Giant resonances in exotic nuclei & astrophysics

Transcription

1 Giant resonances in exotic nuclei & astrophysics 1) Giant resonances: properties & modelisation 2) Giant resonances in exotic nuclei 3) Giant resonances and astrophysics E. Khan

2 1) Properties and modelisation

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4 Harmonic vibrations

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6 The least action principle (I) A physical state of a system is characterised by an action (J.s) which is minimal Variationnal principle : variation of the action S around its minimum is zero Numerous applications : mathematics, mecanics, optics, quantum physics, Fermat (XVII eme ) Maupertuis (XVIII eme ) Lagrange (XVIII eme XIX eme ) Feynman (XX eme )

7 The least action principle (II) Nuclear Hamiltonian: Action: Stationnarity of S (δs=0) for any variation of <Ψ(t) Schrödinger equation Reformulation of the starting point: Energy density functionnal Hohenberg-Kohn theorem: existence

8 The Hohenberg-Kohn (HK) theorem (Chemistry Nobel 98) There exists an energy functionnal E[ρ] which depends on the (local) density. It allows to exactly predict ground state observables (solves the many body problem) Knowledge of this functional in nuclei? HK states the existence of a functional for a given state, not an universal functional for the nuclear chart In nuclear physics coefficients in E[ρ] are adjusted on radii, masses, : takes into account correlations beyond mean field. Nuclei: symmetry restoration (broken in self-bound systems) Kohn-Sham = method to calculate ρ, knowing E[ρ]

9 Independent particles Application of the least action principle to the many body problem: nuclear physics (~1970) Slater determinant Justification: nucleus is a quantum liquid (range and intensity of strong interaction) nucleons are good independent particles (B. Mottelson ~ 2000)

10 Time Dependent Hartree-Fock (TDHF) Variation: ϕ i* (t) ϕ i* (t) + δϕ i* (t) A coupled equations : (self-consistent) mean field: In practice : - treat V NL quasi-locally : Skyrme, Gogny - interactions fitted on nuclei properties : radii, energies, etc. correlations beyond HF - LDA from infinite nuclear matter? L

11 TDHF properties Self consistent Minimum of the functionnal : static HF (stationnarity) HF Fusion, fission, compound nucleus, damping, Numerically heavy, tunnel effect, interpretation of Ψ?

12 Milestones Brueckner-HF : HF calculation with the bare nucleon-nucleon interaction renormalised by the nuclear medium (G matrix). Poor description of exp masses (B/A ~ 5 MeV, Coester line) HF: no suitable phenomenologic interaction able to describe masses and radii (1960) Breakthrough: Skyrme HF (Brink,Vautherin (1972)) Gogny HF (1975) Relativistic DFT RMF (1990,V L ) and RHF (2006) N.B : the 3 above have the best agreement with the data Now, in progress: V lowk = renormalised bare interaction to be used in HF, Bare N n LO potentials : Effective Field Theories (Weinberg, 1990)

13 Excited states in the DFT: GCM or RPA? GCM (~5DCH): mixes the HF solutions with various deformation to obtain the lowest energy states. Adapted for low E and low J states (does not take into account 1p-1h configurations) and for quadrupolar correlations J. -P. Delaroche, M. Girod, J. Libert, H. Goutte, S. Hilaire, S. Péru, N. Pillet, and G. F. Bertsch Phys. Rev. C 81, (2010) RPA: Mixes the 1p-1h configuration on a single HF solution. Adapted for collective states, at low or high E (giant resonances)

14 RPA: the linear response theory External oscillating field: TDHF: ext ext First order: ext N.B. 1) 2) Excited states are a superposition of particle-hole excitations.

15 Small amplitude perturbations RPA HF

16 RPA equation Perturbation of the density : ext Response function TDHF ext Π 0 ext Bethe-Salpeter equation

17 Consistent RPA Small amplitudes perturbation (RPA) in the DFT framework : residual interaction (beyond mean field) V Res 1975 : first calculation with the same EDF for HF and V res Advantage - EDF is the only parameter constrain it with excited states G.F. Bertsch and S.F. Tsai, Phys. Rept. C18 (1975) symmetry restoration - extrapolation for unknown situation (exotic nuclei)

18 The Quasiparticle-RPA (QRPA) Excitation and pairing Method known since ~40 years in nuclear physics Strong peak of activity since year Why? Study of nuclear transition of the whole nuclear chart (isotopic chain, open shell, drip-line, ) N,Z N+2,Z N+1,Z-1 E*, S(E*) inelastic cross section Pairing vibrations, 2n transfer cross sections β half-life, GT strength, charge exchange cross section

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20 Skyrme QRPA Low energy states 32 Mg 30 Ne 36 S 34 Si 38 Ar M. Yamagami and Nguyen Van Giai, Phys. Rev. C 69, (2004)

21 Spatial insight Transition densities N=14 shell closure E. Becheva et al, Phys. Rev. Lett. 96, , (2006)

22 QRPA/shell model Advantages of the QRPA: simplicity, also from the computational point of view; relates easily the interaction to the observable there is no core (that is, no need of effective charges); it is possible to study highly excited states. Provides densities and transition densities Disadvantages: not all the many-body correlations are taken into account. weak predictive power for low energy part of the spectrum

23 2) Exotic nuclei What happen to giant resonances? L=0,1,2 How to measure?

24 Experimental status of GR in exotic nuclei GDR measured in 20 O, 132 Sn, 28 Ne (by Coulomb excitation) GMR and GQR measured in 56 Ni

25 Soft GMR Compression of low-density nuclear matter

26 Unexpected shift of the GR Soft GQR

27 Soft GDR predictions Soft mode : Neutron skin +core in phase +collective Neutron skin

28 Deformation effect on the pygmy mode The pygmy mode is quenched by the deformation because of the reduction of the n skin D. Peña Arteaga, E. Khan, and P. Ring, Phys. Rev. C 79, (2009)

29 3) Astrophysics Neutron stars The r process e capture in core collapse supernovae Ultra high energy cosmic rays

30 Why Neutron stars? Landau (1932) : compact object held by the gravity Remnant of a core-collapse supernova Densiest «active» object (star) of the Universe : emits radio, visible, X, Gamma rays Pulsars (1968), binaries, magnetars (10 11 T) May be a site for the r-process the acceleration of ultra high energy cosmic rays (10 20 ev) GRB,

31 The inner crust ~ ρ 0 ~ 0.5 ρ 0 Wigner-Seitz cells

32 Supergiant resonances 1500 Zr 1800 Sn L=2 QRPA HFB 71% EWSR Impact on the cooling time of the star through the specific heat

33 Astrophysical site? 1) Core-collapse supernovae 2) Ejection from the neutron star crust R-process (n,γ) and β decay drip-line nuclei & free neutrons Neutron star crust

34 The role of dipole strength in (n,γ) rates Statistical model of compound nuclear reaction : Hauser-Feshbach T n (Z,A) + n S n (Z,A+1) T γ = T E1 (E) ρ(e) de 0 S n +E n Photon transmission coefficient sensitive to : T γ the E1 strength distribution T E1 (E) the level density ρ(e)

35 Why using microscopic calculations? Phenomenologic Fast and simple to use Extrapolations? No feedback about nuclear structure Lorentzian (Hybrid) E1 Microscopic E1 Microscopic Efforts consuming? More suited to extrapolate far from stability : neutron skin Characterize the n-n interaction on the whole nuclear chart Test the model validity on a large scale

36 Astrophysical impact T= K (n,γ) rates r-abundance distribution QRPA/Hybrid Discrepancy pheno/micro

37 Electron capture in core collapse supernovae A. Marek, H.Th.Janka Post-bounce evolution of a supernovae QuickTime and a decompressor are needed to see this picture. QuickTime and a decompressor are needed to see this picture. Beta decay and electron capture on A=56 to 120 T ~ 1 MeV

38 Gamow-Teller resonance predictions QuickTime and a decompressor are needed to see this picture. Finite temperature charge exchange RPA QuickTime and a decompressor are needed to see this picture.

39 Electron capture cross section QuickTime and a decompressor are needed to see this picture. n states blocking with increasing N Thermal unblocking QuickTime and a decompressor are needed to see this picture.

40 Are Ultra-High Energy Cosmic Rays made of nuclei? GRB The Pierre Auger collaboration

41 Ultra High energy Cosmic Rays E= ev Ankle GZK ~ E -3 Redressed spectrum (x E 3 )

42 Composition, acceleration & propagation COMPOSITION : Open question! Extra-galactic particles : protons nuclei ( 56 Fe, )? ACCELERATION : Open question! Gamma Ray Bursts, Active Galaxy Nucleus? N(E)~E -β PROPAGATION : Quantitative answers Interaction with the 2.7 K Cosmic microwave background Extra-galactic Magnetic fields Comparison with the measured spectrum on Earth (AUGER, )

43 Accelerators in the Universe GRB RIBF

44 Propagation of UHECR 2.7 K Cosmic Microwave Background Photodisintegration cross section γ= Fe : ev GDR * Photons density Lorentz boosted E (MeV) E (MeV) Photodisintegration rate (~1h -1 )

45 : PSB path Z=8 Z=14 Z=18 Z=22 Z=26 Z N A Photodisintegration (II)

46 Interpretation of the ankle Protons only : β=2.6 Protons & Nuclei : β=2.3 Needs for a galactic CR : Ankle is the galactic/extra-galactic transition

47 Conclusions Giant resonances are high energy collective modes with large cross section Well described by RPA models GR are usefull perturbation to investigate nuclear structure (L,T,S) Specific modes in exotic nuclei such as the pygmy 4 astrophysical applications : cooling of neutron star, r-process nucleosynthesis core-collapse supernovae propagation of ultra-high energy cosmic rays