Towards first-principle description of electromagnetic reactions in medium-mass nuclei

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Canada s National Laboratory for Particle and Nuclear Physics Laboratoire national canadien pour la recherche en physique nucléaire et en physique des particules Towards first-principle

Papenbrock Elba XIII Workshop on Electron-nucleus scattering, June 23-27, 214, Marciana Marina Electromagnetic Reactions Owned and operated as a joint venture by a consortium of Canadian

1 Canada s National Laboratory for Particle and Nuclear Physics Laboratoire national canadien pour la recherche en physique nucléaire et en physique des particules Towards first-principle description of electromagnetic reactions in medium-mass nuclei Nuclear Halo Sonia Bacca Theory Group TRIUMF In collaboration with: N.Barnea, G.Hagen, M.Miorelli, G.Orlandini, T.Papenbrock Elba XIII Workshop on Electron-nucleus scattering, June 23-27, 214, Marciana Marina Electromagnetic Reactions Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada 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 Motivations Electromagnetic probes (coupling constant <<1) With the electro-magnetic probe, we can immediately relate the cross section to the transition matrix element of the current operator, thus to the structure of the target itself [De Forest-Walecka, Ann. Phys. 1966] f J µ 2! = q k k µ µ!, q µ µ µ q = k k µ q = ( ω, q) µ P f µ P June 25th 214 Sonia Bacca 2

3 Motivations Electromagnetic probes (coupling constant <<1) With the electro-magnetic probe, we can immediately relate the cross section to the transition matrix element of the current operator, thus to the structure of the target itself [De Forest-Walecka, Ann. Phys. 1966] f J µ 2! = q k k µ µ!, q µ µ µ q = k k µ q = ( ω, q) µ P f µ P For few-nucleons one can perform exact calculations both for bound and scattering states test the nuclear theory on light nuclei and extend it to heavier mass number June 25th 214 Sonia Bacca 2

4 Motivations Electromagnetic probes (coupling constant <<1) With the electro-magnetic probe, we can immediately relate the cross section to the transition matrix element of the current operator, thus to the structure of the target itself [De Forest-Walecka, Ann. Phys. 1966] f J µ 2! = q k k µ µ!, q µ µ µ q = k k µ q = ( ω, q) µ P f µ P For few-nucleons one can perform exact calculations both for bound and scattering states test the nuclear theory on light nuclei and extend it to heavier mass number Provide important informations in other fields of physics, where nuclear physics plays a crucial role: - Astrophysics: interactions with nucleonic matter, radiative capture reactions, interactions with nucleonic matter (vector current as em) - Atomic physics (nuclear corrections to atomic levels, etc.) PRL 111, (213) arxiv: , to appear on PRC - Particle physics (neutrino-interaction with nuclei) arxiv: June 25th 214 Sonia Bacca 2

5 Electromagnetic Reactions Photonuclear Reactions Electric-Dipole Polarizability... 3

6 Electromagnetic Reactions Photo-nuclear Reactions Reactions resulting from the interaction of a photon with the nucleus For photon energy MeV stable nuclei across the periodic table show a wide and large peak O Ahrens et al. σ γ [mb] E γ [MeV] 4

7 Electromagnetic Reactions Photo-nuclear Reactions Reactions resulting from the interaction of a photon with the nucleus For photon energy MeV stable nuclei across the periodic table show a wide and large peak O Ahrens et al. σ γ [mb] E γ [MeV] Giant Dipole Resonance 5

8 Electromagnetic Reactions Photo-nuclear Reactions Reactions resulting from the interaction of a photon with the nucleus For photon energy MeV stable nuclei across the periodic table show a wide and large peak O Ahrens et al. σ γ [mb] E γ [MeV] Giant Dipole Resonance 5

9 Electromagnetic Reactions 4 35 Photo-nuclear Reactions Reactions resulting from the interaction of a photon with the nucleus For photon energy MeV stable nuclei across the periodic table show a wide and large peak 16 O Ahrens et al. Coulomb excitations Inelastic scattering between two charged particles. Can use unstable nuclei as projectiles. Neutron-rich nuclei show fragmented low-lying strength Leistenschneider et al. 3 σ γ [mb] E γ [MeV] Giant Dipole Resonance 5

10 Electromagnetic Reactions 4 35 Photo-nuclear Reactions Reactions resulting from the interaction of a photon with the nucleus For photon energy MeV stable nuclei across the periodic table show a wide and large peak 16 O Ahrens et al. Coulomb excitations Inelastic scattering between two charged particles. Can use unstable nuclei as projectiles. Neutron-rich nuclei show fragmented low-lying strength Leistenschneider et al. 3 σ γ [mb] E γ [MeV] Giant Dipole Resonance Can we give a microscopic explanation of these observations? 5

11 Ab-initio Theory Tools s 1 r 2 s 2... r 1 s A r A H i = E i i H = T + V NN + V 3N +... High precision two-nucleon potentials: well constraint on NN phase shifts Three nucleon forces: less known, constraint on A>2 observables 6

12 Ab-initio Theory Tools s 1 r 2 s 2... J µ = J µ N + J µ NN +... r 1 s A m + m r A H i = E i i H = T + V NN + V 3N +... High precision two-nucleon potentials: well constraint on NN phase shifts N N N N two-body currents (or MEC) subnuclear d.o.f. J µ consistent with V r J = i[v, ] Three nucleon forces: less known, constraint on A>2 observables 6

13 Ab-initio Theory Tools s 1 r 2 s 2... Traditional Nuclear Physics J µ = J µ N + J µ NN +... r 1 s A AV18+UIX,..., J2 m + m r A H i = E i i H = T + V NN + V 3N +... High precision two-nucleon potentials: well constraint on NN phase shifts Three nucleon forces: less known, constraint on A>2 observables Effective Field Theory N 2 LO, N 3 LO... N N N N two-body currents (or MEC) subnuclear d.o.f. J µ consistent with V r J = i[v, ] 6

14 Ab-initio Theory Tools s 1 r 2 s 2... Traditional Nuclear Physics J µ = J µ N + J µ NN +... r 1 s A AV18+UIX,..., J2 m + m r A H i = E i i H = T + V NN + V 3N +... High precision two-nucleon potentials: well constraint on NN phase shifts Three nucleon forces: less known, constraint on A>2 observables Effective Field Theory N 2 LO, N 3 LO... N N N N two-body currents (or MEC) subnuclear d.o.f. J µ consistent with V r J = i[v, ] f J µ 2 Exact Initial state & Final state in the continuum at different energies and for different A 6

15 Efros, et al., JPG.: Nucl.Part.Phys. 34 (27) R459 R( ) = L(, )= d where Lorentz Integral Transform Method Reduce the continuum problem to a bound-state problem f 2 f Ô (Ef E ) J µ R( ) ( ) 2 + is obtained solving = 2 < 1 (H E + i ) = J Ô µ Due to imaginary part the solution is unique h i Since is finite, has bound state asymptotic behaviour June 25th 214 Sonia Bacca 7

16 Efros, et al., JPG.: Nucl.Part.Phys. 34 (27) R459 R( ) = L(, )= d where Lorentz Integral Transform Method Reduce the continuum problem to a bound-state problem f 2 f Ô (Ef E ) J µ R( ) ( ) 2 + is obtained solving = 2 < 1 (H E + i ) = J Ô µ Due to imaginary part the solution is unique h i Since is finite, has bound state asymptotic behaviour inversion L(, ) R( ) The exact final state interaction is included in the continuum rigorously! June 25th 214 Sonia Bacca 7

17 Efros, et al., JPG.: Nucl.Part.Phys. 34 (27) R459 R( ) = L(, )= d where Lorentz Integral Transform Method Reduce the continuum problem to a bound-state problem f 2 f Ô (Ef E ) J µ R( ) ( ) 2 + is obtained solving = 2 < 1 (H E + i ) = J Ô µ Due to imaginary part the solution is unique h i Since is finite, has bound state asymptotic behaviour inversion L(, ) R( ) The exact final state interaction is included in the continuum rigorously! Solved for A=3,4,6,7 with hyper-spherical harmonics expansions and for A=4 with NCSM June 25th 214 Sonia Bacca 7

18 Photoabsorption of A=6 with Hyperspherical Harmonics E1 = RE1 ( ) = ZX (z i Z cm ) i Li 6 He stable unstable Aumann et al. 6 He at GSI T 1/2 = 86 ms σ γ [mb] Li 1 6 He S.B. et al. PRL (22) ω [MeV] No cluster assumption was used in this calculation. Potential: AV4 8

19 Hyperspherical Harmonics A basis set, mostly used for A=3,4. Challenge to go up to A=7,8 b 1e+5 Ground States 1 # HH states 1 1 A=3 A=4 1 A=6 A= K max (H E + i ) = J Ô µ J µ i For the reactions expanding increase of dimension by at least one order of magnitude if angular momentum is changed 9

20 Hyperspherical Harmonics A basis set, mostly used for A=3,4. Challenge to go up to A=7,8 b 1e+5 Ground States 1 # HH states 1 1 A=3 A=4 1 A=6 A= K max Total number of states: #HH X #Hyper-radial states 1 6 dense matrix (H E + i ) = J Ô µ J µ i For the reactions expanding increase of dimension by at least one order of magnitude if angular momentum is changed 9

21 Extension to medium-mass nuclei Develop new many-body methods that can extend the frontiers to heavier and neutron nuclei Coupled Cluster Theory CC future aims CC theory now CC is optimal for closed shell nuclei ( ± 1, ± 2) Uses particle coordinates ( r 1, r 2,..., r A ) = e T ( r 1, r 2,..., r A ) T = T (A) cluster expansion reference SD with any sp states T 1 = T 2 = 1 4 ia X ij,ab t a i a aa i t ab ij a aa b a ja i... T 1 T 2 T 3 CCSD CCSDT CCSD Computational scaling n 2 on 4 u June 25th 214 Sonia Bacca

22 Extension to medium-mass nuclei Develop new many-body methods that can extend the frontiers to heavier and neutron nuclei Coupled Cluster Theory CC future aims CC theory now CC is optimal for closed shell nuclei ( ± 1, ± 2) Uses particle coordinates ( r 1, r 2,..., r A ) = e T ( r 1, r 2,..., r A ) T = T (A) cluster expansion reference SD with any sp states... CC is a very mature theory for g.s., see e.g. Hagen et al. PRL 11, 9252 (28),PRC 82, 3433 (21) PRL 18, (212), PRL 19, 3252 (212) experiment R. Roth et al., Phys. Rev. Lett. 19, 5251 (212) S. Binder et al, arxiv: June 25th 214 Sonia Bacca 11

23 Extension to medium-mass nuclei Develop new many-body methods that can extend the frontiers to heavier and neutron nuclei Coupled Cluster Theory CC future aims CC theory now CC is optimal for closed shell nuclei ( ± 1, ± 2) Uses particle coordinates ( r 1, r 2,..., r A ) = e T ( r 1, r 2,..., r A ) T = T (A) cluster expansion reference SD with any sp states... CC is a very mature theory for g.s., see e.g. Hagen et al. PRL 11, 9252 (28),PRC 82, 3433 (21) PRL 18, (212), PRL 19, 3252 (212) What about electromagnetic reactions? experiment R. Roth et al., Phys. Rev. Lett. 19, 5251 (212) S. Binder et al, arxiv: June 25th 214 Sonia Bacca 11

24 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass D R( ) L(, )= d = h i L RE = h ( ) ˆL(z) R(z ˆ ) i (H z ) i = J µ i with z = E + + i ( H z ) Ri = i H = e T He T =e T e T ( H z ) ˆR(z ) i = i EoM with source 12

25 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass D R( ) L(, )= d = h i L RE = h ( ) ˆL(z) R(z ˆ ) i (H z ) i = J µ i with z = E + + i ( H z ) Ri = i H = e T He T =e T e T ( H z ) ˆR(z ) i = i EoM with source 12

26 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass D R( ) L(, )= d = h i L RE = h ( ) ˆL(z) R(z ˆ ) i (H z ) i = J µ i with z = E + + i ( H z ) Ri = i H = e T He T =e T e T ( H z ) ˆR(z ) i = i EoM with source 12

27 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass D R( ) L(, )= d = h i L RE = h ( ) ˆL(z) R(z ˆ ) i (H z ) i = J µ i with z = E + + i ( H z ) Ri = i H = e T He T =e T e T ( H z ) ˆR(z ) i = i EoM with source In the CCSD scheme T = T 1 + T 2 ˆR = R + X ia R a i ĉ aĉ i X ˆ ˆ Rˆij ab ĉ aĉ bĉjĉ i +... ijab 12

28 L(, )= d LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass R( ) ( ) = h i D L RE = h L(z) R(z ) i ˆ ˆ (H z ) i = J µ i with z = E + + i ( H z ) Ri = i H = e T He T =e T e T ( H z ) ˆR(z ) i = i EoM with source In the CCSD scheme T = T 1 + T 2 ˆR = R + X ia R a i ĉ aĉ i X ˆ ˆ Rˆij ab ĉ aĉ bĉjĉ i +... ijab Validation for 4 He Dipole Response Functions with NN forces from EFT (N 3 LO) R(ω) [mb/mev] He EIHH Exact HH CCSD ω [MeV] 12

29 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass Extension to Dipole Response Function in 16 O with NN forces derived from EFT (N 3 LO) Convergence in the model space expansion L [fm 2 MeV ] Γ=1 MeV N max hω=26 MeV σ [MeV] Good convergence! 13

30 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass Extension to Dipole Response Function in 16 O with NN forces derived from EFT (N 3 LO) Convergence in the model space expansion L [fm 2 MeV ] Γ=1 MeV N max hω=26 MeV L [fm 2 MeV ] Γ=1 MeV N max =18 hω=26 MeV hω=2 MeV σ [MeV] Good convergence! σ [MeV] Small HO dependence: use it as error bar 13

31 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass Extension to Dipole Response Function in 16 O with NN forces derived from EFT (N 3 LO) Comparison to the experiment L [fm 2 MeV ] = 1 MeV LIT of data CCSD σ [MeV] 14

32 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass Extension to Dipole Response Function in 16 O with NN forces derived from EFT (N 3 LO) Comparison to the experiment 4 = 1 MeV LIT of data 5 16 O Ahrens et al. L [fm 2 MeV ] CCSD σ γ (ω)/4π 2 αω [mb/mev] Ishkanov et al. CCSD σ [MeV] ω[mev] 15

33 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass Extension to Dipole Response Function in 16 O with NN forces derived from EFT (N 3 LO) Comparison to the experiment 4 = 1 MeV LIT of data 5 16 O Ahrens et al. L [fm 2 MeV ] CCSD σ γ (ω)/4π 2 αω [mb/mev] Ishkanov et al. CCSD σ [MeV] ω[mev] The GDR of 16 O is described from first principles for the first time! 15

34 LIT with Coupled Cluster Theory PRL 111, (213) New theoretical method aimed at extending ab-initio calculations towards medium mass Extension to Dipole Response Function in 16 O with NN forces derived from EFT (N 3 LO) Comparison to the experiment L [fm 2 MeV ] = 1 MeV LIT of data CCSD σ γ (ω)/4π 2 αω [mb/mev] O Ahrens et al. Ishkanov et al. CCSD PRL (212) σ [MeV] ω[mev] The GDR of 16 O is described from first principles for the first time! 15

35 LIT with Coupled Cluster Theory Extension to Dipole Response Function in 22 O with NN forces derived from EFT (N 3 LO) L [fm 2 MeV ] Work in Progress O = 1 MeV N max hω=24 MeV σ [MeV] Convergence pattern similar to 16 O 16

36 LIT with Coupled Cluster Theory L [fm 2 MeV ] Extension to Dipole Response Function in 22 O with NN forces derived from EFT (N 3 LO) Work in Progress O = 1 MeV N max hω=24 MeV σ [MeV] L [fm 2 MeV ] Bremsstrahlung sum rule / NZ A 1 22 O 16 O 2 R PN R PN Preliminary Convergence pattern similar to 16 O σ [MeV] 16

37 LIT with Coupled Cluster Theory L [fm 2 MeV ] Extension to Dipole Response Function in 22 O with NN forces derived from EFT (N 3 LO) Work in Progress O = 1 MeV N max hω=24 MeV σ [MeV] L [fm 2 MeV ] Bremsstrahlung sum rule / NZ A 1 22 O 16 O 2 R PN R PN Preliminary Convergence pattern similar to 16 O σ [MeV] The centroid of 22 O seems ~ 3 MeV lower than for 16 O 16

38 LIT with Coupled Cluster Theory with M.Miorelli Calcium isotopes with NN(N 3 LO) L [fm 2 MeV -2 ] Ca N max ~ = 24 MeV Preliminary σ[mev] Theoretical GDR peaks are located at higher energies with respect to experiment: nuclei are over bound with smaller radii and thus one needs higher energy to excited the GDR L(ω ) [fm 2 MeV -2 ] Ca N max ~ = 24 MeV Preliminary ω [MeV] 17

39 LIT with Coupled Cluster Theory with M.Miorelli Electric Dipole Polarizability D = 1 E 2 2 with NN(N 3 LO) Z 1 d! (!)! th! 2 calculated with the Lanczos algorithm α E [fm 3 ] He EIHH hω=2 MeV.9 hω=24 MeV EXPERIMENT hω=26 MeV N max O EXPERIMENT hω = 2MeV hω = 24MeV hω = 26MeV N max α D [fm 3 ] 18

40 LIT with Coupled Cluster Theory with M.Miorelli Electric Dipole Polarizability D = 1 E 2 2 with NN(N 3 LO) Z 1 d! (!)! th! 2 calculated with the Lanczos algorithm α E [fm 3 ] Towards an ab-initio theory for 48 Ca DFT prediction Ca hω = 2MeV hω = 24MeV 1.3 hω = 26MeV 1.2 hω = 28MeV 1.2 Preliminary N max 48 Ca E being measured at RCNP 19

41 LIT with Coupled Cluster Theory with M.Miorelli Electric Dipole Polarizability D = 1 E 2 2 Z 1 d! (!)! th! 2 Energy Density Functional Theory Phys. Rev. C 85, 4132 (212) very correlated to the neutron-skin radius Do we also see such a correlation with ab-initio methods? E 2

42 LIT with Coupled Cluster Theory with M.Miorelli Correlation of polarizability vs radius α E [fm 3 ] n2lo_opt_bare n2lo_opt38 (N=12).6 cdbonn_vlowk2.6 cdbonn_vlowk25 cdbonn_vlowk3 cdbonn_srg35 cdbonn_srg4.5 n3lo5em_srg2.5 n3lo5em_srg25 n3lo5em_srg3 n3lo5em_srg35 n3lo5em_bare.4 av18_vlowk25.4 av18_vlowk3 n3lo6em_srg25 n3lo6em_srg3 n3lo6em_srg35 16 O.3.3 Preliminary Exp +3NF.2.2 C AB = r charge [fm] 21

43 LIT with Coupled Cluster Theory with M.Miorelli Correlation of polarizability vs radius α E [fm 3 ] n2lo_opt_bare n2lo_opt38 (N=12).6 cdbonn_vlowk2.6 cdbonn_vlowk25 cdbonn_vlowk3 cdbonn_srg35 cdbonn_srg4.5 n3lo5em_srg2.5 n3lo5em_srg25 n3lo5em_srg3 n3lo5em_srg35 n3lo5em_bare.4 av18_vlowk25.4 av18_vlowk3 n3lo6em_srg25 n3lo6em_srg3 n3lo6em_srg35 16 O Exp +3NF.3.3 Preliminary Optimized EFT interaction at N 2 LO from Ekström et al..2.2 C AB = r charge [fm] 21

44 LIT with Coupled Cluster Theory with M.Miorelli Correlation of polarizability vs radius α E [fm 3 ] 2.4 n2lo_opt_bare 2.4 n2lo_opt38 (N=12) 2.2 cdbonn_vlowk2 2.2 cdbonn_vlowk25 cdbonn_vlowk3 cdbonn_srg cdbonn_srg NF n3lo5em_srg2 +3NF n3lo5em_srg25 n3lo5em_srg3 n3lo5em_srg n3lo6em_srg2 1.2 n3lo6em_srg25 n3lo6em_srg3 4 Ca Exp Preliminary Optimized EFT interaction at N 2 LO from Ekström et al. C AB = r charge [fm] 22

45 LIT with Coupled Cluster Theory with M.Miorelli Correlation of polarizability vs skin-radius α E [fm 3 ] 48 Ca DFT predictions n2lo_opt38 (N=12) n2lo_opt_bare 2 cdbonn_vlowk3 2 cdbonn_vlowk25 cdbonn_vlowk2 +3NF 1.8 cdbonn_srg4 1.8 cdbonn_srg35 av18_vlowk av18_srg35 av18_srg3 1.4 n3lo5em_srg2 1.4 n3lo5em_srg25 n3lo6em_srg n3lo6em_srg25 n3lo6em_srg Preliminary Optimized EFT interaction at N 2 LO from Ekström et al..6.6 C AB = r skin [fm] 48 Ca E being measured at RCNP 48 Ca parity violating electron scattering at JLab, CREX 23

46 Conclusions and Outlook Electromagnetic break up reactions are very rich observables to test our understanding of nuclear forces Extending these calculations to medium mass nuclei is possible and very exciting, with hopefully more applications/impact on future experiments. June 25th 214 Sonia Bacca 24

47 Conclusions and Outlook Electromagnetic break up reactions are very rich observables to test our understanding of nuclear forces Extending these calculations to medium mass nuclei is possible and very exciting, with hopefully more applications/impact on future experiments. Perspectives Dipole response function of neutron-rich Oxygen isotope Other multipole excitation (quadrupole or monopole) of medium mass nuclei need extension to two-body operators Add triples and three-nucleon forces June 25th 214 Sonia Bacca 24

48 Conclusions and Outlook Electromagnetic break up reactions are very rich observables to test our understanding of nuclear forces Extending these calculations to medium mass nuclei is possible and very exciting, with hopefully more applications/impact on future experiments. Perspectives Dipole response function of neutron-rich Oxygen isotope Other multipole excitation (quadrupole or monopole) of medium mass nuclei need extension to two-body operators Add triples and three-nucleon forces Thank you! June 25th 214 Sonia Bacca 24

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