Many-body correlations in the structure of heavy nuclei Recent developments on relativistic models Elena Litvinova Western Michigan University Interfacing Structure and Reaction Dynamics, Trento, September 1-4, Outline • Nuclear field theory in relativistic framework (10 yrs): Quantum Hadrodynamics and emergent collective phenomena • Approach: Covariant Density Functional Theory + beyond mean-field correlations (Nuclear Field Theory); non-perturbative techniques Current developments: 1) pion degrees of freedom 2) high-order correlations in nuclear response • Isovector excitations: Gamow-Teller resonance, spin dipole resonance, higher multipoles. Precritical phenomenon in exotic nuclei: soft pionic modes (0-,1+,2-,…) • Pion exchange beyond Fock approximation: ‘Isovector’ phonons and their coupling to single-particle motion • *Higher-order correlations in nuclear response: extensions of NFT Building blocks of nuclear structure models Degrees of freedom Separation of the scales at ~1-50 MeV excitation energies: single-particle & collective (vibrational, rotational) NO complete separation of the scales! -Coupling between single-particle and collective: -Coupling to continuum as nuclei are open quantum systems Symmetries -> Eqs. of motion Galilean inv. -> Schrödinger Eq. Lorentz inv. -> Dirac Eq. Interaction VNN : 3 basic concepts Ab initio: from vacuum VNN -> in-medium VNN Configuration interaction: matrix elements for in-medium VNN Density functional: an ansatz for in-medium VNN + correlations = Nuclear Field Theory Here based on QHD ρ mπ ~140 MeV mρ ~770 MeV m ~783 MeV Nuclear models Figure from: G.F. Bertsch, J. Phys.: Conf. Ser. 78, 012005 (2007) Relativistic nuclear field theory: CDFT + CI + ab initio Systematic expansion in the covariant nuclear field theory ≈ Quantum Hadrodynamics („QCD motivated“) Relativistic Mean Field (Walecka, Serot et al.) Covariant DFT (P. Ring et al.) Emergent collective degrees of freedom: ‘phonons‘ New order parameter: phonon coupling vertex Finite size & angular Momentum couplings => Hierarchy: Mean field -> line corrections -> vertex corrections Nuclear Field Theory CopenhagenMilano, St.PetersburgJuelich, … Recent developments: relativistic formulation; pairing correlations; two-phonon coupling; spin-isospin channel; high-order correlations Covariant density functional theory Walecka model + later modifications (P. Ring et al.) Lorentz symmetry Pion π: No contribution to RMF; included in dynamics nucleons interaction mesons (as classical fields) Relativistic mean field Nucleons { Mesons no sea RHB Hamiltonian RMF selfenergy Dirac Hamiltonian Eigenstates Uncorrelated ground state as the zero approximation: Relativistic Mean Field (RMF) Continuum Fermi sea -S-V 0 r FE Dirac sea -S+V 2mN* „No sea“ approximation 2mN Small perturbation => Coherent oscillations of the mean nuclear potential Continuum Fermi sea -S-V 0 r FE … Dirac sea Vibrational modes (phonons Jπ) -S+V 2mN* 2+ 34+ 56+ „No sea“ approximation p P‘ h h‘ 2mN First step beyond relativistic mean field: quasiparticles coupled to vibrations Additional “potential” = “self-energy” = = “mass operator” with energy dependence k1 e Σ = Vibration μ k2 k nucleon coupling “Fish” diagram One-body propagator G: Dyson equation k k‘ G p h Time arrow = k = k‘ + G0 + k k1 e Σ G0 Ʃe k2 k‘ G Energy dependence Pairing correlations: Doubled quasiparticle space: Fragmentation of states in odd and even systems (schematic) Single-particle structure No correlations Correlations Energy Dominant level Strong fragmentation Spectroscopic factors Sk(ν) Response No correlations Correlations Quasiparticle-vibration coupling: Pairing correlations of the superfluid type + coupling to phonons E.L., PRC 85, 021303(R) (2012) Spectroscopic factors in 120Sn (nlj) ν Sth Sexp 2d5/2 0.32 0.43 1g7/2 0.40 0.60 2d3/2 0.53 0.45 3s1/2 0.43 0.32 1h11/2 0.58 0.49 2f7/2 0.31 0.35 3p3/2 0.58 0.54 Spectroscopic factors in E.L., PRC 85, 021303(R)(2012) : 132Sn: (nlj) ν Sth * Sexp ** 2f7/2 0.89 0.86±0.16 3p3/2 0.91 0.92±0.18 1h9/2 0.88 3p1/2 0.91 1.1±0.3 2f5/2 0.89 1.1±0.2 *E. L., A.V. Afanasjev, PRC 84, 014305 (2011) **K.L. Jones et al., Nature 465, 454 (2010) Nuclear shapes and Qα values at Z>90 (Skyrme SLy4) S. Ćwiok, P.-H. Heenen, W. Nazarewicz, Nature 285 (2005) 705 RMF+QVC: Dominant neutron states in Z = 120 Interplay of pairing and particle-vibration coupling Comparable Spectroscopic strengths 0.28 0.30 PC+QVC: Formation of the „shell gap“ ! RMF+BCS …+QVC RMF+BCS Delocalization of the shell closures …+QVC Shell evolution in superheavy Z = 120 isotopes: Quasiparticle-vibration coupling (QVC) in a relativistic framework 1. Relativistic Mean Field: spherical minima 2. π: collapse of pairing, clear shell gap 3. ν: survival of pairing coexisting with the shell gap 4. Very soft nuclei: large amount of low-lying collective vibrational modes (~100 phonons below 15 MeV) Vibration corrections to binding energy (RQRPA) Vibration corrections to -decay Q-values Q [MeV] 13 RMF RMF+QVC Z = 120 12 11 296 298 300 302 304 A Vibrational corrections: 1. Impact on the shell gaps 2. Smearing out the shell effects Shell stabilization & vibration stabilization/destabilization (?) E.L., PRC 85, 021303(R) (2012) Vertex corrections, excited states: nuclear response function QRPA Extension Bethe-Salpeter Equation (BSE): E.L., V. Tselyaev, PRC 75, 054318 (2007) = : δΣRMF V = δρ R(ω) = A(ω) + A(ω) [V + W(ω)] R(ω) Selfconsistency W(ω) = Φ(ω) - Φ(0) δ i δG i δ δG × G = i = δΣe δG = = Ue δΣe =i δG Consistency on 2p2h-level Time blocking 3p3h Problem: NpNh ‘Melting‘ diagrams Approx. schemes Unphysical result: negative cross sections Time Solution: Timeprojection operator: R Partially fixed V.I. Tselyaev, Yad. Fiz. 50,1252 (1989) Allowed terms: 1p1h, 2p2h Time blocking approximation = = „one-fish“ approximation! Blocked terms: 3p3h, 4p4h,… Separation of the integrations in the BSE kernel R has a simple-pole structure (spectral representation) »» Strength function is positive definite! Response function in the neutral channel response interaction Subtraction to avoid double counting Static: RQRPA Dynamic: particlevibration coupling in time blocking approximation Dipole strength in neutron-rich nuclei within Relativistic Quasiparticle Time Blocking Approximation (RQTBA) Neutron-rich Sn Test case: E1 (IVGDR) stable nuclei S [e fm / MeV] 8 132 Sn 2 4 2 6 2 - (a) 1 0 0 5 10 15 20 25 30 35 Experiment* RQTBA** RQTBA with detector response (A. Klimkiewicz) S [e fm / MeV] 8 130 Sn 2 4 2 6 2 - 1 0 (b) 0 5 10 15 20 25 30 35 E [MeV] E. L., P. Ring, and V. Tselyaev, Phys. Rev. C 78, 014312 (2008) * P. Adrich, A. Klimkiewicz, M. Fallot et al., PRL 95, 132501 (2005) **E. L., P. Ring, V. Tselyaev, K. Langanke PRC 79, 054312 (2009) 200 10 15 E [MeV] 20 25 0 10 E5 [MeV] 25 15 E [MeV] 30 20 25 5 10 15 20 E [MeV] 25 8 9 10 0 5 10 E [MeV] Pb 400 0.04 0 -1 200 500 0 5 10 15 5 6 7 8 9 10 0 10 15 20 10 15 15 10 0.02 20 5 10 15 Sn 600 400 0 0 3 4 5 6 7 8 9 10 0 5 10 E [MeV] 15 10 15 25 30 0.08 140 0.04 15 200 20 neutrons protons Sn 0.00 E = 4.65 MeV (RQTBA) -0.04 -0.08 0 0 20 25 15 30 20 25 5 10 15 20 25 30 E [MeV] E [MeV] 20 0 5 20 0 5 10 15 5 10 15 E = 5.18 MeV (RQTBA) 20 0 5 10 15 20 0.04 E = 7.27 MeV (RQTBA) E. L., H.P. Loens, K. Langanke, et al. Nucl. Phys. A 823, 26 (2009). 5 20 E [MeV] 600 400 5 10 E [MeV] E = 6.39 MeV (RQTBA) -0.04 cross section [mb] 136 800 Th 200 Sn E = 5.18 MeV (RQTBA) 20 0 0 25 0.00 E [MeV]-0.02 30 1000 Sn 132 = 3.1 MeV 10 25 RQRPA RQTBA 200 5 20 1200 136 Bn 10 RH-RRPA RH-RRPA-PC 0.04 0 5 1400 RQRPA RQTBA 30 800 E = 4.65 MeV (RQTBA) -0.04 -0.08 0 4 400 0.00 = 2.4 MeV 5 0 5 1800 neutrons protons 2 1000 30 0 3 E = 10.94 MeV 208 20 (RQRPA) E1 Pb 2000 = 2.6 MeV Sn Sn 200 (NL3) 40 RH-RRPA-PC 2400 138 600 400 50 2200 E0 Sn Th 60 20 neutrons RH-RRPA protons 208 800 600 140 15 0.00 208 =0.081.7 MeV 10 2600 30 -1 E0 600 1500 5 800 138 Bn 10 E = 7.18 MeV (RQRPA) -0.1 25 RQRPA RQTBA cross section [mb] 2 2 20 20 1000 40 30 15 1200 -1 5 20 7 1400 10 neutrons protons r [fm] RH-RRPA 800 2 0 15 1000 0 2000 -1 200 0 10 8 E [MeV] 0 4 = 3.1 MeV 200 5 6 1000 r [fm ] 400 = 2.4 MeV 200 3500 r [fm ] 0 1200 0.02 0.00 -0.02 E = 6.39 MeV (RQTBA) -0.04 E = 7.27 MeV (RQTBA) 20 0 5 10 15 20 0 5 20 0 5 10 15 20 0.02 -1 600 4 0.0 E1 -0.04 Pb 400 2 200 500 Sn 600 1400 Th E [MeV] 2500 Sn 400 1000 1600 800 136 Bn 3 4 5 6 730008 9 10 0RH-RRPA-PC 5 10 15 20 25 30 132 = 2.6 MeV 0 0.1 0 0.00 2 E0 600 6 2 0 800 Pb 5 RQRPA RQTBA r [fm ] 10 4 50 2 20 3 60 10 r [fm ] 15 0 20 RQRPA RQTBA 0.04 WS-RPA (LM) 136 WS-RPA-PC 1800 1000 R [e fm /MeV] ISGMR 2 10 RH-RRPA RH-RRPA-PC 800 208 = 1.7 MeV 400 1500 2 2 [mb] 600 2000 5 1800 5 10 15 20 25 30 1200 Sn 30 E = 10.94 MeV 208 20 (RQRPA) E1 Pb 2000 r [fm] RH-RRPA RH-RRPA-PC 800 E0 2500 4 R [e fm /MeV] ISGMR 3000 2 2200 1000 1000 S [ e fm / MeV ] -1 r [MeV ] 2400 Sn 30 1400 RQRPA RQTBA 50 208 0 3500 3 4 5 6 7 8 9 10 0 60 20 0.00 E1 -0.04 Pb 0 neutrons 200 E = 8.46 MeV (RQTBA) -0.02 0 5 10 r [fm] 15 E = 9.94 MeV (RQTBA) 10 r [fm] 15 0.02 -1 15 Sn 400 200 RH-RRPA (NL3) protons 40 RH-RRPA-PC 400 Th 0 RQRPA RQTBA 0.00 2 10 Bn Sn 600 20 10 140 800 Sn r [fm ] 5 2600 138 600 Th cross2 section [mb] -1 r [MeV ] 2 0 Sn 0 1000 140 30 Input for r-process nucleosynthesis: (n,γ) cross sections and reaction rates 800 138 Bn 10 r [fm ] -1 r [MeV ] -0.1 0.04 WS-RPA (LM) WS-RPA-PC 1200 20 E = 7.18 MeV (RQRPA) 1800 1400 30 E1 40 140 S [ e fm / MeV ] 10 neutrons protons [mb] 8 E [MeV] 2 6 0.0 RQRPA RQTBA 1200 1000 40 2 4 S [ e fm / MeV ] 2 0 0.1 1600 RQRPA RQTBA 50 10 2 5 10 15 20 25 30 1400 2 60 20 RQRPA RQTBA 1200 40 50 0 3 4 5 6 7 8 9 10 0 30 2 400 Th 0 2 2 600 1400 RQRPA RQTBA 50 S [ e fm / MeV ] Bn 10 RQRPA RQTBA Sn Sn 2 S [e fm / MeV] 40 140 140 800 Sn S [ e fm / MeV ] E1 2 S [ e fm / MeV ] 50 20 60 1000 140 30 RQRPA RQTBA 1200 40 cross section [mb] 1400 RQRPA RQTBA 50 cross section [mb] 60 cross section [mb] 2 -1 r [MeV ] 2 2 S [e fm / MeV] Response of superheavy nuclei: From giant resonances‘ widths to transport coefficients E = 8.46 MeV (RQTBA) -0.02 E = 9.94 MeV (RQTBA) 20 0 5 10 r [fm] 15 10 r [fm] 15 20 Isospin splitting of the pygmy dipole resonance in J. Endres, E.L., D. Savran et al., PRL 105, 212503 (2010) & 124Sn E. Lanza, A. Vitturi, E.L., D. Savran, PRC 89, 041601(R) (2014) 2q+phonon IS-E1 RQRPA 2q 3-phonon 3-phonon 2q+phonon Electromagnetic E1 2q+2phonon configurations Included Recently: E.L. PRC 91, 034332 (2015), See below) Spin-isospin response function response interaction Static: RRPA Dynamic: particlevibration coupling in time blocking approximation Subtraction to avoid double counting Gamow-Teller Resonance with finite momentum transfer pn-RRPA pn-RTBA GT-+IVSM Fig. & calculation from T. Marketin (U Zagreb) Isovector Spin Monopole Resonance RRPA RTBA Finite q: a correction for Isovector spin monopole resonance (IVSMR) – overtone of GTR ΔL = 0 ΔT = 1 ΔS = 1 „Microscopic“ quenching of B(GT): (i) relativistic effects, , (ii) (ii) ph+phonon configurations, (iii) finite momentum transfer Spin-dipole resonance: beta-decay, electron capture T. Marketin, E.L., D. Vretenar, P. Ring, PLB 706, 477 (2012). SRRPA RTBA S+ W.H. Dickhoff et al., PRC 23, 1154 (1981) J. Meyer-Ter-Vehn, Phys. Rep. 74, 323 (1981) A.B. Migdal et al., Phys. Rep. 192, 179 (1990) Existence of low-lying unnatural parity states indicates that nuclei may be close to the pion condensation point. However, it is not clear which observables are sensitive to this phenomenon. Only nuclear matter and doubly-magic nuclei were studied ΔL = 1 ΔT = 1 ΔS = 1 λ = 0,1,2 Neutron-rich nuclei: softening of the pion modes Recently measured in RIKEN RQRPA RQTBA 2- In some exotic nuclei 2- states are found at very low energy. Similar situation with 0-, 4-, 6-,… states. Precritical phenomenon: Vicinity of the onset of pion condensation 2- ΔL = 1 ΔT = 1 ΔS = 1 λ = 0,1,2 Isovector part of the interaction: diagrammatic expansion IV interaction: pion ρ-meson Free-space pseudovector coupling RMFRenormalized Landau-Migdal contact term (g’-term) + Fixed strength Infinite sum: … … Low-lying states in ΔT=1 channel and nucleonic self-energy (N,Z) (N+1,Z-1) In spectra of neighboring odd-odd nuclei we see low-lying (collective) states with natural and unnatural parities: 2+, 2-, 3+, 3-,… Their contribution to the nucleonic self-energy is expected to affect single-particle states: Nucleonic self-energy beyond mean-field: Forward Backward Underlying Mechanism for pn-pairing? Isoscalar Isovector Single-nucleon Self-energy Spin dipole resonance in 100Sn and RQRPA RQTBA • Low-lying states with high transition probabilities in 132-Sn: 2-, 4-, 6-: collective! • Strongly coupled to single-particle and other collective states • Generic for neutron-rich nuclei? 132Sn ΔL = 1 ΔT = 1 ΔS = 1 λ = 0,1,2 Low-lying isovector states of unnatural parities: 100-Sn; pn-RRPA r2τ+[σxY1]0 r2τ-[σxY1]0 0 rτ+[σxY1]2 - 2 r3τ+[σxY3]4 r3τ-[σxY3]4 4 rτ-[σxY1]2 r5τ+[σxY5]6 - E [MeV] - r5τ-[σxY5]6 6 λp-λn ≈ 14 MeV - E [MeV] Single-particle states in 100-Sn Truncation scheme Phonon basis: T=0 phonons: 2+, 3-, 4+, 5-, 6+ No backward going terms T=1 phonons: 2±, 3±, 4±, 5±, 6± Single-particle states in 132-Sn Truncation scheme Phonon basis: T=0 phonons: 2+, 3-, 4+, 5-, 6+ No backward going terms T=1 phonons: 2±, 3±, 4±, 5±, 6± Effects of ground state correlations -? TBD Fine structure of spectra: next-order correlations from “2q+phonon” to “2 phonons” P. Schuck, Z. Phys. A 279, 31 (1976) V.I. Tselyaev, PRC 75, 024306 (2007) & Mode Coupling Theory Time Blocking Replacement of the uncorrelated propagator inside the Φ amplitude by QRPA response Nuclear response: R = A + A (V + Φ – Φ0) R Poles may appear at lower energies: ‘2q+phonon’ response: Φiji’j’(ω) ~ Σμk αijkμ/(ω - Ei’- Ek - Ωμ) ‘2 phonon’ response: Φiji’j’(ω) ~ Σμν αiji’j’/(ω - Ων - Ωμ) Fine features of dipole spectra: two-phonon effects First two-phonon state 1-1 : [2+ x 3-] 2 phonon 2q+phonon E(1-1) B(E1) 120Sn Pygmy dipole resonance in neutron-rich Ni: 2q+phonon vs 2 phonon S [arb. units] Does not exist 2 1 0 E.L., P.Ring, V.Tselyaev, PRL 105, 02252 (2010) PRC 88, 044320 (2013) ddE [mb / MeV] 3 68Ni 1- 6 8 10 E [MeV] 12 3 2 1 0 3 70Ni 2 1- 6 1 8 10 E [MeV] 12 0 72Ni 1- 6 8 10 E [MeV] 12 Data: O. Wieland et al., PRL 102, 092502 (2009) Multiphonon RQTBA: toward a unified description of high-frequency oscillations and low-energy spectroscopy Bethe-Salpeter Equation: “Conventional” NFT: Extension: n-th order correlated propagtor: E.L. PRC 91, 034332 (2015) Convergence E.L. PRC 91, 034332 (2015) Amplitude Φ(ω) in a coupled form (spherical basis): Fragmentation: n=1 (1p1h) n=2 (2p2h) n=3 (3p3h) … Conclusions • Correlations beyond mean field are important for the structure of heavy nuclei and the relativistic NFT offers a powerful framework for introducing them. However, in its ‘standard’ formulation NFT is often not sufficient. • Effects of isospin dynamics are introduced within a self-consistent covariant framework. Pion exchange is included with a free-space coupling constant. • Gamow-Teller resonance and other spin-isospin excitations are studied. Considerable softening of the pion modes is found in (some) exotic nuclei. • Pion exchange is included into the nucleonic self-energy non-perturbatively beyond Fock approximation in the spirit of quasiparticle-phonon coupling model. • The effects of the corresponding new terms in the self-energy on single-particle states (excited states of odd-even nuclei) are found noticeable. • The influence of the ‘isovector’ phonons on excited states of even-even nuclei is expected (work in progress). • Nuclear response theory is extended for multiphonon couplings toward a unified description of high-frequency oscillations and low-energy spectroscopy. Many thanks for collaboration: Peter Ring (Technische Universität München) Victor Tselyaev (St. Petersburg State University) Tomislav Marketin (U Zagreb) B.A. Brown (NSCL), D.-L. Fang (NSCL) R.G.T. Zegers (NSCL) A. Afanasjev (MisSU) D. Ackermann (GSI & GANIL) E. Kolomeitsev (UMB Slovakia) D. Savran (GSI/EMMI) V. Zelevinsky (NSCL) Nuclear theory group at Western Graduate Students: Postdoc: Dr. Caroline Robin Herlik Wibowo Irina Egorova Hasna Alali This work was supported by NSCL @ Michigan State University and by US-NSF Grants PHY-1204486 and PHY-1404343 Correlations in the models based on the density functional: NpNh: … p P‘ h h‘ P‘ p P‘ h‘ h p h h‘ 2p2h correlations: p P‘ p P‘ p P‘ h h‘ h h‘ h h‘ 1p1h correlations: p P‘ h h‘ V= δ2E[R] δR2 Uncorrelated ground state: Density functional theory E[R] σ (J,T)=(0+,0) ω (J,T)=(1-,0) ρ (J,T)=(1-,1) (covariant: 7-9 parameters) Self-consistent Self-consistent 3p3h correlations: iterative scheme Mechanism of the RSF formation at low 1. Saturation of RSF with Δ at Δ = 10 keV for T>0 2. The low-energy RSF is not a tail of the GDR and not a part of PDR! 3. The nature of RSF at Eγ-> 0 is continuum transitions from the thermally unblocked states 4. Spurious translation mode should be eliminated exactly Eγ Low-energy limit of the RSF in even-even Mo isotopes a = aEGSF => Tmin (RIPL-3) Tmax (microscopic) Exp-1: NLD norm-1, M. Guttormsen et al., PRC 71, 044307 (2005) Exp-2: NLD norm-2, S. Goriely et al., PRC 78, 064307 (2008) Theory: E. Litvinova, N. Belov, PRC 88, 031302(R)(2013) Data: A.C. Larsen, S. Goriely, PRC 014318 (2010) Low-energy limit of the RSF in 116,122Sn No upbend? Larger microscopic level density parameter a => Lower upper limit for the temperature at Sn Other effects (ideally, all to be combined in one approach) At 3-4 MeV: •2-phonon state (as above) Above 4-5 MeV: •Coupling to vibrations (as above), •Thermal fluctuations: M. Gallardo et al., NPA443, 415 (1985) •More correct for γ-emission: „final temperature“, V. Plujko, NPA649, 209c (1999) Theory: E. Litvinova, N. Belov, PRC 88, 031302(R)(2013) Data: H.K. Toft et al., PRC 81, 064311 (2010), PRC 83, 044320 (2011) Nucleons, mesons, phonons Short range: Mean-field approximation ρ mπ ~140 MeV, mρ ~770 MeV, m ~783 MeV + superfluidity! Strong coupling: non-perturbative techniques Nucleon separation energies: ~1-10 MeV Emergent collective phonons: ~1-10 MeV Long range: Time blocking Single-quasiparticle Green‘s function Doubled quasiparticle space: Spectroscopic factors Energies One-body Green’s function in N-body system (Lehmann): Model dependence of S! Excited state (N+1) Ground state (N) Response to an external field: strength function Nuclear Polarizability: External field Strength function: Transition density: Response function: Nuclear vibrational motion Gamow-Teller Monopole L = 0 Dipole L = 1 Quadrupole L = 2 T = 0 S = 0 T = 1 S = 0 T = 0 S = 1 T = 1 S = 1 * M. N. Harakeh and A. van der Woude: Giant Resonances Spin-orbit splittings: Tensor force or meson-nucleon dynamics? A. Afanasjev and E. Litvinova, arXiv:14094855 Energy splittings between dominant states which are used to adjust the mean-field tensor interaction. Here no tensor. A conventional description including isoscalar phonons is used in the quasiparticle-vibration coupling (QVC) self-energy. The discrepancies at larger isospin asymmetries may point out to the missing isospin vibrations. Pion dynamics is to be included in the QVC In progress. Giant Dipole Resonance within Relativistic Quasiparticle Time Blocking Approximation (RQTBA)* ΔL = 1 ΔT = 1 ΔS = 0 1p1h 2p2h *E. L., P. Ring, and V. Tselyaev, Phys. Rev. C 78, 014312 (2008) Covariant NFT for nuclear response (RQTBA) E. Litvinova, P. Ring, V. Tselyaev, PRC 88, 044320 (2013). PRL 105, 022502 (2010) Giant resonances (here dipole) PRC 78, 014312 (2008). Perspectives: inclusion higher-order correlations Description of low-energy spectroscopy: From giant resonances‘ widths to transport coefficients J. Endres et al. PRL 105, 212503 (2010), PRC 85, 064331 (2012). E. Lanza et al., PRC 89, 041601(R) (2014). R. Massarczyk et al. PRC 86, 014319 (2012). And other… B. Ozel-Tashenov, PRC (2014). Fragmentation of pygmy dipole resonanse E. L., P. Ring, and V. Tselyaev, Phys. Rev. C 78, 014312 (2008) Low-lying dipole strength in Experiment* Fine structure 116Sn Gross structure 2+,3-,… surface vibrations Integral 5-8 MeV: ΣB(E1)↑ [e2 fm2] QPM up to 3p3h (V.Yu. Ponomarev) * K. Govaert et al., PRC 57, 2229 (1998) RQTBA 2p2h RQRPA 1p1h vs RQTBA 2p2h Exp. 0.204(25) QPM 0.216 RQTBA 0.27 RQTBA dipole transition densities in 68Ni at 10.3 MeV Theory: -0.04000 Neutrons Protons -0.03000 -0.02000 -0.01000 E.L., P.Ring, V.Tselyaev, PRL 105, 02252 (2010) -0.005000 Experiment: 0.005000 25 0.01000 0,03 0.02000 15 neutrons protons 0,02 0,01 10 r [fm -1] counts 20 2 5 0.03000 0,00 -0,01 = 10.6 MeV E =E10.3 MeV -0,02 0 5.0 7.5 10.0 12.5 Energy [MeV] O.Wieland et al., PRL 102, 092502 (2009) -0,03 Experiment: Coulomb excitation of 68Ni at 600 AMeV -0,04 0 2 4 6 8 r [fm] 10 12 14 0.04000 RQTBA dipole transition densities in 68Ni at 10.3 MeV Theory: RQTBA-2 Neutrons Protons E.L., P.Ring, V.Tselyaev, PRL 105, 02252 (2010) Experiment: 25 0,03 neutrons protons 0,02 2 r [fm -1] 0,01 counts 20 15 10 0,00 5 -0,01 = 10.6 MeV E = E10.3 MeV -0,02 0 5.0 -0,03 -0,04 0 2 4 6 8 r [fm] 10 12 14 7.5 10.0 12.5 Energy [MeV] O.Wieland et al., PRL 102, 092502 (2009) Dipole strength in Sn isotopes E.L. et al, PRC 79, 054312 (2009) 6 7 8 9 10 11 5 10 15 20 25 2 400 200 5 6 7 8 10 15 20 25 800 10 114 114 Sn 8 Sn 600 6 2 400 4 200 2 0 5 6 7 8 9 10 11 5 10 15 20 25 30 15 20 25 cross section [mb] 30 RQRPA RQTBA Sn 15 120 Sn 600 400 10 200 5 0 5 6 7 8 9 10 5 10 15 20 25 30 1200 RQRPA RQTBA 30 RQRPA RQTBA 1000 800 25 130 130 Sn 20 Sn 600 15 400 10 200 5 0 0 4 120 35 2 12 RQRPA RQTBA 10 800 40 1000 10 5 1000 2 RQRPA RQTBA 9 40 30 1200 14 8 RQRPA RQTBA 4 S [ e fm / MeV ] 16 9 10 11 5 7 0 0 4 6 1200 2 Sn Sn 0 5 2 106 Sn 0 200 45 S [ e fm / MeV ] 1200 1 2 4 cross section [mb] RQRPA RQTBA 2 106 400 50 1400 116 600 4 30 1600 RQRPA RQTBA Sn 0 0 5 800 116 20 cross section [mb] 200 22 RQRPA RQTBA 1000 cross section [mb] 400 3 2 Sn cross section [mb] 2 1 4 S [ e fm / MeV ] 100 600 RQRPA RQTBA 2 Sn 2 100 1200 24 S [ e fm / MeV ] 800 0 2 RRPA RTBA 1000 2 2 S [ e fm / MeV ] RRPA RTBA S [ e fm / MeV ] 26 1200 cross section [mb] 3 0 4 5 6 7 8 E [MeV] 9 10 5 10 15 20 E [MeV] 25 30 Dipole strength Sn isotopes Dipole strength in Sninisotopes E.L. et al, PRC 79, 054312 (2009) 134 Sn 600 15 Bn 10 Exp Bn 400 Th 5 200 0 0 3 4 5 6 7 8 9 10 0 Sn 400 10 5 200 0 0 5 6 Bn 40 8 Th 9 10 0 Bn 30 5 1200 130 130 800 Sn 20 Sn 600 2 15 400 10 200 5 0 0 3 4 5 6 E [MeV] 7 Bn Exp 8 9 10 0 Bn 5 6 7 8 RQRPA RQTBA 10 15 20 25 30 10 15 20 25 30 RQRPA RQTBA 1000 800 138 30 Sn 20 Bn 138 Sn 600 400 Th 200 0 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 1400 RQRPA RQTBA 50 RQRPA RQTBA 1200 1000 40 136 10 Sn 600 20 Bn 136 800 Sn 30 400 Th 200 0 5 5 1200 40 10 9 10 0 1400 60 RQRPA RQTBA 1000 25 0 4 0 10 15 20 25 30 1400 RQRPA RQTBA 35 2 7 Exp 2 4 2 3 S [ e fm / MeV ] Sn S [ e fm / MeV ] 15 132 600 2 800 132 20 200 50 2 1000 25 cross section [mb] 2 2 S [ e fm / MeV ] 30 400 Th 60 RQRPA RQTBA 1200 S [ e fm / MeV ] RQRPA RQTBA Sn 600 20 Bn 140 800 Sn 3 1400 35 140 30 0 10 15 20 25 30 cross section [mb] 40 5 1000 40 10 RQRPA RQTBA 1200 0 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 Th E [MeV] cross section [mb] Sn 20 RQRPA RQTBA cross section [mb] 800 2 134 1400 50 2 1000 25 2 2 S [ e fm / MeV ] 30 60 RQRPA RQTBA 1200 S [ e fm / MeV ] RQRPA RQTBA 35 E [MeV] E [MeV] cross section [mb] 1400 cross section [mb] 40 Spin-isospin response: Gamow-Teller Resonance in 28-Si „Proton-neutron“ relativistic time blocking approximation (pn-RTBA): ρ, π, phonons 0,7 r SGT [MeV -1] 0,6 0,5 GT_ 0,4 14 Fermi sea contribution 12 10 5 28 Si GT_ 0,3 3 0,2 2 0,1 1 0,0 0 -1800 -1600 -1400 -1200 -1000 5 Ikeda Sum rule (model independent): 28 Si 4pn-RRPA pn-RTBA ΔL = 0 ΔT = 1 ΔS = 1 10 15 20 25 30 35 40 E [MeV] E [MeV] 12 10 S- - S+ = 3(N – Z), S± = ∑ B(GT ±) „Microscopic“ quenching of B(GT): (i) relativistic effects, , (ii) ph+phonon configurations, 28 GT_ 8 B(GT) 0 Dirac sea contribution 6 Si pn-RRPA pn-RTBA (Ewin = 90 MeV) 70% 4 100% 2 0 10 20 30 40 50 60 70 80 90 (?) 28Si: N=Z ΔL = 0 ΔT = 1 ΔS = 1 ? ? Problem: finite basis Low-lying dipole strength in 136-Ba R. Massarczyk, R. Schwengner, F. Doenau, E. Litvinova, G. Rusev et al., Phys. Rev. C 86, 014319 (2012) RQTBA systematics for PDR: A proper definition of Pygmy Dipole Resonance is important! PDR = all states with the “isoscalar” underlying structure! 8 6 2 120Sn 4 α = (N – Z)/A (Asymmetry parameter) 132Sn Mean energies 18 100Sn 78Ni 68Ni 0 0,00 0,02 Sn 16 14 0,04 0,06 0,08 2 132Sn: 1h11/2 (n) 68Ni 78Ni: 1g9/2 (n) 120Sn Intruder orbits ! E.L. et al. PRC 79, 054312 (2009) E [MeV] 2 Strength vs α2 140Sn Z = 50 (Sn) Z = 28 (Ni) Z = 82 (Pb) 2 B(E1) [e fm ] 10 <E>GDR 12 <E>PDR 10 8 6 115 120 125 130 A 135 140 GTR in 78-Ni: G-matrix+QRPA, RRPA and RTBA Beta-decay window ΔL = 0 ΔT = 1 ΔS = 1 G-matrix+QRPA based on Skyrme DFT with m* = 1 (D.-L. Fang & A. Fässler & B.A. Brown) RTBA: Relativistic RPA + phonon coupling (T. Marketin & E.L.) E.L., B.A. Brown, D.-L. Fang, T. Marketin, R.G.T. Zegers, PLB 730, 307 (2014) 2 2 S [ e fm / MeV ] Outlook 1400 RQRPA RQTBA 50 RQRPA RQTBA 1200 cross section [mb] 60 1000 40 140 Bn Sn 600 20 10 140 800 Sn 30 400 Th 200 50 E1 S [e fm / MeV] 40 140 0 RQRPA RQTBA Sn 0 3 30 4 5 6 7 8 9 10 0 7 8 9 10 0 10 15 20 25 30 5 10 15 20 25 30 1400 2 60 5 8 2 0 5 1800 10 2 15 0.00 E0 600 5 6 15 20 RQRPA RQTBA 1200 1000 136 136 800 Sn 30 Bn 10 Sn 600 400 Th 200 0 0 3 4 5 6 7 8 9 10 0 5 10 15 20 25 30 E [MeV] 132 Sn Nuclear matter, Neutron stars, … Applications 1400 RQRPA RQTBA 2 2 [mb] 10 r [fm] 800 Pb = 1.7 MeV E [MeV] 600 = 2.6 MeV 0.08 400 1500 140 400 0.04 200 20 25 30 5 10 15 20 25 30 10 E5 [MeV] 15 20 25 E [MeV] E [MeV] E = 4.65 MeV (RQTBA) 5 10 15 E = 5.18 MeV (RQTBA) 20 0 5 20 0 5 20 0 5 10 15 20 0.04 -1 15 0 2 25 0.02 0.00 -0.02 E = 6.39 MeV (RQTBA) -0.04 0 5 10 15 E = 7.27 MeV (RQTBA) 10 15 20 0.02 -1 10 20 0.00 2 15 E [MeV] r [fm ] 10 -0.08 0 0 5 5 r [fm ] 0 0 neutrons protons 0.00 -0.04 200 500 Sn -1 = 3.1 MeV = 2.4 MeV 2 200 1000 r [fm ] 400 4 2 5 1800 RH-RRPA RH-RRPA-PC 800 208 600 0 E = 10.94 MeV 208 20 (RQRPA) E1 Pb 2000 0 RH-RRPA RH-RRPA-PC 800 E0 2 2200 208 E1 -0.04 Pb 1000 1000 Sn 400 4 60 20 138 600 Th 200 3 (NL3) 40 RH-RRPA-PC 2400 -1 r [MeV ] 1400 1200 2500 2000 Bn 0 neutrons RH-RRPA protons 0.04 WS-RPA (LM) WS-RPA-PC 1600 3500 3000 Sn 20 10 50 2600 RQRPA RQTBA 800 138 30 E = 7.18 MeV (RQRPA) S [ e fm / MeV ] -1 r [MeV ] neutrons protons 1200 1000 40 10 E [MeV] 2 6 cross section [mb] S [ e fm / MeV ] 4 0.0 cross section [mb] 2 50 0 R [e fm /MeV] ISGMR Consistent input for r-process nucleosynthesis RQRPA RQTBA 20 10 0.1 -0.1 E = 8.46 MeV (RQTBA) -0.02 0 5 10 r [fm] 15 E = 9.94 MeV (RQTBA) 10 15 20 r [fm] Timedependent CEDFT ??? 3p3h excitations: iterative PVC p P‘ p P‘ h‘ h h h‘ p P‘ h‘ h 2p2h excitations: Particle-Vibration Coupling p p P‘ p P‘ h h‘ h‘ h h 1p1h excitations: RQRPA p SelfP‘ consistency h h‘ P‘ h‘ δ2E[R] V= δR2 Ground state: Covariant EDFT DD-MEδ CEDFT: Ab initio Brückner + 4 adjustable parameters PRC 84, 054309 (2011) σ ω ρ Toward „ab initio“ E[R] Data => Constraints from RIB facilities Data => Constraints from RIB facilities np-nh Generalized CEDFT ??? Pion dynamics