Low-lying gamma-strength within microscopic models Elena Litvinova 1,2 1 GSI Helmholtzzentrum für Schwerionenforschung mbh, Darmstadt, Germany 2 Institut für Theoretische Physik, Goethe Universität, Frankfurt am Main, Germany Dresden - Rossendorf August 3 September 3 21
OUTLINE Pygmy dipole resonance within relativistic many-body methods Microscopic models based on the covariant density functional: - Relativistic mean field (RMF) model - Self-consistent (parameter-free) many-body methods beyond relativistic quasiparticle random phase approximation (RQRPA) Applications: Nuclear low-energy response, neutron capture cross sections and reaction rates Transitions between excited states: Finite temperature continuum QRPA: origin of the lowest gammastrength and Brink hypothesis
Mean-field based models: 3p3h excitations SELF-CONSISTENT Coupling schemes: I. 2p2h (4q) = SRPA II. 2q+phonon III. 2 phonon 2p2h excitations: Particle-Vibration Coupling (PVC) p P p P h h h h p h 1p1h excitations: Quasiparticle Random Phase Approximation (QRPA) P h Selfconsistency V = δ2 E[R] δr 2 Ground state: Relativistic Mean Field (RMF) σ ω ρ E[R] (J π,t)=( +,) (J π,t)=(1 -,) (J π,t)=(1 -,1)
Relativistic mean field { RHB Hamiltonian no sea Nucleons Mesons Dirac Hamiltonian RMF selfenergy Eigenstates
Mean Field First step beyond relativistic mean field: r Coupling to vibrations EF QRPA phonon (vibration) First order coupling: self-energy diagram fish Σ e = p P One-body propagation: p 1 p 2 p = 1 p 2 p + 1 p Σ e P p 2 (Dyson equation) p RMF+PVC h Time s arrow Splitting and shift of single-quasiparticle levels & distribution of single-particle strength» spectroscopic factors E. L., P. Ring, PRC 73, 44328 (26) Not complete: pairing vibrations have to be studied!
Nuclear response function Functional derivative of the nucleon self-energy i δ δg i δ δg G = i δσe δg = = = Nuclear response function R: two-body propagation in the nuclear medium Bethe-Salpeter equation (BSE) in the p-h channel 2p2h: Energydependent 1p1h: static U e = i δσ e δg V = δσ δρ Bethe-Salpeter equation is solved in the particle-hole (1p1h) basis: all the job on complex configurations is done by intermediate summations. NO huge matrices! QRPA R = A + A (V + Φ) R
3p3h Time blocking* Problem: Melting diagrams NpNh Unphysical result: negative cross sections Solution: Timeprojection operator: Time s arrow R Partially fixed Allowed terms: 1p1h, 2p2h Blocked terms: 3p3h, 4p4h, Time s arrow *V.I. Tselyaev, Yad. Fiz. 5,1252 (1989). S.S. Wu, Scientia Sinica 16, 347 (1973). F.J.W. Hahne and W.D. Heiss, Z. Phys. A 273, 269 (1975). Time blocking approximation = one-fish approximation! Separation of the integrations in the BSE kernel R has a simple-pole structure (spectral representation)»» Strength function is positive definite!
Calculations within the Relativistic Quasiparticle Time Blocking Approximation (RQTBA) Input Dirac equation for nucleons RQRPA for phonons 2+,3-,4+,5-,6+ Relativistic Lagrangian: 1 parameters RMF Klein-Gordon equation for meson fields RQTBA equations Closed scheme: NO fitting procedures! Output
Giant Dipole Resonance within Relativistic Quasiparticle Time Blocking Approximation (RQTBA)* 1p1h 2p2h *E. L., P. Ring, and V. Tselyaev, Phys. Rev. C 78, 14312 (28)
Skin Core Pygmy dipole resonanse in the mode coupling interpretation Low-lying dipole strength in 116 Sn Experiment* Fine structure Gross structure 2+,3-, surface vibrations Integral 5-8 MeV: ΣB(E1) [e 2 fm 2 ] QPM up to 3p3h (V.Yu. Ponomarev) * K. Govaert et al., PRC 57, 2229 (1998) RQTBA 2p2h RQRPA 1p1h vs RQTBA 2p2h Exp..24(25) QPM.216 RQTBA.27
Isospin properties of the pygmy dipole resonance in 124 Sn Experiment (J. Enders, D. Savran et al.) 4e+5 Theory: RQTBA S [e 2 fm 6 / MeV] 3e+5 2e+5 1e+5 ISE1 RQTBA 124 Sn 3 4 5 6 7 8 9 1 5 S [e 2 fm 2 / MeV] 4 3 2 1 IVE1 RQTBA 124 Sn 3 4 5 6 7 8 9 1 Hadron vs Coulomb excitation J.Endres et al, subm. to PRL Transition Densities δρ(r) ρ(r,t) = ρ (r) + δρ(r,t) r 2 ρ [fm -1 ] r 2 ρ [fm -1 ].6.3 neutrons protons -.3 E = 7.133 MeV -.6 5 1 15.6.3 -.3 E = 8.737 MeV -.6 5 1 15 r [fm]
35 3 25 2 15 1 5 RH-RRPA RH-RRPA-PC 5 1 15 2 25 E 28 Pb Γ = 1.7 MeV Γ = 2.4 MeV 1 8 6 4 2 Γ = 2.6 MeV Γ = 3.1 MeV 5 4 3 2 1.1. -.1.4. -.4 5 1 15 2 25 E 132 Sn E1 14 Sn RQRPA RQTBA 4 6 8 1 neutrons protons E = 7.18 MeV (RQRPA) 5 1 15 2 neutrons protons E = 1.94 MeV (R Q RP A) 5 1 15 2 r [fm] RH-RRPA RH-RRPA-PC 6 5 4 3 2 1 6 5 4 3 2 1 6 5 4 3 2 1 14 12 1 8 6 4 2 14 12 1 8 6 4 2 14 12 1 8 6 4 2 r r r Dipole strength in neutron-rich nuclei.8 14 neutrons Sn.4 protons. -.4 E = 4.65 MeV E = 5.18 MeV (RQTBA) (RQTBA) -.8 5 1 15 2 5 1 15 2.4.2. -.2 E = 6.39 MeV E = 7.27 MeV (RQTBA) (RQTBA) -.4 5 1 15 2 5 1 15 2.2. E = 8.46 MeV E = 9.94 MeV -.2 (RQTBA) (RQTBA ) 5 1 15 2 5 1 15 2 r [fm] r [fm] S [e 2 fm 2 / MeV] S [e 2 fm 2 / MeV] 8 6 4 2 132 Sn 1 - Neutron-rich Sn 5 1 15 2 25 Experiment* 3 35 8 RQTBA** 6 13 Sn RQTBA with detector response (A. Klimkiewicz) 4 1 - (b) 2 5 1 15 2 25 3 35 (a) * P. Adrich, A. Klimkiewicz, M. Fallot et al., PRL 95, 13251 (25) **E. L., P. Ring, V. Tselyaev, K. Langanke PRC 79, 54312 (29) S [arb. units] 3 2 1 68 Ni 1-6 8 1 12 Neutron-rich Ni 3 dσ / de [mb / MeV] 2 1 7 Ni 1-3 2 1 6 8 1 12 72 Ni 1-6 8 1 12 RQTBA RQTBA-2 E. Litvinova et al., PRL 15, 2252 (21) Exp. O.Wieland et al., PRL 12, 9252 (29) R [e 2 fm 4 /MeV] ISGMR σ [mb] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] B n Th RQRPA RQTBA 14 Sn 3 4 5 6 7 8 9 1 B n Th RQRPA RQTBA 138 Sn 3 4 5 6 7 8 9 1 RQRPA 18 26 RQTBA W S-RPA (LM) RH-RRPA (NL3) 16 W S-RPA-PC 24 RH-RRPA-PC 136 Sn 14 22 E1 28 Pb 2 E1 28 Pb Th 12 B n 18 1 3 4 5 6 7 8 9 1 8 8 6 6 4 4 2 2 5 1 15 2 25 3 5 1 15 2 25 3 r 2 ρ [MeV -1 ] r 2 ρ [MeV -1 ] S [e 2 fm 2 / MeV] RQRPA RQTBA 14 Sn 5 1 15 2 25 3 RQRPA RQTBA 138 Sn 5 1 15 2 25 3 136 Sn 5 1 15 2 25 3 2ρ [fm-1] 2ρ [fm-1] 2ρ [fm-1] RQRPA RQTBA cross section [mb] cross section [mb] cross section [mb] Input Application to astrophysics: (n,γ) cross sections and reaction rates E. L., H.P. Loens, K. Langanke, G. Martìnez-Pinedo, T. Rauscher, P. Ring, F.-K. Thielemann, V. Tselyaev, Nucl. Phys. A 823, 26 (29).
Theory: RQTBA-2 RQTBA dipole transition densities in 68 Ni at 1.3 MeV Neutrons Protons -.4 -.3 -.2 -.1 -.5.5,3,2,1 neutrons protons.1 r 2 ρ [fm -1], -,1 -,2 -,3 E = 1.6 E = 1.3 MeV -,4 2 4 6 8 1 12 14 r [fm] 68 Ni.2.3.4
Neutron-rich nuclei: neutron skin oscillations Theory*: RQTBA-2 2 Neutrons Protons Strength 1 68 Ni 5, 7,5 1, 12,5 Experiment**: Coulomb excitation of 68Ni at 6 AMeV 25 2 68 Ni counts 15 1 5 Th: *E. Litvinova et al., PRL 15, 2252 (21) Exp: **O.Wieland et al., PRL 12, 9252 (29) 5. 7.5 1. 12.5 Energy [MeV]
RQTBA systematics for PDR: A proper definition of Pygmy Dipole Resonance is highly important! PDR = all states with the isoscalar underlying structure! ΣB(E1) [e 2 fm 2 ] 1 8 6 4 2 1 Sn Z = 5 (Sn) Z = 28 (Ni) Z = 82 (Pb) 12 Sn 68 Ni,,2,4,6,8 α 2 132 Sn 14 Sn 78 Ni 12 Sn 132 Sn: 1h11/2 (n) 68 Ni 78 Ni: 1g9/2 (n) Intruder orbits! E.L. et al. PRC 79, 54312 (29) 18 16 14 12 1 8 6 Strength vs α 2 α = (N Z)/A (Asymmetry parameter) Mean energies <E> GDR <E> PDR Sn 115 12 125 13 135 14 A
Radiative neutron capture in the Hauser-Feshbach model: standard Lorentzians and microscopic input* 1 2 1 1 1 1 115 Sn(n,γ) 116 Sn 119 Sn(n,γ) 12 Sn 1 1 σ [b] 1-1 1-2 1-3 Exp (ENDF/B-VII.) RQTBA (microscopic) Thielemann & Arnould (1983) RIPL-2 (theor) 1 3 1 4 1 5 1 6 1 7 1 E n [ev] σ [b] 1-1 1-2 1 3 1 4 1 5 1 6 1 7 1 E n [ev] 1-1 129 Sn(n,γ) 13 Sn 1-1 131 Sn(n,γ) 132 Sn σ [b] 1-2 σ [b] 1-2 1-3 1-3 1-4 1-4 1 3 1 4 1 5 1 6 1 7 E [ev] n *E. L., H.P. Loens, K. Langanke, G. Martínez-Pinedo, T. Rauscher, P. Ring, F.-K. Thielemann, V. Tselyaev, Nucl. Phys. A 823, 26 (29). 1-5 1 3 1 4 1 5 1 6 1 7 E n [ev] 132 Sn: PDR at the neutron threshold!
1 1 (n,γ) stellar reaction rates* 1 1 N A <σv> [cm 3 s -1 mole -1 ] 1 9 1 8 1 7 115 Sn(n,γ) 116 Sn RQTBA (microscopic) RIPL-2 (theor) Thielemann & Arnould (1983) 1 9 1 8 1 7 119 Sn(n,γ) 12 Sn 1 6 1 6 1-1 1 1 1 1-1 1 1 1 1 8 1 8 N A <σv> [cm 3 s -1 mole -1 ] 1 7 1 6 1 5 129 Sn(n,γ) 13 Sn 1 7 1 6 1 5 131 Sn(n,γ) 132 Sn 1 4 1 4 1-1 1 1 1 1-1 1 1 1 T [GK] T [GK] *E. L., H.P. Loens, K. Langanke, G. Martínez-Pinedo, T. Rauscher, P. Ring, F.-K. Thielemann, V. Tselyaev, Nucl. Phys. A 823, 26 (29). 132 Sn: PDR at the neutron threshold!
Is there a dependence of the gamma-strength on the excitation energy?
Temperature dependence of low-lying dipole strength: Continuum QRPA at finite temperature revisited* U(r) Single-particle continuum Violation of the Brink hypothesis? r FS Thermal Population (Fermi-Dirac) Low-energy continuum transitions: finite strength at ε γ S [e 2 fm 2 / MeV] 1 2 E1 12 Sn 1 1 1 1-1 1-2 1-3 1-4 = 1 kev T = T =.5 MeV T = 1. MeV T = 2 MeV 1-5 *E.L. et al., in preparation. 2 4 6 8 1 ε [MeV] γ
How good the thermal mean field is? Temperature dependent covariant energy density functional E[ρ] = Thermal Relativistic Mean Field (RMF) E * [MeV] 4 3 2 1 4 3 28 Pb 132 Sn 2 1 * FG RMF 1 2 3 4 T [MeV] 1 2 3 4 T [MeV] *T. Rauscher, Astrophys. J. Suppl. Ser. 147, 43 (23).
Dipole gamma-strength in 132 Sn r Τ E*[ρ,τ] = S n 1 ɣ-emission S [e 2 fm 2 / MeV] 1 1 1,1,1 1E-3 1E-4 τ = τ =.88 MeV τ = 1.76 MeV Δ = 1 kev 132 Sn E1 ɣ-absorption 1E-5 1E-6-7 -6-5 -4-3 -2-1 1 2 3 4 5 6 7
From S E1 (Eɣ) to f E1 (E ɣ ) Dipole radiative strength in 28 Pb? S E1 (E ɣ ) f E1 (E ɣ ) S [e 2 fm 2 / MeV] 1 1 1 1,1,1 1E-3 1E-4 τ = τ =.83 MeV τ = 1.66 MeV Δ = 1 kev 28 Pb E1 f E1 [MeV -1 ] 1E-3 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 1E-1 τ =.83 MeV τ = Exp.* Δ = 1 kev 28 Pb E1 1E-5 1E-11 1E-6-7 -6-5 -4-3 -2-1 1 2 3 4 5 6 7 Eγ [MeV] 1E-12-7 -6-5 -4-3 -2-1 1 2 3 4 5 6 7 Eγ [MeV] *Oslo data: N.U.H. Syed et al., PRC 79, 24316
S [e 2 fm 2 / MeV] 1 1 1 1,1,1 1E-3 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 1E-1 1E-11 τ = τ =.47 MeV τ =.94 MeV Gamma-strength in 94 Mo (preliminary) Δ = 1 kev -9-8 -7-6 -5-4 -3-2 -1 1 2 3 4 5 6 7 8 9 94 Mo E1
Present status: Summary & Outlook I. Recently developed microscopic approaches based on the covariant DFT with consistent treatment of many-body correlations by the parameter-free Green s function techniques have been applied to description of the nuclear excited states Giant resonances shapes, low-energy fraction of the pygmy dipole resonance and two-phonon states in medium-mass and heavy spherical nuclei including neutron-rich ones are reproduced well within the fully consistent scheme The microscopic strength functions are used as an input for the (n,ɣ) cross sections and astrophysical reaction rates II. Thermal continuum QRPA is considered as a possible explanation of the finite radiative dipole strength functions at lowest gamma-energies Open problems & perspectives: Improvements of the RMF forces, inclusion of the next orders of many-body correlations Combined approach: Consistent combination of I & II Comparison to data for radiative dipole strength
Thanks for collaboration: Hans Feldmeier (GSI) Hans Peter Loens (GSI) Karlheinz Langanke (GSI) Gabriel Martínez-Pinedo (GSI) Thomas Rauscher (Basel University) Peter Ring (Technische Universität München) Friedrich-Karl Thielemann (Basel University) Victor Tselyaev (St. Petersburg State University)