Low-energy nuclear response: structure and underlying mechanisms

Transcription

1 Low-energy nuclear response: structure and underlying mechanisms Elena Litvinova National Superconducting Cyclotron Michigan State University, East Lansing, USA In collaboration with: P. Ring, V. Tselyaev, T. Marketin, N. Belov 4-th Workshop on Nuclear Level Density and Gamma Strength, Oslo, May 27-31, 213

2 Building blocks of nuclear structure models Degrees of freedom Separation of the scales at ~1-5 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 V NN : 3 basic concepts Ab initio: from vacuum V NN -> in-medium V NN Density functional: an ansatz for in-medium V NN Configuration interaction: matrix elements for in-medium V NN

3 Nuclear models Figure from: G.F. Bertsch, J. Phys.: Conf. Ser. 78, 125 (27)

4 Self-consistent Correlations in the models based on the density functional: NpNh: 3p3h correlations: iterative scheme p h 2p2h correlations: p h 1p1h correlations: p h P h P h P h p h Ground state: Density functional theory p h P h P h p h p h V = δ2 E[R] δr 2 E[R] P h P h Self-consistent σ ω ρ (covariant: 7-9 parameters) (J,T)=( +,) (J,T)=(1 -,) (J,T)=(1 -,1)

5 Excited states: nuclear response function Bethe-Salpeter Equation (BSE): QRPA Extension E.L., V. Tselyaev, PRC 75, (27) = : R(ω) = A(ω) + A(ω) [V + W(ω)] R(ω) V = δσrmf δρ W(ω) = Φ(ω) - Φ() Selfconsistency i δ δg G = i δσe δg = U e = i δσ e δg Consistency on 2p2h-level

6 Time blocking Problem: Melting diagrams Time 3p3h NpNh Approx. schemes Unphysical result: negative cross sections Solution: Timeprojection operator: V.I. Tselyaev, Yad. Fiz. 5,1252 (1989) R Partially fixed Allowed terms: 1p1h, 2p2h Blocked terms: 3p3h, 4p4h, 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!

7 Giant Dipole Resonance within Relativistic Quasiparticle Time Blocking Approximation ()* ΔL = 1 ΔT = 1 ΔS = 1p1h 2p2h *E. L., P. Ring, and V. Tselyaev, Phys. Rev. C 78, (28)

8 Gamow-Teller Resonance in 28-Pb Proton-Neutron relativistic time blocking approximation: ρ, π, phonons Fig. & calculation by T. Marketin (TU-Darmstadt) ΔL = ΔT = 1 ΔS = 1 Natural quenching of S - due to ph+phonon configurations, relativistic effects and finite momentum transfer

9 S Spin-dipole resonance: beta-decay, electron capture ΔL = λ =,1,2 ΔT = 1 ΔS = 1 Neutron skin thickness Sum rule: T. Marketin, E.L., D. Vretenar, P. Ring, PLB 76, 477 (212).

10 Fragmentation of pygmy dipole resonanse E. L., P. Ring, and V. Tselyaev, Phys. Rev. C 78, (28) Low-lying dipole strength in 116 Please, do not compare this PDR to data! 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) 2p2h 1p1h vs 2p2h Exp..24(25) QPM

11 Isospin structure of the pygmy dipole resonance in 124 J. Endres et al., PRL 15, (21). 3-phonon 2q+phonon Electromagnetic E1 2q+2phonon to be included

12 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, 2436 (27) & Mode Coupling Theory Time Blocking Replacement of the uncorrelated propagator inside the Φ amplitude by QRPA response Nuclear response: R = A + A (V + Φ Φ ) R 2q+phonon response: Φ iji j (ω) ~ Σ μk α ijkμ /(ω - E i - E k - Ω μ ) Poles may appear at lower energies: 2 phonon response: Φ iji j (ω) ~ Σ μν α iji j /(ω - Ω ν - Ω μ )

13 B(E1) [ 1-3 e 2 fm 2 ] Fine features of dipole spectra: two-phonon effects 2q+phonon 2 phonon First two-phonon state 1-1 : E(1-1) B(E1) Exp A Data: I.Pysmenetska et al., PRC73 (26) A Does not exist E.L., P.Ring, V.Tselyaev, PRL 15, 2252 (21) S [arb. units] Pygmy dipole resonance in neutron-rich Ni: 2q+phonon vs 2 phonon Ni d de [mb / MeV] Ni 72 Ni Data: O. Wieland et al., PRL 12, 9252 (29)

14 N A < v> [cm 3 s -1 mole -1 ] N A < v> [cm 3 s -1 mole -1 ] (n,γ) stellar reaction rates E. L., H.P. Loens, K. Langanke, et al. Nucl. Phys. A 823, 26 (29) (n, ) (n, ) (microscopic) RIPL-2 (theor) Thielemann & Arnould (1983) Factor (n, ) (n, ) T [GK] T [GK] PDR at neutron threshold

15 (n,γ) via compound nucleus: γ-transitions between excited states in the quasicontinuum Low-energy enhancement of γ-strength A. Voinov et al., PRL 93, (24) M. Guttormsen et al., PRC 71, 4437 (25) Oslo method M. Wiedeking et al., PRL 18, (212): Correlations due to coupling to single-particle continuum 95 Mo (n,γ) reaction rate (enh.) = η (n,γ) reaction rate (no enh.) A.C. Larsen, S. Goriely, PRC (21) Oslo data

16 Nuclear response at finite temperature Density matrix variation at T > : Thermal continuum quasiparticle random phase approximation E.L. et al., Phys. Atomic Nuclei 66, 558 (23) (TCQRPA) Radiative strength function (RSF): Matsubara GF Exp. energy resolution

17 Structure of the TCQRPA propagator in ph-channel 2 u 12 (T) = 1-v 12 (T)

18 Mechanism of the RSF formation at low Eγ 1. Saturation of RSF with Δ at Δ = 1 kev for T> 2. The low-energy RSF is not a tail of the GDR and not a part of PDR! 3. The nature of RSF at E γ -> is continuum transitions from the thermally unblocked states 4. Spurious translation mode should be eliminated exactly.

19 Elimination of the spurious state Condition 1 Condition 2 V. Tselyaev: S. Kamerdzhiev et al., PRC 58, 172 (1998) M.I. Baznat et al., Sov. J. Nucl. Phys. 52, 627 (199)

20 RSF in even-even Mo isotopes a = a EGSF => T min (RIPL-3) => T max Exp-1: NLD norm-1, M. Guttormsen et al., PRC 71, 4437 (25) Exp-2: NLD norm-2, S. Goriely et al., PRC 78, 6437 (28) Theory: E. Litvinova, N. Belov, arxiv: , submitted to Phys. Rev. Data: A.C. Larsen, S. Goriely, PRC (21)

21 RSF in 116,122 No upbend? Larger microscopic level density parameter a => Lower upper limit for the temperature at S n 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, 29c (1999) Data: H.K. Toft et al., PRC 81, (21), PRC 83, 4432 (211)

22 f E1 [MeV -1 ] Absorption vs emission (preliminary) 1E-6 1E-7 abs, T = 1.55 MeV abs, T = emis, T i = 1.55 MeV emis, no back-shift, T i = 1.8 MeV Exp-1 Exp-2 1E-8 1E-9 96 Mo 1E E [MeV]

23 Many thanks for collaboration: Peter Ring (Technische Universität München) Victor Tselyaev (St. Petersburg State University) Tomislav Marketin (TU-Darmstadt) Anatoli Afanasjev (Mississippi State University) Nikolay Belov (Heidelberg) Thomas Aumann (TU-Darmstadt) Janis Endres (University of Köln) Hans Feldmeier (GSI) Hans Peter Loens (GSI) Karlheinz Langanke (GSI) Gabriel Martínez-Pinedo (GSI) Thomas Rauscher (University of Basel) Deniz Savran (EMMI, Darmstadt) Friedrich-Karl Thielemann (University of Basel)

24 -S-V Static description as zero approximation: Relativistic Mean Field (RMF) -S+V Continuum r Fermi sea FE 2m N * 2m N Dirac sea No sea approximation

25 -S+V -S-V Oscillations of the mean nuclear potential Fermi sea FE Continuum r 2m N * Vibrational modes (phonons J π ) 2m N p h P h Dirac sea No sea approximation

26 First step beyond relativistic mean field: quasiparticles coupled to vibrations Additional potential = self-energy = = mass operator with energy dependence Σ e = k 1 k 2 k Fish diagram nucleon Vibration μ coupling One-body propagator G: Dyson equation k k k k k k k = + 1 k Σ e 2 G = G + G Ʃ e G Energy dependence p Doubled quasiparticle space: h Time arrow

27 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)

28 Quasiparticle-vibration coupling: Pairing correlations of the superfluid type + coupling to phonons Open shell Closed shell Spectroscopic factors in 119,121 : (nlj) ν S th S exp 2d 5/ g 7/ d 3/ s 1/ h 11/ f 7/ p 3/ Spectroscopic factors in 133 : (nlj) ν 1h 9/2 S th *.88 S exp ** 2f 7/ ±.16 3p 3/ ±.18 3p 1/ ±.3 2f 5/ ±.2 E.L., PRC 85, 2133(R)(212) *E. L., A.V. Afanasjev, PRC 84, 1435 (211) **K.L. Jones et al., Nature 465, 454 (21)

29 Transitions: fragmentation mechanism (schematic) Mean field: Free Q Q+phonons 1p1h 2p2h, 3p3h, FE

30 Relativistic mean field { RHB Hamiltonian no sea Nucleons Mesons Dirac Hamiltonian RMF selfenergy Eigenstates

31 Response to an external field: strength function Nuclear Polarizability: External field Strength function: Transition density: Response function:

32 Algebraic equation for the response function Mean field propagator Subtraction to avoid double counting 2q-phonon coupling amplitude

33 Next-order for 3p-3h configurations & iterative procedure for multiphonon response R (n+1) = GG + GG [V + Φ(R (n) )] R (n+1) R R R R Nested configurations γ 4 terms in Φ-amplitude: 3p3h: two-fish approximation,

34 S [e 2 fm 2 / MeV] S [e 2 fm 2 / MeV] Dipole strength in neutron-rich nuclei: importance for astrophysics R [e 2 fm 4 /MeV] ISGMR [mb] RH-RRPA RH-RRPA-PC 8 E 28 Pb 6 = 1.7 MeV 4 = 2.4 MeV WS-RPA (LM) WS-RPA-PC E 5 [MeV] = 2.6 MeV = 3.1 MeV r 2 [MeV -1 ] r 2 [MeV -1 ] S [e 2 fm 2 / MeV] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] neutrons RH-RRPA protons (NL3) 4 RH-RRPA-PC r [fm] RH-RRPA RH-RRPA-PC E 132 E neutrons protons E = 7.18 MeV () E = 1.94 MeV () S [ e 2 fm 2 / MeV ] B n Th B n Th B n Th R [e 2 fm 4 /MeV] ISGMR r 2 [fm -1 ] cross section [mb] [MeV -1 cross section [mb] cross section [mb] neutrons 1 WS-RPA (LM) RH-RRPA protons (NL3) 4 16 WS-RPA-PC 24 RH-RRPA-PC E = 1.94 MeV () Th 12 B n r [fm] RH-RRPA RH-RRPA RH-RRPA-PC RH-RRPA-PC E 28 Pb E = 1.7 MeV 6 = 2.6 MeV.8 14 neutrons 4 protons = 2.4 MeV = 3.1 MeV E = 4.65 MeV E = 5.18 MeV () () E 5 [MeV] E = 6.39 MeV E = 7.27 MeV () () [mb] r 2 [fm -1 ] r 2 [fm -1 ] E = 8.46 MeV () r [fm] E = 9.94 MeV () r [fm] E neutrons protons E = 7.18 MeV () S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] B n Th B n Th r 2 [fm -1 ] r 2 [fm -1 ] r 2 [fm -1 ] E = 4.65 MeV () E = 6.39 MeV () E = 8.46 MeV () r [fm] cross section [mb] cross section [mb] cross section [mb] neutrons protons E = 5.18 MeV () E = 7.27 MeV () E = 9.94 MeV () r [fm] Neutron-rich Experiment* ** 6 13 with detector response (A. Klimkiewicz) 4 (a) (b) E1 28 Pb E1 28 Pb E1 28 Pb E1 28 Pb Input for astrophysics: cross sections, reaction rates etc. under astrophysical conditions *P. Adrich, et al., PRL 95, (25) **E. L., P. Ring, V. Tselyaev, K. Langanke PRC 79, (29)

35 S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] Dipole strength in isotopes RRPA RTBA RRPA RTBA S [ e 2 fm 2 / MeV ] E.L. et al, PRC 79, (29) cross section [mb] cross section [mb] cross section [mb] cross section [mb] cross section [mb] cross section [mb]

36 S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] Exp Th B n B n S [ e 2 fm 2 / MeV ] Dipole strength in in isotopes isotopes B n Exp B n Th E.L. et al, PRC 79, (29) 13 cross section [mb] cross section [mb] cross section [mb] B n Th B n Th B n Th cross section [mb] cross section [mb] cross section [mb] Exp Th B n B n

37 Low-lying dipole strength in 136-Ba R. Massarczyk, R. Schwengner, F. Doenau, E. Litvinova, G. Rusev et al., Phys. Rev. C 86, (212)

38 B(E1) [e 2 fm 2 ] systematics for PDR: A proper definition of Pygmy Dipole Resonance is important! PDR = all states with the isoscalar underlying structure! Z = 5 () Z = 28 (Ni) Z = 82 (Pb) Ni,,2,4,6, Ni : 1h11/2 (n) 68 Ni 78 Ni: 1g9/2 (n) Intruder orbits! E.L. et al. PRC 79, (29) Strength vs α 2 α = (N Z)/A (Asymmetry parameter) Mean energies <E> GDR <E> PDR A

39 Radiative neutron capture in the Hauser-Feshbach model: standard Lorentzians and microscopic structure 1 2 E. L., H.P. Loens, K. Langanke, et al. Nucl. Phys. A 823, 26 (29). 1 1 [b] Exp (ENDF/B-VII.) (microscopic) Thielemann & Arnould (1983) RIPL-2 (theor) 115 (n, ) E n [ev] [b] (n, ) E n [ev] (n, ) (n, ) 132 [b] 1-2 [b] E [ev] n E n [ev]

40

41 Gamma-strength Nuclei are heated in astrophysical environment! New correlations: transitions to continuum from thermally unblocked states: T s ~ 1 MeV T = E. Litvinova, N. Belov, arxiv: (n,γ) reaction rate (T=Ts) (n,γ) reaction rate (T=) = η A.C. Larsen, S. Goriely, PRC (21)

42 f E1 [MeV -1 ] Dipole gamma-strength function (preliminary) 1E-3 1E-4 1E-5 1E-6 1E-7 =.83 MeV = Exp.* = 1 kev 1E-8 1E-9 1E-1 1E Pb 1E E [MeV] U(r) Consequences for (n,γ) reaction rates -? For electric dipole polarizability (EDP) -??? For EDP neutron skin correlation -?? FS r

43 R [e 2 fm 4 /MeV] ISGMR [mb] RH-RRPA RH-RRPA-PC 8 E 28 Pb 6 = 1.7 MeV 4 = 2.4 MeV WS-RPA (LM) WS-RPA-PC = 3.1 MeV r 2 [MeV -1 ] E1 28 Pb -.4 = 2.6 MeV r 2 [MeV -1 ] S [e 2 fm 2 / MeV] S [ e 2 fm 2 / MeV ] S [ e 2 fm 2 / MeV ] B nth neutrons RH-RRPA protons (NL3) 4 RH-RRPA-PC E = 1.94 MeV () E1 28 Pb r [fm] RH-RRPA RH-RRPA-PC E 132 E Data => Constraints neutrons protons E = 7.18 MeV () S [ e 2 fm 2 / MeV ] B nth B nth r 2 [fm -1 ] r 2 [fm -1 ] r 2 [fm -1 ] E = 4.65 MeV () E = 6.39 MeV () E = 8.46 MeV () cross section [mb] cross section [mb] cross section [mb] neutrons protons E = 5.18 MeV () E = 7.27 MeV () r [fm] E = 9.94 MeV () r [fm] Outlook Nuclear structure & Astrophysics np-nh Applications Nuclear matter, Neutron stars, 3p3h excitations: iterative PVC p P p P h h h h 2p2h excitations: Particle-Vibration Coupling p P p p h h h h P h 1p1h excitations: p P Selfh h consistency p h V = δ2 E[R] δr 2 P h P h Data => Constraints Timedependent CEDFT??? Ground state: Covariant EDFT σ ω ρ E[R] Generalized CEDFT??? DD-MEδ CEDFT: Ab initio Brückner + 4 adjustable parameters PRC 84, 5439 (211) Toward ab initio UNEDF: DFT from EFT Chiral DFT,