Electromagentic Reactions and Structure of Light Nuclei

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Electromagentic Reactions and Structure of Light Nuclei Sonia Bacca CANADA'S NATIONAL

consortium of Canadian universities via a contribution through the National Research

LABORATOIRE NATIONAL CANADIEN POUE RECHERCHE EN PHYSIQUE NUCLEAIRE ET EN PHYSIQUE DES

1 Electromagentic Reactions and Structure of Light Nuclei Sonia Bacca CANADA'S NATIONAL LABORATORY FOR PARTICLE AND NUCLEAR PHYSICS Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada. LABORATOIRE NATIONAL CANADIEN POUE RECHERCHE EN PHYSIQUE NUCLEAIRE ET EN PHYSIQUE DES PARTICULES Propriété d'un consortium d'universités canadiennes, géré en co-entreprise à partir d'une contribution administrée par le Conseil National de Recherches Canada

2 Outline Frontiers in Nuclear Theory Ab-initio Approaches to Light Nuclei Nuclear Reactions - Electromagnetic Induced Inelastic Reactions Nuclear Structure - Halo Nuclei in the Helium Isotope Chain Summary and Outlook

3 Frontiers in Nuclear Theory Crab pulsar SN1987a Proton Number Interaction challenges How can we connect nuclear forces to QCD? Few and many-body challenges How do nuclear forces give rise to halos, shell structure, pairing? Neutron Number Astrophysical challenges How does nuclear physics drive phenomena like SN explosions and the creation of the elements? 3

Interaction challenges The chiral EFT approach Separation of scales H = T + V NN + V 3N + V N + NN 3N 3N N N Limited resolution at low energy, can expand in powers of Q Λ

4 Interaction challenges The chiral EFT approach Separation of scales H = T + V NN + V 3N + V N + NN 3N 3N N N Limited resolution at low energy, can expand in powers of Q Λ Details of short distance physics not resolved, but captured in the low energy constants (LEC), fit to experiment once Systematic and can provide error estimate V NN >V 3N >V N

5 Interaction challenges The chiral EFT approach Separation of scales H = T + V NN + V 3N + V N + NN 3N 3N N N Limited resolution at low energy, can expand in powers of Q Λ Details of short distance physics not resolved, but captured in the low energy constants (LEC), fit to experiment once Systematic and can provide error estimate Frontier in nuclear physics: V 3N Investigate the role of on bound and scattering properties of nuclei V NN >V 3N >V N

6 Few- and many-body challenges Past: few-body benchmark with AV8 He PRC 6 (1) 1 5

7 Few- and many-body challenges Past: few-body benchmark with AV8 He PRC 6 (1) 1 5

8 Few- and many-body challenges Past: few-body benchmark with AV8 He PRC 6 (1) 1 Present: develop new many-body methods that can extend the frontiers to heavier systems, e.g. Coupled Cluster Theory heavier sytem! can Vlowk from AV18 He Hagen et al. 7, 8 Ca CCSD from N 3 L 5

9 Few- and many-body challenges Past: few-body benchmark with AV8 He PRC 6 (1) 1 Present: develop new many-body methods that can extend the frontiers to heavier systems, e.g. Coupled Cluster Theory heavier sytem! can Vlowk from AV18 He Hagen et al. 7, 8 Ca CCSD from N 3 L Future: - advance ab-initio methods to heavier and neutron rich nuclei - test nuclear forces at the extremes 5

10 Few- and many-body challenges Three-nucleon forces play a fundamental role in many observables Binding energies without V 3N (Λ) Nogga et al. () Elastic Nuclear Reactions n He n He Nollett et al. (7) AV18+UIX AV18 Vlowk AV18 no 3NF 6

11 Few- and many-body challenges Three-nucleon forces play a fundamental role in many observables Binding energies without V 3N (Λ) Nogga et al. () Elastic Nuclear Reactions n He n He Nollett et al. (7) AV18+UIX AV18 Vlowk AV18 no 3NF Future: - Find out other observables sensitive to 3NF to learn more about it 6

12 Few- and many-body challenges Three-nucleon forces play a fundamental role in many observables Binding energies without V 3N (Λ) Nogga et al. () Elastic Nuclear Reactions n He n He Nollett et al. (7) AV18+UIX AV18 Vlowk AV18 no 3NF Future: - Find out other observables sensitive to 3NF to learn more about it Inelastic Electromagnetic Reactions Binding energy of nuclei far from stability 6

13 Ab-initio approaches to light nuclei s Start from neutrons and protons as building blocks (center of mass coordinates, spins, isospins) s 1 r... r 1 s A r A Solve the non-relativistic quantum mechanical problem of A-nucleons interacting with H = T + V NN + V 3N +... H ψ i = E i ψ i A-body wave function - EFT potentials - Traditional potentials (meson exchange + phenomenology) Calculate low-energy observables form the A-body wave function and compare with experiment Test nuclear forces and investigate the role of many-nucleon forces on nuclear properties which have not been used to fix the parameters of the interaction 7

14 Ab-initio approaches to light nuclei s Start from neutrons and protons as building blocks (center of mass coordinates, spins, isospins) s 1 r... r 1 s A r A Solve the non-relativistic quantum mechanical problem of A-nucleons interacting with H = T + V NN + V 3N +... H ψ i = E i ψ i A-body wave function - EFT potentials - Traditional potentials (meson exchange + phenomenology) Calculate low-energy observables form the A-body wave function and compare with experiment Test nuclear forces and investigate the role of many-nucleon forces on nuclear properties which have not been used to fix the parameters of the interaction Methods: GFMC, NCSM, CC, HH,... 7

15 Ab-initio approaches to light nuclei s Start from neutrons and protons as building blocks (center of mass coordinates, spins, isospins) s 1 r... r 1 s A r A Solve the non-relativistic quantum mechanical problem of A-nucleons interacting with H = T + V NN + V 3N +... H ψ i = E i ψ i A-body wave function - EFT potentials - Traditional potentials (meson exchange + phenomenology) Calculate low-energy observables form the A-body wave function and compare with experiment Test nuclear forces and investigate the role of many-nucleon forces on nuclear properties which have not been used to fix the parameters of the interaction Methods: GFMC, NCSM, CC, HH,... 7

16 Electromagnetic Inelastic Reactions Electron scattering off He 8

17 The Inelastic Response Function R(ω) = ψ f J Ô ψ δ(ef E ω) f 9

18 The Inelastic Response Function R(ω) = ψ f J Ô ψ δ(ef E ω) f a direct calculation is difficult! 9

19 The Inelastic Response Function R(ω) = ψ f J Ô ψ δ(ef E ω) f a direct calculation is difficult! The Lorentz Integral Transform L(σ, Γ) = where R(ω) dω (ω σ) + Γ σ ψ = ψ ψ is obtained solving (H E σ + iγ) ψ = J Ô ψ Γ Efros, Leidemann, Orlandini, PLB 338 (199) 13 Efros, Leidemann, Orlandini, Barnea, JPG.: NPP 3 (7) R59 ψ Due to imaginary part Γ the solution is unique If the r.h.s. is finite ψ has bound state asymptotic behavior 9

20 The Inelastic Response Function R(ω) = ψ f J Ô ψ δ(ef E ω) f a direct calculation is difficult! The Lorentz Integral Transform L(σ, Γ) = where R(ω) dω (ω σ) + Γ σ ψ = ψ ψ is obtained solving (H E σ + iγ) ψ = J Ô ψ Γ Efros, Leidemann, Orlandini, PLB 338 (199) 13 Efros, Leidemann, Orlandini, Barnea, JPG.: NPP 3 (7) R59 ψ Due to imaginary part Γ the solution is unique If the r.h.s. is finite ψ has bound state asymptotic behavior L(σ, Γ) inversion R(ω) The exact final state interaction is included 9

21 The Lorentz Integral Transform (H E σ + iγ) ψ = Ô ψ Bound-state method to expand ψ, ψ J in terms of a complete set of basis state σ Γ - We solved A=3,,6,7 with hyper-spherical harmonics expansions - Has been solved with no core shell model A= - Plans to use in CC theory for medium-mass nuclei Barnea, Leidemann, Orlandini PRC 61 () 51 1

The Lorentz Integral Transform (H E σ + iγ) ψ = Ô ψ Bound-state method to expand ψ, ψ J in terms of a complete set of basis state σ Γ - We solved A=3,,6,7 with hyper-spherical harmonics expansions -

22 The Lorentz Integral Transform (H E σ + iγ) ψ = Ô ψ Bound-state method to expand ψ, ψ J in terms of a complete set of basis state σ Γ - We solved A=3,,6,7 with hyper-spherical harmonics expansions - Has been solved with no core shell model A= - Plans to use in CC theory for medium-mass nuclei Barnea, Leidemann, Orlandini PRC 61 () 51 Benchmarks: Nucl.Phys. A () Phys.Rev.C 69 ()

23 Electron scattering reaction Virtual Photon k P f (ω, q) k q = k k q = ( ω, q) P can vary independently d σ dωdω = σ M Inclusive cross section A(e,e )X [ Q q (ω, q) + ( Q q + tan θ with Q = q = q ω and scattering angle θ ) ] R T (ω, q) and σ M Mott cross section 11

24 Electron scattering reaction Virtual Photon k P f (ω, q) k q = k k q = ( ω, q) P can vary independently d σ dωdω = σ M Inclusive cross section A(e,e )X [ Q q (ω, q) + ( Q q + tan θ ) ] R T (ω, q) ) (ω, q) = Ψ f ρ(q) Ψ δ (E f E ω + q M f ) R T (ω, q) = Ψ f J T (q) Ψ δ (E f E ω + q M f 1

25 Electron scattering reaction He First step: Study (ω, q) (no MEC) to investigate the effect of 3NF 13

26 Electron scattering reaction He First step: Study (ω, q) (no MEC) to investigate the effect of 3NF Study of R T (ω, q) requires to introduce the MEC πm + πm N N N N 13

27 Electron scattering reaction - He(e,e )X k P f Comparison with experiment (ω, q) Calculation of Medium-q kinematics with the LIT k q = k k q = ( ω, q) P [1-3 MeV -1 ] Bates Saclay q=3 MeV/c [1-3 MeV -1 ] Bates Saclay q= MeV/c [1-3 MeV -1 ] S.B. et al., PRL 1, 1651 (9) Bates Saclay q=5 MeV/c e AV18+UIX: PWIA e γ * p Full FSI: He 3 H 1

28 Electron scattering reaction - He(e,e )X k P f Comparison with experiment (ω, q) Calculation of Medium-q kinematics with the LIT k q = k k q = ( ω, q) P [1-3 MeV -1 ] Bates Saclay q=3 MeV/c [1-3 MeV -1 ] Bates Saclay q= MeV/c [1-3 MeV -1 ] S.B. et al., PRL 1, 1651 (9) Bates Saclay q=5 MeV/c e AV18+UIX: PWIA e γ * p Full FSI: He 3 H Strong effect of FSI: known form Carlson and Schiavilla PRL 68 (199) and PRC 9 R88 (199) but now we can look at the energy dependence of FSI 1

29 Electron scattering reaction - He(e,e )X k P f Comparison with experiment (ω, q) Calculation of Medium-q kinematics with the LIT k q = k k q = ( ω, q) P [1-3 MeV -1 ] Bates Saclay q=3 MeV/c [1-3 MeV -1 ] Bates Saclay q= MeV/c [1-3 MeV -1 ] S.B. et al., PRL 1, 1651 (9) Bates Saclay q=5 MeV/c e AV18+UIX: PWIA e γ * p Full FSI: He 3 H Strong effect of FSI: known form Carlson and Schiavilla PRL 68 (199) and PRC 9 R88 (199) but now we can look at the energy dependence of FSI Discrepancy with experiment at large momentum and energy More activity at JLab Meziani et al. E-5-11, Hall A 1

30 Electron scattering reaction - He(e,e )X k P f Comparison with experiment (ω, q) Calculation of Medium-q kinematics with the LIT Searching for 3N effects k q = k k q = ( ω, q) P S.B. et al., PRL 1, 1651 (9) [1-3 MeV -1 ] Bates Saclay q=3 MeV/c [1-3 MeV -1 ] Saclay q= 35 MeV/c [1-3 MeV -1 ] Bates Saclay q= MeV/c Full FSI: AV18 AV18+UIX 15

31 Electron scattering reaction - He(e,e )X k P f Comparison with experiment (ω, q) Calculation of Medium-q kinematics with the LIT Searching for 3N effects k q = k k q = ( ω, q) P S.B. et al., PRL 1, 1651 (9) [1-3 MeV -1 ] Bates Saclay q=3 MeV/c [1-3 MeV -1 ] Saclay q= 35 MeV/c [1-3 MeV -1 ] Bates Saclay q= MeV/c Full FSI: AV18 AV18+UIX 3NF reduce the peak of 1% 15

32 Electron scattering reaction - He(e,e )X k P f Comparison with experiment (ω, q) Calculation of Medium-q kinematics with the LIT Searching for 3N effects k q = k k q = ( ω, q) P S.B. et al., PRL 1, 1651 (9) [1-3 MeV -1 ] Bates Saclay q=3 MeV/c [1-3 MeV -1 ] Saclay q= 35 MeV/c [1-3 MeV -1 ] Bates Saclay q= MeV/c Full FSI: AV18 AV18+UIX 3NF reduce the peak of 1% Comparison with experiment improves with 3NF 15

33 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects S.B. et al., PRL 1, 1651 (9) 3 1 [1-3 MeV -1 ] 1 q=5 MeV/c [1-3 MeV -1 ] q=1 MeV/c [1-3 MeV -1 ] (d) AV18 AV18+UIX MT q= MeV/c Full FSI: AV18 AV18+UIX B.E./MeV MT

34 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects S.B. et al., PRL 1, 1651 (9) 3 1 [1-3 MeV -1 ] 1 q=5 MeV/c [1-3 MeV -1 ] q=1 MeV/c [1-3 MeV -1 ] (d) AV18 AV18+UIX MT q= MeV/c Full FSI: AV18 AV18+UIX B.E./MeV MT 3.56 Larger sensitivity to 3NF at low q 16

35 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects S.B. et al., PRL 1, 1651 (9) 3 1 [1-3 MeV -1 ] 1 q=5 MeV/c [1-3 MeV -1 ] q=1 MeV/c [1-3 MeV -1 ] (d) % AV18 AV18+UIX MT q= MeV/c Full FSI: AV18 AV18+UIX B.E./MeV MT 3.56 Larger sensitivity to 3NF at low q 16

36 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects [1-3 MeV -1 ] 3 1 % 8 % 15 q=5 MeV/c Full FSI: AV18 AV18+UIX B.E./MeV.7 8. [1-3 MeV -1 ] q=1 MeV/c. MT [1-3 MeV -1 ] (d) S.B. et al., PRL 1, 1651 (9) AV18 AV18+UIX MT q= MeV/c Larger sensitivity to 3NF at low q 16

37 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects [1-3 MeV -1 ] 3 1 % 8 % 15 q=5 MeV/c Full FSI: AV18 AV18+UIX B.E./MeV.7 8. [1-3 MeV -1 ] q=1 MeV/c. MT [1-3 MeV -1 ] (d) S.B. et al., PRL 1, 1651 (9) AV18 AV18+UIX MT q= MeV/c Larger sensitivity to 3NF at low q It is not a simple binding effect! 16

38 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects using different 3NFs 3 1 S.B. et al., arxiv:99.81 [1-3 MeV -1 ] q=5 MeV/c [1-3 MeV -1 ] 8 6 q=1 MeV/c [1-3 MeV -1 ] q= MeV/c Full FSI: AV18 AV18+UIX B.E./MeV AV18+TM

39 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects using different 3NFs 3 1 S.B. et al., arxiv:99.81 [1-3 MeV -1 ] q=5 MeV/c [1-3 MeV -1 ] 8 6 q=1 MeV/c [1-3 MeV -1 ] q= MeV/c Full FSI: AV18 AV18+UIX B.E./MeV NF: AV18+TM

40 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects using different 3NFs 3 1 S.B. et al., arxiv:99.81 [1-3 MeV -1 ] q=5 MeV/c [1-3 MeV -1 ] 8 6 q=1 MeV/c [1-3 MeV -1 ] q= MeV/c Full FSI: AV18 AV18+UIX B.E./MeV NF: AV18+TM Strong 3NF effects confirmed, details depend on force model 17

41 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects using different 3NFs 3 1 S.B. et al., arxiv:99.81 [1-3 MeV -1 ] q=5 MeV/c [1-3 MeV -1 ] 8 6 q=1 MeV/c [1-3 MeV -1 ] q= MeV/c Full FSI: AV18 AV18+UIX B.E./MeV NF: AV18+TM Strong 3NF effects confirmed, details depend on force model Quest for measurements: data taken in Mainz 17

42 Electron scattering reaction - He(e,e )X k P f k q = k k q = ( ω, q) P Calculation of Low-q kinematics (ω, q) with the LIT Searching for 3N effects using different 3NFs 3 1 S.B. et al., arxiv:99.81 [1-3 MeV -1 ] q=5 MeV/c [1-3 MeV -1 ] 8 6 q=1 MeV/c [1-3 MeV -1 ] q= MeV/c Full FSI: AV18 AV18+UIX B.E./MeV NF: AV18+TM Strong 3NF effects confirmed, details depend on force model Quest for measurements: data taken in Mainz Future: Investigate R T (ω, q) 17

43 Structure of Nuclei far from stability Binding Energy of Halo Nuclei 18

44 Halo nuclei 8 Pb one proton halo two proton halo 1 fm one neutron halo 11 Li two neutron halo four neutron halo Sonia Bacca LANL, Aug 9 19

45 Halo Nuclei - Experiment New Era of Precision Measurements for masses and radii Mass measurement of 8 He with the Penning trap 8 8 He TRIUMF, Ryjkov et al. PRL 11, 151 (8)

46 Halo Nuclei - Experiment New Era of Precision Measurements for masses and radii Mass measurement of 8 He with the Penning trap Measurement of charge radii via isotope shift rms point-proton matter Experiment He Theory 6 He 8 Nuclear scattering NCSM GFMC 8 He TITAN 8 He Nuclear scattering NCSM GFMC TRIUMF, Ryjkov et al. PRL 11, 151 (8) Nuclear radii [fm] ARGONNE, Wang et al. PRL 93, 151 () GANIL, Mueller et al. PRL 99, 551 (7) δν AA = δνa,a mass + Kδ r ch AA rp = rch R p 3 Mp N Z R n

47 Previous calculations GFMC Uses local two- and three-nucleon forces Pieper et al. () 1

48 Previous calculations GFMC Uses local two- and three-nucleon forces Pieper et al. () 1

49 Previous calculations GFMC Uses local two- and three-nucleon forces AV18 does not bind the helium halo with respect to n emission IL V ijk = V π ijk + V 3π,R ijk + V R ijk N.B.: parameters of the IL force are obtained from a fit of 17 states of A<9 including the binding energy of 6 He and 8 He Pieper et al. () 1

50 Previous calculations GFMC Uses local two- and three-nucleon forces AV18 does not bind the helium halo with respect to n emission IL V ijk = V π ijk + V 3π,R ijk + V R ijk N.B.: parameters of the IL force are obtained from a fit of 17 states of A<9 including the binding energy of 6 He and 8 He Pieper et al. () NCSM Used CD-Bonn (meson exchange theory potential) has the incorrect asymptotic for the halo ψ nl (r) e νr L l+1/ n (νr ) ν = mω/ 1

51 Previous calculations GFMC Uses local two- and three-nucleon forces AV18 does not bind the helium halo with respect to n emission IL V ijk = V π ijk + V 3π,R ijk + V R ijk N.B.: parameters of the IL force are obtained from a fit of 17 states of A<9 including the binding energy of 6 He and 8 He Pieper et al. () NCSM Used CD-Bonn (meson exchange theory potential) has the incorrect asymptotic for the halo ψ nl (r) e νr L l+1/ n (νr ) ν = mω/ There is no prediction of halo nuclei from chiral interactions! 1

52 Low Momentum Interactions Effective field theory potentials and low-momentum evolution V low k evolve to lower resolution (cutoffs) by integrating out high-momenta Bogner, Kuo, Schwenk (3) need smaller basis Evolution of N chiral forces: phase-shift equivalent k (fm - ) 5

53 Low Momentum Interactions Effective field theory potentials and low-momentum evolution V low k evolve to lower resolution (cutoffs) by integrating out high-momenta Bogner, Kuo, Schwenk (3) need smaller basis Evolution of N chiral forces: phase-shift equivalent k (fm - ) H(Λ) =T + V NN (Λ)+V 3N (Λ)+... Variation of the cutoff provides a tool to estimate the error of neglected short range 3N forces 5

chiral forces: phase-shift equivalent k (fm - ) H(Λ) =T + V NN (Λ)+V 3N (Λ)+.

54 Low Momentum Interactions Effective field theory potentials and low-momentum evolution V low k evolve to lower resolution (cutoffs) by integrating out high-momenta Bogner, Kuo, Schwenk (3) need smaller basis Evolution of N chiral forces: phase-shift equivalent k (fm - ) H(Λ) =T + V NN (Λ)+V 3N (Λ)+... Variation of the cutoff provides a tool to estimate the error of neglected short range 3N forces Can evolve consistently 3N forces: Jurgenson, Navratil, Furnstahl, (9) 5

55 Our Approach Hyper-spherical Harmonics Expansion for 6 He Cluster Cluster Theory for 8 He

56 Hyperspherical Harmonics Few-body method - uses relative coordinates ψ( r 1, r,..., r A ) = ϕ( R CM )Ψ( η 1, η,..., η A 1 ) η = A R CM Recursive definition of hyper-spherical coordinates ρ, Ω η 1,..., η A 1 ρ = A ri = i=1 A 1 i=1 η i H(ρ, Ω) =T ρ + K (Ω) ρ b ρ b Asymptotic e aρ ρ Model space truncation Can use non-local interactions, Matrix Diagonalization K K max ψ H () ψ = A(A 1) ψ H (A,A 1) ψ Most applications in few-body; challenge in A> Barnea and Novoselsky, Ann. Phys. 56 (1997) 19 3

57 Coupled Cluster Theory Many-body method- uses particle coordinates ψ( r 1, r,..., r A ) = e T φ( r 1, r,..., r A ) T = T (A) T 1 = ia t a i a aa i reference SD T 1 T T 3 T = ia t ab ij a aa b a ja i CCSD Equations CCSD CCSDT E = φ e T He T φ = φ a i e T He T φ = φ ab ij e T He T φ CC is flexible in single particle w.f. adopted If use HF φ i e k ir Asymptotic i r Use it for 8 He, closed shell nucleus Model space truncation N N max 1p1/ Can use non-local interactions 1p3/ 1s1/ Applicable to medium-mass nuclei p n

58 Benchmark on He H(Λ) =T + V NN (Λ)+V 3N (Λ) V low k NN from N 3 LO (5 MeV) E [MeV] 15 5 He Λ = 1.8 fm 1 Λ =. fm 1 Λ =. fm 1 3 HH K max - Benchmark HH-CC-FY on He - Λ =. fm 1 E exp =-8.96 MeV 6

59 Helium Halo Nuclei - Binding Energy - H(Λ) =T + V NN (Λ)+V 3N (Λ) HH V low k NN from N 3 LO CCSD Λ =. fm hω =1 MeV hω =1 MeV E [MeV] 5 E [MeV] 6 He 8 He 5 3 Exp 3 Exp K max S.Bacca et al., arxiv: N max = Max(n + l) 7

60 Helium Halo Nuclei - Binding Energy - H(Λ) =T + V NN (Λ)+V 3N (Λ)+... E [MeV] HH V low k NN from N 3 LO CCSD Exp Λ = 1.8 fm 1 Λ =. fm 1 Λ =. fm 1 E [MeV] hω =1 MeV hω =1 MeV hω =16 MeV 6 He 8 He 3 3 Exp K max N max = Max(n + l) S.Bacca et al., arxiv:

61 Binding Energy of 6 He -1 - Extrapolation - V low k NN from N 3 LO Λ=. fm He HH E [MeV] Exp K max E(K max )=E + Ae BK max Λ E(K max = 1) E (3) (13) (19) 9

62 Binding Energy of 8 He - CC Theory: Add Triples Correction - Hilbert space: 15 major shell Values in MeV Λ E[CCSD] E[Lambda-CCSD(T)] Triples corrections are larger for larger cutoff Their relative effect goes from 3 to 6% 3

63 Binding Energy Summary He -6-6 NCSM -7 NCSM -7 E [MeV] GFMC He previous Experimental data our HH -3 GFMC previous our CCSD(T) 31

64 Binding Energy Summary He -6-6 NCSM -7 NCSM -7 E [MeV] GFMC He previous Experimental data our HH -3 GFMC previous our CCSD(T) Our estimated error in neglected For cutoff. fm-1 He and 6 He are close to experiment, but 8 He is under-bound Low momentum 3NF are overall repulsive in s-shell nuclei and nuclear matter, but two-pion exchange ci are attractive in He and could provide further attractive spin-orbit (LS) contributions for the halo neutrons 31

65 Summary and Outlook Progress done in ab-initio approaches to nuclear structure and reactions The LIT is a very powerful method to an exact study of electro-weak reactions It is presently the only approach to inelastic reactions for A>3 Shed more light on role of 3NF Future Calculate the transverse response function with explicit MEC Extend the formalism to use EFT forces/currents HH and CC are two promising methods for the investigation of nuclei far from stability First description of helium halo isotopes with correct asymptotic from evolved chiral NN forces Future Work needs to be done to incorporate 3NF 3

66 Thanks to my collaborators: Nir Barnea Gaute Hagen Thomas Papenbrock Winfried Leidemann Giuseppina Orlandini Achim Schwenk 33

A path to lepton-nucleus reactions from first principles

Canada s National Laboratory for Particle and Nuclear Physics Laboratoire national canadien pour la recherche en physique nucléaire et en physique des particules A path to lepton-nucleus reactions from