Canada’s National Laboratory for Particle and Nuclear Physics Laboratoire national canadien pour la recherche en physique nucléaire et en physique des particules Electromagnetic strengths in ab-initio approaches Sonia Bacca | TRIUMF Nuclear Halo Electromagnetic Reactions 25 22 O 20 Leistenschneider et al. CCSD σ γ ( ω ) [mb] 15 10 5 0 5 10 15 20 25 Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada ω [MeV] Propriété d’un consortium d’universités canadiennes, géré en co-entreprise à partir d’une contribution administrée par le Conseil national de recherches Canada Pigmy Resonance Tuesday, 15 September, 15
“Ab-initio” methods • Start from neutrons and protons as building blocks s 2 (centre of mass coordinates, spins, isospins) s 1 • Solve the non-relativistic quantum mechanical problem of r 2 ... A-interacting nucleons s A r 1 H | ψ i � = E i | ψ i � H = T + V NN ( Λ ) + V 3 N ( Λ ) + . . . r A • Find numerical solutions with no approximations or controllable approximations (error bars) Sept 15 2015 Sonia Bacca 2 Tuesday, 15 September, 15
“Ab-initio” methods • Start from neutrons and protons as building blocks s 2 (centre of mass coordinates, spins, isospins) s 1 • Solve the non-relativistic quantum mechanical problem of r 2 ... A-interacting nucleons s A r 1 H | ψ i � = E i | ψ i � H = T + V NN ( Λ ) + V 3 N ( Λ ) + . . . r A • Find numerical solutions with no approximations or controllable approximations (error bars) • Calculate low-energy observables and compare with experiment to test nuclear forces and provide predictions for future experiments or quantity that cannot be measured Sept 15 2015 Sonia Bacca 2 Tuesday, 15 September, 15
“Ab-initio” methods • Start from neutrons and protons as building blocks s 2 (centre of mass coordinates, spins, isospins) s 1 • Solve the non-relativistic quantum mechanical problem of r 2 ... A-interacting nucleons s A r 1 H | ψ i � = E i | ψ i � H = T + V NN ( Λ ) + V 3 N ( Λ ) + . . . r A • Find numerical solutions with no approximations or controllable approximations (error bars) • Calculate low-energy observables and compare with experiment to test nuclear forces and provide predictions for future experiments or quantity that cannot be measured Sept 15 2015 Sonia Bacca 2 Tuesday, 15 September, 15
Observables Dipole strength functions Giant dipole resonance ω Sept 15 2015 Sonia Bacca 3 Tuesday, 15 September, 15
Observables Dipole strength functions Giant dipole resonance ω Sept 15 2015 Sonia Bacca 3 Tuesday, 15 September, 15
Observables Dipole strength functions Giant dipole resonance ω Pigmy dipole resonance in neutron-rich nuclei core Sept 15 2015 Sonia Bacca 3 Tuesday, 15 September, 15
Observables Electric dipole polarizability A Sept 15 2015 Sonia Bacca 4 Tuesday, 15 September, 15
Observables Electric dipole polarizability ∗ A D = α D E E D Z ∞ d ω R ( ω ) α D = 2 α ω ω th Low-energy part of response dominates Very interesting for neutron-rich nuclei: soft modes at low energy enhance the polarizability Sept 15 2015 Sonia Bacca 5 Tuesday, 15 September, 15
Experimental status Stable Nuclei Unstable Nuclei Fewer data, pigmy dipole resonances We have data on ~180 stable nuclei Giant dipole resonances Leistenschneider et al. 40 16 O Ahrens et al. 35 30 25 σ γ [mb] 20 15 10 5 0 0 20 30 40 10 50 E γ [MeV] ω From Coulomb excitation experiments From photoabsorption experiments e - e - e - Sept 15 2015 Sonia Bacca 6 Tuesday, 15 September, 15
Experimental status Stable Nuclei Unstable Nuclei Fewer data, pigmy dipole resonances We have data on ~180 stable nuclei Giant dipole resonances Leistenschneider et al. 40 16 O Ahrens et al. 35 30 25 σ γ [mb] 20 15 10 5 0 0 20 30 40 10 50 E γ [MeV] ω From Coulomb excitation experiments From photoabsorption experiments e - e - e - Do we see the emergence of collective motions from first principle calculations? Sept 15 2015 Sonia Bacca 6 Tuesday, 15 September, 15
48 Ca - an interesting case While neutron-rich, for all practical purposes it can be considered a stable nucleus • (p,p’) scattering to extract the electric dipole polarizability at RCNP, Japan is related to the symmetry energy in the EOS of nuclear matter α D • Parity violation electron scattering Calcium Radius Experiment (CREX) at JLab to measure R skin ≈ − G F q 2 Q W F W ( q 2 ) A pv = d σ /d Ω R − d σ /d Ω L √ d σ /d Ω R + d σ /d Ω L ZF ch ( q 2 ) 4 πα 2 The weak force probes the neutron distribution Q n W ≈ − 1 R skin W = 1 − 4 sin 2 θ W ≈ 0 Q p Sept 15 2015 Sonia Bacca Tuesday, 15 September, 15
48 Ca - an interesting case While neutron-rich, for all practical purposes it can be considered a stable nucleus • (p,p’) scattering to extract the electric dipole polarizability at RCNP, Japan is related to the symmetry energy in the EOS of nuclear matter α D • Parity violation electron scattering Calcium Radius Experiment (CREX) at JLab to measure R skin ≈ − G F q 2 Q W F W ( q 2 ) A pv = d σ /d Ω R − d σ /d Ω L √ d σ /d Ω R + d σ /d Ω L ZF ch ( q 2 ) 4 πα 2 The weak force probes the neutron distribution Q n W ≈ − 1 R skin W = 1 − 4 sin 2 θ W ≈ 0 Q p Can we give a first principle predictions for these future experiments? Sept 15 2015 Sonia Bacca Tuesday, 15 September, 15
Theoretical Status • These observables on medium and heavy nuclei have been the subject of intense theoretical studies within density functional theory, shell model, etc... • Not much has been done with ab-initio methods and we want to fill this gap! Sept 15 2015 Sonia Bacca 8 Tuesday, 15 September, 15
Theoretical Status • These observables on medium and heavy nuclei have been the subject of intense theoretical studies within density functional theory, shell model, etc... • Not much has been done with ab-initio methods and we want to fill this gap! Electromagnetic Reactions on Light Nuclei S. Bacca and S. Pastore J. Phys. G: Nucl. Part. Phys. 41 123002 (2014). Sept 15 2015 Sonia Bacca 8 Tuesday, 15 September, 15
Ab-initio Approach s 2 s 1 r 2 ... s A r 1 r A H | ψ i � = E i | ψ i � H = T + V NN + V 3 N + ... Sept 15 2015 Sonia Bacca 9 Tuesday, 15 September, 15
Ab-initio Approach s 2 J µ = J µ N + J µ s 1 NN + ... r 2 ... s A r 1 π m π m + r A N N N N two-body currents (or MEC) H | ψ i � = E i | ψ i � subnuclear d.o.f. H = T + V NN + V 3 N + ... J µ consistent with V r · J = � i [ V, ρ ] Sept 15 2015 Sonia Bacca 9 Tuesday, 15 September, 15
Ab-initio Approach s 2 J µ = J µ N + J µ s 1 NN + ... r 2 ... s A r 1 π m π m + r A Chiral Effective Field Theory N N N N two-body currents (or MEC) H | ψ i � = E i | ψ i � subnuclear d.o.f. H = T + V NN + V 3 N + ... J µ consistent with V r · J = � i [ V, ρ ] Sept 15 2015 Sonia Bacca 9 Tuesday, 15 September, 15
Chiral Effective Field Theory Quark/gluon (high energy) dynamics In the limit of vanishing quark masses the QCD Lagrangian is invariant under chiral symmetry QCD chiral symmetry quarks Chiral symmetry is explicit and spontaneous broken Sept 15 2015 Sonia Bacca 10 Tuesday, 15 September, 15
Chiral Effective Field Theory Quark/gluon (high energy) dynamics In the limit of vanishing quark masses the QCD Lagrangian is invariant under chiral symmetry QCD chiral symmetry quarks Chiral symmetry is explicit and spontaneous broken n Nucleon/pion (low energy) dynamics L eff = L ππ + L π N + L NN + . . . p Compatible with explicit and spontaneous chiral symmetry breaking Sept 15 2015 Sonia Bacca 10 Tuesday, 15 September, 15
Chiral Effective Field Theory ✓ Q ◆ ν X Systematic expansion L = c ν Λ b π (q/ Λ ) 0 ν LO ν = 0 Details of short distance physics not resolved, (q/ Λ ) 2 NLO but captured in low energy constants (LEC) ν = 2 (q/ Λ ) 3 N2LO ν = 3 N3LO (q/ Λ ) 4 ν = 4 Sept 15 2015 Sonia Bacca 11 Tuesday, 15 September, 15
Chiral Effective Field Theory ✓ Q ◆ ν X Systematic expansion L = c ν Λ b π (q/ Λ ) 0 ν LO ν = 0 Details of short distance physics not resolved, (q/ Λ ) 2 Future: lattice QCD? NLO but captured in low energy constants (LEC) Now fit to experiment ν = 2 LEC fit to experiment - NN sector - (q/ Λ ) 3 N2LO ν = 3 NLO N2LO N3LO (q/ Λ ) 4 N3LO ν = 4 Traditional Paradigm: Epelbaum et al. (2009) (i) Fit NN on scattering data first 0 50 100 150 200 250 Lab. Energy [MeV] Sept 15 2015 Sonia Bacca 11 Tuesday, 15 September, 15
Chiral Effective Field Theory ✓ Q ◆ ν X Systematic expansion L = c ν Λ b π (q/ Λ ) 0 ν LO ν = 0 Details of short distance physics not resolved, (q/ Λ ) 2 Future: lattice QCD? NLO but captured in low energy constants (LEC) Now fit to experiment ν = 2 LEC fit to experiment - NN sector - (q/ Λ ) 3 N2LO ν = 3 NLO N2LO N3LO (q/ Λ ) 4 N3LO ν = 4 Traditional Paradigm: Epelbaum et al. (2009) (i) Fit NN on scattering data first 0 50 100 150 200 250 (ii) add 3N forces fitting on 3 H/ 3 He Lab. Energy [MeV] Sept 15 2015 Sonia Bacca 11 Tuesday, 15 September, 15
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