ⇒ PLB 755, 380 (2016)







-9.58(38) meV ⇒ PRL 111, 143402 (2013) -1.727(20) meV ⇒ PLB 736, 334 (2014)

-15.46(39) meV ⇒ PLB 755, 380 (2016) -0.767(25) meV ⇒ PLB 755, 380 (2016)

1%

3%

6%







Recent experimental news - R.Pohl et al., Science 2016

𝜇D: There is a puzzle! 7.5 deviations from 𝜇D and CODATA�

-9.58(38) meV ⇒ PRL 111, 143402 (2013) -1.727(20) meV ⇒ PLB 736, 334 (2014)

-15.46(39) meV ⇒ PLB 755, 380 (2016) -0.767(25) meV ⇒ PLB 755, 380 (2016)

1%

3%

6%










-9.58(38) meV ⇒ PRL 111, 143402 (2013) -1.727(20) meV ⇒ PLB 736, 334 (2014)

-15.46(39) meV ⇒ PLB 755, 380 (2016) -0.767(25) meV ⇒ PLB 755, 380 (2016)

1%

3%

6%


𝜇4He+ : No puzzle!

muonic atom: 1.679XX(20)exp(52)theo fme-scattering: 1.6810(40)









-9.58(38) meV ⇒ PRL 111, 143402 (2013) -1.727(20) meV ⇒ PLB 736, 334 (2014)

-15.46(39) meV ⇒ PLB 755, 380 (2016) -0.767(25) meV ⇒ PLB 755, 380 (2016)

1%

3%

6%


𝜇4He+ : No puzzle!

muonic atom: 1.679XX(20)exp(52)theo fme-scattering: 1.6810(40)

Stay tuned!Vanderhaeghen talk on Fri.




LIT with Coupled-cluster method

L(�,�) =�

d⇥R(⇥)

(⇥ � �)2 + �2�

�=

��|�

⇥< 1

Merging the Lorentz integral transform method with coupled-cluster theory :New many-body method to extend ab initio calculations of em reactions to medium-mass-nuclei

S.B. et al., Phys. Rev. Lett. 111, 122502 (2013)

⇥ = e�T⇥eTH = e�THeT

(H � E0 � � + i�)| Ri = ⇥|�0i

| Ri = R|�0i

R = R0 + R1 + R2

Presenting results in the CCSD scheme



LIT with Coupled-cluster method

L(�,�) =�

d⇥R(⇥)

(⇥ � �)2 + �2�

�=

��|�

⇥< 1

Merging the Lorentz integral transform method with coupled-cluster theory :New many-body method to extend ab initio calculations of em reactions to medium-mass-nuclei

S.B. et al., Phys. Rev. Lett. 111, 122502 (2013)

⇥ = e�T⇥eTH = e�THeT

(H � E0 � � + i�)| Ri = ⇥|�0i

| Ri = R|�0i

R = R0 + R1 + R2

Presenting results in the CCSD scheme

20 40 60 80 100 ω [MeV]

0

0.1

0.2

0.3

0.4

0.5

R(ω

) [m

b/M

eV]

EIHHCCSD

4HeExact

Successful benchmark for 4He at CCSD M.Miorelli et al., Phys. Rev. C 94, 034317 (2016)


recent developments in nuclear structure theory

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