+Ab initio electroweak reactions with nuclei
Sonia Bacca
Johannes Gutenberg Universität Mainz

November 1st, 2022

International Symposium on“Clustering as a window on the hierarchical structure of quantum systems”
Sendai, Japan

Sonia Bacca

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Ab initio nuclear theory
Start from neutrons and protons as building blocks• (centreof mass coordinates, spins, isospins)

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

H| i = Ei | i
H = T + VN N (⇤) + V3N (⇤) + . . .
using phenomenological potentials or interactions from chiral effective field theory (𝝌EFT)• Find numerical solutions with no approximations or controllable approximations
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Hierarchical Structure of 𝝌EFT
from E. Epelbaum (2018), see yesterday’s talkSonia Bacca

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Hierarchical Structure of 𝝌EFT
from E. Epelbaum (2018), see yesterday’s talk

Sequential fit of LECs with:
Two-nucleon force fit on
NN scattering data
Three-nucleon force fit on
A=3,4 nuclei••

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Hierarchical Structure of 𝝌EFT
from E. Epelbaum (2018), see yesterday’s talk

Simultaneous fit of LECs with:
Two-nucleon force fit on
NN scattering data
Three-nucleon force fit on
selected nuclei up to A=25••

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Progress of ab initio theory

0ass 1umber (A)Ab initio calculations starting from
NN+3N interactions

100
80
60
402001980

1990

2000

2010

2020

Year
J.Simonis, SB, G.Hagen, Eur. Phys. J. A 55, 241 (2019).

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Progress of ab initio theory
208Pb

0ass 1umber (A)Ab initio calculations starting from
NN+3N interactions

Nature Phys. 18, 1196 (2022)

100
80
60
40
2001980

1990

2000

2010

2020

Year
J.Simonis, SB, G.Hagen, Eur. Phys. J. A 55, 241 (2019).

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Electroweak reactions

Cross
Sectionem ⇠ R(⇤) =ew⇧⌅ ⇥⇥f J⇥
Ôµ ⇥0f⇤2(EfE0⇤)

Electroweak operator

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The continuum problem
R(⇤) =⇧⌅ ⇥⇥f J⇥
Ôµ ⇥0f⇤2(EfE0⇤)

Depending on Ef , many channels may be involved““

boundexcited state

2-body break-up

400

Counts
Cross
Sectionground state

3-body break-up...

Excitation Energy

A-body break-up

continuum

300

giant
resonances

200

narrow
resonances

100

00510203025Excitation
Energyω [MeV]
1535

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Lorentz Integral TransformR(⇤) =⇧⌅ ⇥f⇥f J⇥Ôµ ⇥0⇤2(EfE0⇤)

Exact knowledge limited inenergy and mass numberSonia Bacca

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Lorentz Integral TransformR(⇤) =

⇧⌅ ⇥f

⇥f J⇥
Ôµ ⇥0⇤2(EfE0⇤)

Exact knowledge limited inenergy and mass numberR(⇥)
L( , ) = d⇥(⇥)2 +⇡Sonia Bacca

˜| ˜i Efros, et al.,=hJPG.Nucl.Part.Phys.34 (2007)
2R459

9

Lorentz Integral TransformR(⇤) =⇧⌅ ⇥⇥f J⇥
Ôµ ⇥0f⇤2(EfE0⇤)

Exact knowledge limited inenergy and mass numberR(⇥)
L( , ) = d⇥(⇥)2 +⇡(HE0˜| ˜i Efros, et al.,=hJPG.Nucl.Part.Phys.34 (2007)
2˜ = Ô+ i ) | ⇥⇥⇥ | ⇥0 ⇥Sonia Bacca

R459

Bound-state-likeequation

9Lorentz Integral TransformR(⇤) =⇧⌅ ⇥⇥f J⇥
Ôµ ⇥0f⇤2(EfExact knowledge limited inenergy and mass numberR(⇥)
L( , ) = d⇥(⇥)2 +⇡(HE0E0⇤)

inversion

˜| ˜i Efros, et al.,=hJPG.Nucl.Part.Phys.34 (2007)2

˜ = Ô
+ i ) | ⇥⇥⇥ | ⇥0 ⇥Sonia Bacca

R459

Bound-state-likeequation

9Lorentz Integral TransformR(⇤) =⇧⌅ ⇥⇥f J⇥Ôµ ⇥0f⇤2(EfExact knowledge limited inenergy and mass numberR(⇥)
L( , ) = d⇥(⇥)2 +⇡(HE0E0⇤)inversion

˜| ˜i Efros, et al.,=hJPG.Nucl.Part.Phys.34 (2007)2

˜ = Ô
+ i ) | ⇥⇥⇥ | ⇥0 ⇥R459

Bound-state-likeequation

Solved with:• Hyper-spherical Harmonics• No core shell model• Coupled Cluster theory
Sonia Bacca9Coupled-cluster theory|⇥(⌥r1 , ⌥r2 , ..., ⌥rA ) = eT | (⌥r1 , ⌥r2 , ..., ⌥rA )
00

T1

T2T3

T =T(A)cluster expansion

CCSD
CCSDTSonia Bacca

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Coupled-cluster theory|⇥(⌥r1 , ⌥r2 , ..., ⌥rA ) = eT | (⌥r1 , ⌥r2 , ..., ⌥rA )
00

T1

T2

T3

T =T(A)cluster expansion

CCSD
CCSDT

SB et al., Phys. Rev. Lett. 111, 122502 (2013)(H̄E0¯+ i )| ˜ R i = ⇥|0i

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Coupled-cluster theory|⇥(⌥r1 , ⌥r2 , ..., ⌥rA ) = eT | (⌥r1 , ⌥r2 , ..., ⌥rA )0T =0T1T2T(A)cluster expansion

T3

CCSD
CCSDT

SB et al., Phys. Rev. Lett. 111, 122502 (2013)(H̄E0¯+ i )| ˜ R i = ⇥|0i

Sonia Bacca{H̄ = eTHeT¯ = e T ⇥eT⇥| ˜ R i = R̂|0i

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Coupled-cluster theory|⇥(⌥r1 , ⌥r2 , ..., ⌥rA ) = eT | (⌥r1 , ⌥r2 , ..., ⌥rA )0T =0T1T2

T(A)cluster expansion

T3

CCSD
CCSDT

SB et al., Phys. Rev. Lett. 111, 122502 (2013)(H̄E0¯+ i )| ˜ R i = ⇥|0i{H̄ = eTHeT¯ = e T ⇥eT⇥| ˜ R i = R̂|0iResults with implementation at CCSD level + some study of triples contributions
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Validation in 4He
Dipole response function
Comparison of CCSD with exact hyperspherical harmonics with NN forces at N3LO

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

R(ω) [mb/MeV]

0.54HeHH
EIHH

CCSD

0.4
0.3
0.2
0.1
020406080100

ω [MeV]
Sonia Bacca

11Emergence of structures in nuclei
Stable Nuclei
We have data on ~180 stable nuclei
Giant dipole resonances
10040Ca
Ahrens et al.

σγ(ω) [mb]806040200020406080

100

ω[MeV]!

From photoabsorption experiments(p,p’) experiments

ee-e-Sonia Bacca

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Emergence of structures in nuclei
Unstable Nuclei

Stable Nuclei
We have data on ~180 stable nuclei
Giant dipole resonances
100Fewer data, pigmy dipole resonances
Leistenschneider et al.

40

Ca
Ahrens et al.

σγ(ω) [mb]8060402000core
20406080100

ω[MeV]!

From photoabsorption experiments(p,p’) experiments

From Coulomb excitation experiments

ee-e-Sonia Bacca

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Emergence of structures in nuclei
Unstable Nuclei

Stable Nuclei
We have data on ~180 stable nuclei
Giant dipole resonances
100Fewer data, pigmy dipole resonances
Leistenschneider et al.

40CaAhrens et al.

σγ(ω) [mb]

80
60
40
2000core
2040

60

80

100

ω[MeV]!

From photoabsorption experiments(p,p’) experiments

From Coulomb excitation experiments

ee-e-Do we see the emergence of collective motions from first principle calculations?
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Giant dipole resonances
SB et al., PRC 90, 064619 (2014)

10040Ca
Ahrens et al.

σγ(ω) [mb]80

LIT-CCSD
NN(N3LO)

60402000 Spexp

2040

60

80

100

ω[MeV]
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Pygmy dipole resonance
SB et al., PRC 90, 064619 (2014)

2522

σγ(ω) [mb]

20O
Leistenschneider et al.
NN (N3LO)
CCSD

1510coreSp

50510Snexp

15

ω [MeV]
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Connections to astrophysics
Nuclear Equation of State

Slope parameter, related topressure of pure neutron matter atsaturation densityLaboratory measurements
on finite nuclei are crucial

Roca-Maza et al.,Phys. Rev. C 88, 024316 (2013)

S0Symmetry energy atsaturation density

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The 48Ca nucleus
Birkhan, Miorelli, SB et al., Phys. Rev. Lett. 118, 252501 (2017)

RCPN (p,p’) experiment

New constraint on the EOS

DFT28.5  S0v  33.3 MeV
43.8  L  48.6 MeV

Z Ex
↵D !
d!
0(!)
!2(CCSD)

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The 48Ca nucleus
Birkhan, Miorelli, SB et al., Phys. Rev. Lett. 118, 252501 (2017)

RCPN (p,p’) experiment

New constraint on the EOS

DFT28.5  S0v  33.3 MeV
43.8  L  48.6 MeV

Z Ex
↵D !
d!
0(!)
!2(CCSD)

Improved correlations: CCSD-T1
Miorelli, SB et al., PRC 98, 014324 (2018)
Simonis, SB, Hagen, EPJA 55, 241 (2019)

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The 68Ni nucleus
S.Kaufmann, J. Simonis, SB et al., PRL 104 (2020) 132505

2.0/2.0 (EM)2.2/2.0 (EM)NNLOsat2.0/2.0 (PWA)

Exp.: Rossi et al.
Exp.: This work

1.8/2.0 (EM)6.5

↵D(68Ni) [fm3]6.05.568Ni

5.0
4.5
4.0
3.5
3.0
3.6

3.7

3.8

3.9

4.0

4.1

Rc(68Ni) [fm]Sonia Bacca

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The 68Ni nucleus
S.Kaufmann, J. Simonis, SB et al., PRL 104 (2020) 132505

2.0/2.0 (EM)2.2/2.0 (EM)NNLOsat2.0/2.0 (PWA)

Exp.: Rossi et al.
Exp.: This work

1.8/2.0 (EM)

6.5
CCSD

↵D(68Ni) [fm3]

6.0
5.5

68Ni
CCSD-T1

5.0
4.5
4.0
3.5
3.0
3.6

3.7

3.8

3.9

4.0

4.1

Rc(68Ni) [fm]Sonia Bacca

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The Halo 8He nucleus8He
F. Bonaiti, SB, G.Hagen, PRC 105, 034313 (2022)

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The Halo 8He nucleus
8He

Electric dipole polarizability, running sum
F. Bonaiti, SB,G.Hagen, PRC 105, 034313 (2022)↵D = 2↵

Z "1!exthd!

R(!)!

CCSD-T1
CCSD

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Theory:brand spanning
NNLOsat∆NNLOGO

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The Halo 8He nucleus
8He

Electric dipole polarizability, running sum
F. Bonaiti, SB,G.Hagen, PRC 105, 034313 (2022)↵D = 2↵

Z "1!exthd!

R(!)!

Exp (preliminary)
C. Lehr et al.
SAMURAIcollaboration
CCSD-T1
CCSD

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Theory:brand spanning
NNLOsat∆NNLOGO

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The Halo 8He nucleus
8He

Electric dipole polarizability, running sum
F. Bonaiti, SB,G.Hagen, PRC 105, 034313 (2022)↵D = 2↵

Z "1!exthd!

R(!)!

Exp (preliminary)
C. Lehr et al.
SAMURAI
collaboration
CCSD-T1
CCSD

Theory:brand spanning
NNLOsat∆NNLOGO

Are we seeing missing higher
order𝝌EFT effects or is the halo
structure challenging CC theory?

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4He monopole transition

54He32|FM | /4π 10-44

Koebschall et al.
Walcher
Frosch et al.
Hiyama et al.

2100122-234q [fm ]Sonia Bacca

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4He monopole transition
SB et al., Phys. Rev. Lett. 110, 042503 (2013)

54He

32|FM | /4π 10-4

4

Koebschall et al.
Walcher
Frosch et al.
Hiyama et al.
AV18+UIX
3NN(N LO)+23NF(N LO)

2100122-234q [fm ]• Hiyama’s calculation agree with data but our computation disagree• Experimental data have large error bars
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4He monopole transition
Kegel et al., arXiv:2112.10582

4He
EFT potentials• New experiment in Mainz with dramatically improved problem is in the theory
done with different methods and different interactions.
• Calculations
Can the different methods be the problem?
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4He monopole transition
Kegel et al., arXiv:2112.10582

4He
Our new calc.
EFT potentials• We perfectly reproduce Hiyama’s results within error bars.
• Puzzle remains to be solved.
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Conclusions• Remarkable progress in first principle calculations of electromagnetic
properties and more work is ahead of usThanks to all my collaborators:
B. Acharya, F. Bonaiti, S. Li Muli, W. Jiang, J.E.Sobczyk,
N. Barnea, G. Hagen, W. Leidemann, T. Papenbrock, G. Orlandini,
J. Simonis, C. Payne, et al.

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Conclusions• Remarkable progress in first principle calculations of electromagnetic
properties and more work is ahead of us

Thanks to all my collaborators:
B. Acharya, F. Bonaiti, S. Li Muli, W. Jiang, J.E.Sobczyk,
N. Barnea, G. Hagen, W. Leidemann, T. Papenbrock, G. Orlandini,
J. Simonis, C. Payne, et al.

Thanks for your attention!
Sonia Bacca

2525th European Conference on Few-Body
Problems in Physics

Mainz

Mainz, 30 July - 4 Aug, 2023

Topics:••••••••Hadron physics
Nuclei and hypernuclei
Electroweak processes
Nuclear astrophysics
Cold atoms and quantum gases
Atoms and molecules
Few-body methods
Few-body aspects of many-body systems

Strong overlap with this Symposium:
Keywords mentioned in Nakamura’s introduction:
Three-body forces
Halo nuclei
Hoyle states
Universality
Effimov physics
Feshbach resonance
Sonia Bacca26Backup

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Halo nuclei
8He

F. Bonaiti, SB,G.Hagen, PRC 105, 034313 (2022)
Halo nucleus

D → CCSD
T-1 → CCSDT-1

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The Halo 8He nucleus
8He
F. Bonaiti, SB, G.Hagen, PRC 105, 034313 (2022)

Halo nucleus

CCSDT-1

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Halo nuclei
8HeAcharya, SB, Bonaiti, Li Muli, Sobczyk, 2210.04632
Nmax = 14
T-1/T-1

Halo nucleus

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Inversion of the LIT
The inversion is performed numerically with a regularization procedure (ill-posed problem)
Ansatzfit

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Inversion of the LIT
The inversion is performed numerically with a regularization procedure (ill-posed problem)
Ansatzfit

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Inversion of the LIT
The inversion is performed numerically with a regularization procedure (ill-posed problem)
Ansatzfit

Message: Inversions are stable if the LIT is calculated precisely enough
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Sum Rules
mn =Z 10d! ! n R(!) = hˆ†0 |⇥ (ĤˆE0 )n ⇥|0iThe polarizability is an inverse-energy weighted sum rule of the dipole response function↵D = 2 ↵ m 1 = 2 ↵ h0 |⇥†1(HSonia BaccaE0 )⇥|0i32

Sum Rules
mn =Z 10d! ! n R(!) = hˆ†0 |⇥ (ĤˆE0 )n ⇥|0i

The polarizability is an inverse-energy weighted sum rule of the dipole response function↵D = 2 ↵ m 1 = 2 ↵ h0 |⇥†1(HE0 )⇥|0i

Can be obtained from the Lorentz Integral Transform in the limit of 𝚪→0Sonia Bacca

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