giant resonances in exotic nuclei & astrophysics · • giant resonances are high energy...
TRANSCRIPT
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Giant resonances in exotic nuclei & astrophysics
1) Giant resonances: properties & modelisation
2) Giant resonances in exotic nuclei
3) Giant resonances and astrophysics
E. Khan
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1) Properties and modelisation
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Harmonic vibrations
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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 (XVIIeme) Maupertuis (XVIIIeme) Lagrange (XVIIIeme
XIXeme)Feynman (XXeme)
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Reformulation of the starting point:
Nuclear Hamiltonian:
Action:
Stationnarity of S (δS=0) for any variation of <Ψ(t)|Schrödinger equation
Energy density functionnalHohenberg-Kohn theorem: existence
The least action principle (II)
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The Hohenberg-Kohn (HK) theorem(Chemistry Nobel 98)
• Knowledge of this functional in nuclei ?
• HK states the existence of a functional for a given state, not an universal functionalfor the nuclear chart
• In nuclear physics coefficients in E[ρ] are adjusted on radii, masses, … : takes intoaccount correlations beyond mean field.
• Nuclei: symmetry restoration (broken in self-bound systems)
• Kohn-Sham = method to calculate ρ, knowing E[ρ]
•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)
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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)
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Time Dependent Hartree-Fock (TDHF)
Variation: ϕi*(t) ϕi
*(t) + δϕi*(t)
A coupled equations : (self-consistent)
mean field:
In practice : - treat VNL quasi-locally : Skyrme, Gogny- interactions fitted on nuclei properties : radii, energies, etc.
correlations beyond HF- LDA from infinite nuclear matter ?
L
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TDHF properties
•Self consistent•Minimum of the functionnal : static HF (stationnarity)
• Fusion, fission, compound nucleus, damping, …• Numerically heavy, tunnel effect, interpretation of Ψ ?
HF
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•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,VL) and RHF (2006)N.B : the 3 above have the best agreement with the data
•Now, in progress:Vlowk= renormalised bare interaction to be used in HF,Bare NnLO potentials : Effective Field Theories (Weinberg, 1990)
Milestones
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J. -P. Delaroche, M. Girod, J. Libert, H. Goutte, S. Hilaire, S. Péru, N. Pillet, and G. F. BertschPhys. Rev. C 81, 014303 (2010)
Excited states in the DFT:GCM or RPA ?
•GCM (~5DCH): mixes the HF solutions with various deformation to obtainthe lowest energy states.Adapted for low E and low J states (does not take into account 1p-1h configurations)and for quadrupolar correlations
•RPA: Mixes the 1p-1h configuration on a single HF solution.Adapted for collective states, at low or high E (giant resonances)
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RPA: the linear response theory
N.B. 1)
TDHF:
2) Excited states are a superposition of particle-hole excitations.
External oscillating field:ext
ext
First order:ext
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HF
Small amplitude perturbations
RPA
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Bethe-Salpeter equation
Response function
RPA equation
TDHFext
Π0 ext
Perturbation of the density :ext
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Consistent RPA
• Small amplitudes perturbation (RPA) in the DFT framework: residual interaction (beyond mean field)
• 1975 : first calculation with the same EDF for HF and Vres
VRes
•Advantage - EDF is the only parameter
constrain it with excited states
- symmetry restoration - extrapolation for unknownsituation (exotic nuclei)
G.F. Bertsch and S.F. Tsai, Phys. Rept. C18 (1975) 125
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•Excitation and pairing •Method known since ~40 years in nuclear physics• Strong peak of activity since year 2000. Why ?
Pairing vibrations, 2n transfer cross sections
N+2,Z
β half-life, GT strength, charge exchange cross section
N+1,Z-1
Study of nuclear transition of the whole nuclear chart (isotopic chain, open shell, drip-line, …)
The Quasiparticle-RPA (QRPA)
E*, S(E*) inelasticcross section
N,Z
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30Ne
32Mg
36S34Si 38Ar
Skyrme QRPALow energy states
M. Yamagami and Nguyen Van Giai, Phys. Rev. C 69, 034301 (2004)
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Spatial insight
N=14 shell closure
Transition densities
E. Becheva et al, Phys. Rev. Lett. 96, 012501, (2006)
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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
QRPA/shell model
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• What happen to giant resonances ? L=0,1,2
• How to measure ?
2) Exotic nuclei
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Experimental status of GR in exotic nuclei
• GDR measured in 20O, 132Sn, 28Ne(by Coulomb excitation)
• GMR and GQR measured in 56Ni
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Soft GMR
Compression of low-density nuclear matter
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Soft GQR
Unexpected shift of the GR
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Soft GDR predictions
Neutron skin
Soft mode :Neutron skin+core in phase+collective
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Deformation effect on the pygmy mode
D. Peña Arteaga, E. Khan, and P. Ring, Phys. Rev. C 79, 034311 (2009)
The pygmy mode is quenched by the deformation because of the reduction of the n skin
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3) Astrophysics
• Neutron stars
•The r process
•e capture in core collapse supernovae
• Ultra high energy cosmic rays
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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 (1011 T)
•May be a site for the r-processthe acceleration of ultra high energy cosmic
rays (1020 eV) GRB, …
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The inner crust
Wigner-Seitz cells
~ ρ0 ~ 0.5 ρ0
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Supergiant resonances
L=2
71% EWSR
QRPAHFB
1500Zr1800Sn
Impact on the cooling time of the starthrough the specific heat
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Astrophysical site ?
1) Core-collapse supernovae
R-process (n,γ) and β decay
drip-line nuclei& free neutrons Neutron star crust
2) Ejection from the neutron star crust
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The role of dipole strength in (n,γ) rates
•Statistical model of compound nuclear reaction : Hauser-Feshbach
Photon transmission coefficient sensitive to :
Sn
Tn
(Z,A) + n
(Z,A+1)
Tγ = TE1(E) ρ(E) dE0
Sn+En
Tγ • the E1 strength distribution TE1(E)
• the level density ρ(E)
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Why using microscopic calculations ?
Microscopic•Efforts consuming ?•More suited to extrapolatefar from stability : neutron skin•Characterize the n-n interaction on the whole nuclear chart•Test the model validity on a large scale
Lorentzian (Hybrid) Microscopic
Phenomenologic•Fast and simple to use•Extrapolations ?•No feedback about nuclear structure
E1E1
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Astrophysical impact
QRPA/Hybrid
Discrepancy pheno/micro
T=1.5 109 K
(n,γ) rates
r-abundance distribution
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Electron capture in core collapse supernovae
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•Beta decay and electron capture on A=56 to 120•T ~ 1 MeV
A. Marek, H.Th.JankaPost-bounce evolution of a supernovae
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Gamow-Teller resonance predictions
Finite temperaturecharge exchange RPA
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n states blocking with increasing N
Thermal unblocking
Electron capture cross section
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Are Ultra-High Energy Cosmic Raysmade of nuclei ?
The Pierre Augercollaboration
GRB990123
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Ultra High energy Cosmic Rays
E=1018-21 eV
AnkleGZK
Redressed spectrum (x E3)
~ E-3
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Composition, acceleration & propagation
Comparison with the measured spectrum on Earth (AUGER, …)
• Open question ! • Extra-galactic particles : protons
nuclei (56Fe, …) ?COMPOSITION :
• Open question ! • Gamma Ray Bursts, Active Galaxy Nucleus ?• N(E)~E-β
ACCELERATION :
• Quantitative answers• Interaction with the 2.7 K Cosmic microwave background• Extra-galactic Magnetic fields
PROPAGATION :
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Accelerators in the Universe
GRB
RIBF
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Propagation of UHECR
2.7 K Cosmic Microwave Background
Photons density
E (MeV)
γ=2.1010
0.1 1 10 100 1000
Lorentz boosted
*10 100
E (MeV)
Photodisintegration cross section
GDR
Photodisintegration rate (~1h-1)
56Fe : 1021 eV
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555453
54535251
51504948
50494847
4544
4443
414038
40393736
3634
35
30
26
22
18
15
1413
11 14
9
56
55
545352
51
5049484746
45
4443424140
39
38
3735
36343332
31
302928
27
262524
23
222120
19
181716
15
1312
1110
: PSB path
Z=8
Z=14
Z=18
Z=22
Z=26
Z
N
A
Photodisintegration (II)
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Protons & Nuclei : β=2.3
Needs for a galactic CR :Ankle is the galactic/extra-galactic transition
Protons only : β=2.6
Interpretation of the ankle
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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